ACTAUNIVERSITATISUPSALIENSISUPPSALA2006

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 189

Optical Studies of PeriodicMicrostructures in Polar Materials

HERMAN HÖGSTRÖM

ISSN 1651-6214ISBN 91-554-6578-1urn:nbn:se:uu:diva-6896

Omistettu mummolleni Elsa Laurinheimolle, todelliselle sankarittarelle…

Dedicated to my Grandmother Elsa Laurinheimo, a true hero…

List of papers

I H. Högström and C. G. Ribbing, “Polaritonic and photonic gaps in Si/SiO2 and SiO2/air periodic structures”, Photonics and nano-structures – fundamentals and application 2, p.23-32, 2004

II H. Högström, G. Forssell, and Carl G Ribbing, “Realization of selective low emttance in both thermal atmospheric windows”,Optical Engineering 44(2), 026001, 2005

III H. Högström and C. G. Ribbing, “On the angular dependence of gaps in 1-D Si/SiO2 periodic structures”, Submitted 2006 to Op-tics Communications

IV H. Högström, S. Valizadeh, C. G. Ribbing, “Optical excitation of surface phonon polaritons in silicon carbide by a hole array fab-ricated by a focused ion beam”, Submitted 2006 to Optics ex-press

V H. Högström and C. G. Ribbing, “Experimental observation of photonic and polaritonic gaps in a silica opal”, Submitted 2006 to Applied optics.

Work not included in the thesis

1. Carl G. Ribbing, Herman Högström, and Andreas Rung, “Studies of polaritonic gaps in photonic crystals”, Applied Optics, 45(7), 1575-1582, 2006

2. Carl G. Ribbing, H. Högström, A. Rung, “Interaction between photonic gaps and lattice excitations in 1-3 dimensions”, Deutsche Forschungs-gemeinschaft, Annual meeting, Berlin, Mars 7-8 (2005), invited presen-tation HL-42.5

3. Herman Högström, Andreas Rung, Carl G. Ribbing, “Si/SiO2 multilayer – a 1-dimensional photonic crystal with a polaritonic gap”, in proceed-ings of SPIE 5184 (Ed. P. Lalanne, San Diego, August 2003) p. 22-29

4. Andreas Rung, Herman Högström, Carl G. Ribbing, “Interaction be-tween photonic and polaritonic gaps studied with photonic band struc-ture calculations”, in proceedings of SPIE 5184 (Ed. P. Lalanne, San Diego, August 2003) p. 126-133

5. M. Karlsson, H. Högström, and F. Nikolajeff, ”Diamond micro-optics”,Proceeding of the Seventh applied diamond conference/Third frontier carbon technology joint conference 2003, M. Murakwa, Y. Koga, M. Miyoshi (Editors)

Contents

List of papers ..................................................................................................v

Work not included in the thesis .....................................................................vi

Contents ....................................................................................................... vii

1. Introduction.................................................................................................9

2. Optical materials .......................................................................................112.1 Electromagnetic waves in matter .......................................................112.2 Dielectric materials ............................................................................142.3 Polar materials....................................................................................15

2.3.1 The Lorentz model......................................................................152.3.2 The polaritonic gap .....................................................................17

2.4 Metals .................................................................................................19

3. Effect of periodicity ..................................................................................213.1 The light line and the Brillouin zone..................................................213.2 The photonic band gap .......................................................................223.2 Polaritonic photonic crystals ..............................................................27

4. Surface polaritons .....................................................................................314.1 General theory ....................................................................................31

4.1.1 Coupling by periodic structure ...................................................344.1.2 Coupling by ATR and nano structures .......................................35

4.2 Enhanced optical transmission ...........................................................36

5. Experimental .............................................................................................385.1 Fabrication of periodic structures.......................................................38

5.1.1 One-dimensional structures ........................................................385.1.2 Two-dimensional structures........................................................415.1.3 Three-dimensional structures......................................................45

5.2 Optical analysis ..................................................................................475.2.1 One-dimensional structures ........................................................475.2.2 Two-dimensional structures........................................................475.2.3 Three-dimensional structures......................................................48

6. Signature management in the thermal infrared .........................................49

6.1 Black-body radiation ..........................................................................496.2 Atmospheric windows........................................................................506.3 Infrared camouflage ...........................................................................516.4 Emittance determination.....................................................................53

7. Conclusions and discussion ......................................................................56

8. Summary in Swedish ................................................................................58

Acknowledgements.......................................................................................61

References.....................................................................................................63

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1. Introduction

Historically it has often been the discovery of new materials or new ways of using already existing materials that has radically developed our society. The materials humans use play such an important part that epochs have been named after the material, e.g., the Stone Age and the Bronze Age.

During the last 40 years the society has seen enormous developments be-cause of the efforts in semiconductor physics that has given the possibility to tailor the conducting properties of these materials. In the field of semicon-ductors the engineers are striving for smaller and better components such that the products, e.g. computers and mobile phones, will be faster and smaller.

The developments of semiconductor components lead to the rise of an-other field, MEMS (micro electro-mechanical systems), which in the begin-ning was using the same materials and the same fabrication techniques. The main advantage with MEMS was to make high quality small mechanical structures that would be much cheaper, thanks to the miniaturization, than the larger counterpart. In future history our days on the planet may be la-beled the Semiconductor era…?

Thus, semiconductor physics made it possible to control the conducting behavior of the material and MEMS made it possible to fabricate micro-sized mechanical structures. What was/is the next challenge in the materials “evolution”? With a growing field of optical communication it became more and more interesting to control the propagation of light in matter, just as it had been important to control the conducting behavior of semiconductors. It was well known that the optical reflectance and transmittance in one dimen-sion could be engineered by a multilayer composed of a high and a low re-fractive index material, where the thickness of each layer was a quarter-wavelength thick. The result of this kind of structures was a material with almost 100% reflectance for a certain wavelength interval. So, if it was pos-sible to control light in one dimension, how would it be possible in two and three dimensions?

In 1987 Eli Yablonovitch[1] and Sajeev John[2] published reports that suggested that this kind of light-control was possible. It was the birth of a new field in solid state physics: photonic crystals. Their idea was to extend the periodic structure into two and three dimensions and thereby create photonic band gaps in which there are no allowed states for photons. In the beginning the field was widely applauded for creating the possibility of lo-

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calization of photons, wave guiding and construction of optical components of very small size. However, skeptical comments were also aired[3].

Within the photonic gap in a photonic crystal the propagation constant, the wave vector k, is imaginary. This is also the case for metals, for frequen-cies below the plasma frequency, and in polar materials, for the frequency interval between the transverse and longitudinal optical phonon resonance frequencies. So, we therefore have three different origins of an imaginary wave vector, one associated with a periodic structure and two originating from the optical properties of the bulk material. When a material posses an imaginary wave vector in an interval several phenomena can be noticed. It becomes highly reflective, it quenches emittance and it can support surface waves.

The field of photonics has mostly focused on materials with “simple” op-tical behavior. But during the last years the field has matured and more in-terest has been focused on using materials with more complex optical prop-erties, and the new optical phenomena discovered and applications associ-ated with them.

In this thesis we have worked with the combination of the bulk optical properties of polar materials and the effects added by a periodic structure. The bulk properties appear, for the material at specific wavelengths, whilst the structural behavior can be shifted in position by changing the lattice con-stant of the periodic structure. When working with this project during the last four years we have tried to combine both possible applications and basic research.

In the first part of the thesis a general introduction is given to the fields dis-cussed in the papers (second part) together with some results cited from them.

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2. Optical materials

2.1 Electromagnetic waves in matter Already in the 19’th century James Clerk Maxwell summarized the know-ledge concerning electromagnetism in four equations. Even though it was not Maxwell who had developed all the theory included in the equations, they were named after him.

tDjH

BtBE

D

0 (1 a-d)

These equations are valid and describe the behavior of electromagnetic fields in different kinds of environment. They need to be supplemented by two constitutive equations that include the response of the material to the applied electromagnetic field.

MHBPED

0

0 (2 a, b)

Assuming that the electromagnetic radiation is traveling through vacuum, the following apply: P = 0; M = 0; = 0 and j = 0. The wave equation

EE 002 (3)

can then easily be derived by eliminating the magnetic fields H and B. One of the most important features of Maxwell’s equations was that an electro-magnetic field could propagate as a plane complex wave

E=E0ei(k·r- t), (4)

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where E0 is the amplitude, the angular frequency and k the wave vector. The fact that electromagnetic radiation propagates as a transverse wave was of great importance since it supported the theories suggested by Thomas Young. When Maxwell determined the velocity of an electromagnetic wave in vacuum he ended up with the expression that the phase and group veloci-ties were c=1/(µ0 0)1/2. By using empirically determined values for these quantities, he obtained a numerical value for the speed, which was equal to the experimentally determined value for the speed of light. Since then there has not been any doubts that the field of optics was a special case of elec-tromagnetism. From this point it was possible to derive e.g. Snell’s law[4] of refraction and Fresnel’s law[4] by using the theories of electromagnetism, and thereby get a deeper understanding of optical phenomena.

Maxwell’s equations give a complete description of the electromagnetic field. So, by inserting (4) into (1b) one can deduce that the magnetic field appears similar, but perpendicular, to the electric field and that electromag-netic waves are transverse. It is also possible to describe the propagation of light in different media.

If it is assumed that no free space charges are present, i.e. =0, the wave equation in a medium will have the general form

MjPEE 00002 . (5)

(5) is the inhomogeneous analogue to (3), and states that an electromagnetic wave can be generated by a polarization with a non-vanishing second deriva-tive, a time varying current density or the curl of a time-varying magnetiza-tion. The magnetic field appears similar also for this case.

The different optical behavior for various materials can all be described by using (5). The materials studied in this thesis are assumed to have no free space charges and that they are nonmagnetic. Actually, all materials have a diamagnetic contribution but it is of the order of 10-6, and therefore ne-glected. Materials that are para- or ferromagnetic can have a countable mag-netic contribution for lower frequencies, <1012, but the contribution van-ishes rapidly with increased frequency because of magnetic inertia. This inertia is so high that even ferromagnetic materials can be treated as non-magnetic, µ ~ 1, for > 1012. M will therefore be neglected henceforth.

The current density term, j, will be determined by the electric field and the conductivity, , of the material:

Ej . (6)

In anisotropic cases j does not need to be parallel to E and the conductivity will then be a tensor. If non-conducting materials are considered, j is ne-

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glected. In this thesis conducting materials will only be considered in section 2.3 where the optical properties of metals are discussed.

The polarization term, P, is the dipole moment per unit volume. It de-scribes the material response both to the applied and the local electric field[5]. A linear relationship is often assumed for E and P:

EP0

1 (7)

When (7) is inserted into (2a) the displacement field will appear as:

D = 0E. (8)

The quantities and are called the dielectric function (or permittivity) and the dielectric susceptibility respectively, and they are the linear response functions describing the polarization of the material. Both depend on the frequency, and in general they both have a real and an imaginary part, ( )= 1( )+i 2( ).

The optical properties of matter thus are determined by the coupling be-tween incoming electromagnetic (EM) radiation and charged parti-cles/charges in the material. The charged particles/charges are accelerated by the electromagnetic field and cause a polarization. The macroscopic polari-zation created by the dipoles adds to the vacuum contribution and sums up to the displacement field D, (2a). For different frequencies, different types of oscillators will dominate the response. The strength of this response depends also on the oscillator density and on the inertia of the excitation mechanism. Figure 1 presents a schematic picture of different polarization mechanisms that occur in solid materials.

Figure 1. A schematic picture of the frequency dependence of the real part of the dielectric function and the differ-ent polarization mecha-nisms that can occur in a material. The parts of the spectrum where the resonances are located are indicated above each peak. Cited from [5]

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The figure shows that for different frequencies, different oscillators are ex-cited. In these frequency intervals, close to the oscillator resonances, the polarization/dielectric function of the material varies strongly with fre-quency, i.e., dispersion. For frequencies between the resonances the dielec-tric function is almost constant. It is characteristic for an oscillator that there is a resonance region with strong absorption and dispersion. A resonance located at a high frequency will give a frequency independent contribution at all lower frequencies, whilst a low frequency resonance will not contribute at sufficiently high frequencies due to inertia. It should be noted that the low frequency excitations of permanent dipoles is characteristic only for a small group of materials containing molecules with dipole character, such as H2O.

In the next sections the optical properties for materials will be discussed with (5) as the starting point.

2.2 Dielectric materials Materials that are purely dielectric for all frequencies do actually not exist. For some frequency range in the electromagnetic spectrum the material will have a resonance and the polarization of the material will vary with fre-quency, as indicated in figure 1. But if we assume that there is no strong coupling between the electromagnetic radiation and oscillators within the frequency region considered, then the dielectric function is constant and real. For dielectric materials j is neglected in (5) and the wave equation will then look like

EE 002 )( . (9)

When inserting the plane wave (4) into (9) a relation between the wave vec-tor and the frequency is obtained, i.e., a dispersion relation

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2

)(kc . (10)

c is the speed of light in vacuum and is the complex dielectric function. For the dielectric case, when is constant and real, the dispersion relation will look like a straight line called the lightline. Glass is a typical dielectric material for visible frequencies and is therefore used in windows and optical components such as lenses and optical fibers. Glass is made of silicon diox-ide, and it will be discussed in the next section that it is not purely dielectric throughout the entire spectrum.

The square root of (10) will have a factor which is ( )1/2. For simplicity a new symbol, N( ), which is the complex refractive index factor, was in-troduced. N( )=n( )+ik( )= ( )1/2, where n is associated with the propaga-tion characteristics of the light (phase velocity, wavelength, refraction at an

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interface) and k is a damping parameter indicating the propagation length within a material. For dielectric materials k<10-4. It is important to distin-guish the k belonging to the refractive index from the wave vector k.

2.3 Polar materials The second type of materials that will be discussed are polar materials. They typically have a lattice resonance in the infrared part of the spectrum caused by the bonds in the material that are ionic, or partly ionic. It is neighboring ion pairs that constitute dipoles that interact, i.e., move and create phonons, i.e. quantified lattice vibrations with the EM radiation, and form quasi-particles named polaritons. The oscillations caused by the electromagnetic radiation are additional movements, besides the ordinary lattice vibrations, phonons. Since both polaritons and phonons include lattice vibrations, the optical response from the material within the resonance region will be somewhat affected by changes in the temperature[6].

2.3.1 The Lorentz model Close to the resonance, the dielectric function varies strongly with fre-quency. The optical behavior in this wavelength region can be described by a Lorentz one-oscillator model[7]. Although the oscillator is classical, the model shows good agreement with optical measurements using only a few parameters. The equation of motion for one oscillator is

)(r2

2

Eqrdtrd

dtd

(11)

where µ is the reduced mass of the dipole, a “spring constant” and q the charge. is a phenomenological damping constant representing the “fric-tion” the particles experience in the material. The driving force is an oscillat-ing electric field E, with frequency , as given in (4). Since the materials studied here are dense, corrections for the local electric field exciting the oscillator are included in E. Equation (11) has a homogenous and a particular solution, and the former is damped after a small number of periods 2 / , so we only need to consider the particular solution.

iEqr 22

0

)/( , (12)

where 0 = ( /µ )1/2 is the resonance frequency of the oscillator. If there are N oscillators per unit volume, the total macroscopic polarization of the mate-rial will be

16

Ei

µNqrNqpNP 220

2 / . (13)

The polarization is used in the constitutive relation for the displacement field D equation (2a), which is then inserted in (1a)

0)()( 00 PEED . (14)

The complex dielectric function is obtained by using the middle expressions in (14), as

iµNq

220

02 )/(

1)( . (15)

Because of the damping, , there will be both a real ( 1) and an imaginary ( 2) part of the dielectric function. In figure 2 they are both plotted for silicon dioxide. The data used for this calculation where published optical constant values from the literature[8, 9].

Figure 2. The real, 1, and the imaginary, 2, part of the complex dielectric function for silicon dioxide. The corresponding reflectance is also plotted and indicated on the right y-axis. Data from[8, 9].

So far, the contributions from other sources of polarization within the mate-rial have been neglected when deriving this particular response for the infra-red region. When taking them into account in the simplest way, the dielectric function will appear as

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iµNq

220

02 )/()( , (16)

where is a constant contribution, named screening constant. It originates from oscillators within the material. It is necessary for this simple represen-tation that these oscillators have resonance frequencies that are much higher than 0.

If =0 is inserted in equation 10, the static dielectric constant, (0), is ob-tained as

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02 )/()0( µNq . (17)

The Maxwell equation 1a implies that the electromagnetic field has to be transverse in vacuum. However, in a polarizable material with a varying dielectric function, can be equal to zero, allowing excitations that are not purely transverse. If is inserted in (14), E can be parallel to the wave vector, and D will still fulfill Maxwell’s equation. In this case P= - oE.This shows that longitudinal waves are possible inside a material at a fre-quency where . The frequency where is therefore named L(longitudinal mode), and 0 is renamed as T (transverse mode). As seen in figure 2 the real part of the dielectric function is negative between T and

L. If the damping, , is neglected and L in (16), T and L are related to the static and screening dielectric constants by

)0(2

2

T

L . (18)

This famous equation is named the Lyddane-Sachs-Teller (LST) relation [5]. It has been found that this relation is valid for a surprisingly wide range of materials and it can be generalized to cases with more than one resonance frequency[10].

2.3.2 The polaritonic gap In the interval between L and T, <0, as seen in figure 2. When this is the case the dispersion relation, (10) implies that the wave vector is imagi-nary. An imaginary wave vector causes a strong attenuation of the wave. This results in an interval of high reflectance: the Reststrahlen band.

In the vicinity of the resonance frequency the Lorentz model provides a surprisingly good description of the optical behaviour. A material can exhibit more than one resonance frequency caused by ions. This is actually the case for silicon dioxide. The second oscillator is much weaker, but it can be no-ticed as the shoulder on the short wavelength side of the high reflectance

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interval. These additional oscillators typically have their resonance frequen-cies close to the major resonance, and then a screening constant cannot be used. For a complete analysis all the oscillators in the vicinity have to be summarized in a multi-oscillator expression for the dielectric function[7]. The case of multiple oscillators will not be discussed in more detail.

To excite the oscillator in the material a photon must couple to a phonon. This means that their energies and momenta have to be equal. To illustrate where this is possible, the dispersion relations for phonons and light are sketched together in figure 3.

Figure 3. Schematic picture of the free photon (dashed line) and phonon dispersion relations in a crystal. The gray square shows where coupling between photons and phonons occurs, and the zone boundary represents the atomic Brillouin zone. The slope of the light line is underestimated in this representation.

The grey rectangle at the intersection of the light line and the transverse op-tical phonon represents the only interval where the two can couple to first order. In this region the polariton is formed. To show how this coupling will affect the dispersion relation, the area around the intersection is enlarged in figure 4.

Figure 4. A schematic picture of the polariton dispersion relation. Between Tand L a polaritonic gap is formed.

In figure 4 we see that the coupling between the photon and the phonon cre-ates a gap in the dispersion relation, the polaritonic gap (PG). The energies

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associated with the polaritonic gap are in the meV range, whilst visible light has energies around and above 1 eV. It should be underlined that this gap originates from the interaction between oscillators in the material and elec-tromagnetic waves, and not from any kind of periodicity.

In this thesis we have chosen to work with crystalline silicon carbide and amorphous silicon dioxide as polaritonic material, but there are many other materials that exhibit polaritonic behavior[5, 11].

2.4 Metals A semi-classical model dielectric function for metals is obtained much in the same way as for polar materials. The difference is that here moving elec-trons, which are treated as free, are causing the polarization of the material. Because of the free electrons some adjustments needs to be done in (11). 0is set to zero since we are dealing with free oscillators – the conduction elec-trons, and which represents the damping is replaced by its inverse , a parameter describing the time between scattering events. With these changes the equation for the conduction electron motion will be:

)(r2

2

Eqdt

rddtd

. (19)

The metallic dielectric function is then derived in the same way as in the previous section. The final expression will be

ip

2

2

1)( (20)

where p = (Nq2/ 0µ)1/2, the plasma frequency[5], which is a collective lon-gitudinal oscillation of the free electrons. The dielectric function for metals also has a real and an imaginary part. Figure 5 is a schematic picture of 1

and 2 for metals on a normalized -axis.

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Figure 5. A Schematic picture showing the real and imaginary parts of the metal dielectric function plotted as a function of / p. When = p the real part goes from negative to positive values.

From figure 5 it can be seen that the dielectric function will be negative for frequencies below p. With the dispersion relation (10) in mind one realizes that the wave vector will be complex for these values, create evanescent waves and cause high bulk reflectance.

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3. Effect of periodicity

3.1 The light line and the Brillouin zone When studying the dispersion relation, (k), (mentioned in section 2) for a material with a constant (vacuum or a purely dielectric material), it is ob-vious that it appears as a straight line named the light line, with the slope c/ 1/2.

22

2

)(kc . (10)

In section 2.3 figure 3, the typical light line is plotted together with the pho-non (quantified lattice vibrations) dispersion relations for a diatomic lat-tice[5]. The optical phonon frequencies in figure 3 belong to the microwave and infrared parts of the spectrum. The right part of the plot represents the Brillouin zone (BZ) boundary[12] for a normal atomic unit cell and the grey square indicates where coupling between EM waves and optical phonons can occur, as discussed in section 2.3. The size of the “atomic” Brillouin zone is determined by the inverse of the typical inter-atomic distance, i.e., a~0.5 nm, whilst the k-vector of light is 2 For ~1.55 µm, 1/a >> 1/ . It is well known that when the dispersion relation for propagating waves in a periodic medium interacts with the BZ, energy gaps may appear. One can see that the ordinary Brillouin zone boundary is too distant to affect the light line for visible/infrared light. The slope of the light line is much too steep. Eventu-ally the light line intersects the atomic Brillouin zone boundaries. This will occur far above the part of the dispersion plot shown in the diagram, i.e., in the X-ray region. At these frequencies the order of magnitude of the wave-length and the inter-atomic distance in the material are equal. The result is well known, X-rays are diffracted in crystals and the diffraction pattern is characteristic for the symmetry of the atomic crystal.

So, to get an effect of a Brillouin zone for optical or infrared frequencies the zone boundary needs to be moved to the left, i.e. to lower k-values. The BZ is characterized by the crystalline structure of the material, and the size is determined by the lattice constant[13]. This means that a periodic structure on the same length scale as the wavelength of light needs to be accomplished in order to have effects of the interaction for visible/IR wavelengths ( =

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0.3-13µm). We have thus arrived at a generalized grating concept as a tool for diffraction of electromagnetic waves with any wavelength.

3.2 The photonic band gap Electromagnetic wave propagation through periodic media was studied by Lord Rayleigh already in 1887[14]. He noticed that some frequency ranges of the waves could be totally reflected by the periodic structure.

His results later opened up the field of multi layers[15], where it became possible to design the optical properties since the range of frequencies that are totally reflected are determined by the materials and the lattice constant. The structures designed have e.g. been used in lasers. The common feature of X-ray diffraction in crystals and multilayer reflectance is that the wave-length of the electromagnetic radiation that is diffracted is of the same or-der of magnitude as the period of the diffracting structure. An essential dif-ference is that X-rays are diffracted in specific directions by atomic planes and that light is reflected by the boundaries between the different materials in the multilayer, and not in several directions within the structure. The re-flectance for visible wavelengths in a multilayer is possible to accomplish by creating a man-made periodic structure. We can describe that as a construc-tion that shifts the Brillouin zone to smaller k-values. As mentioned above, it is when the Brillouin zone interacts with the lightline that effects of the pe-riodicity appear.

Much work has been performed on one-dimensional periodic struc-tures[16] and the applications range from frequency selective lasers to win-dow coatings. In 1970 Bloembergen et al. discussed “stop bands” and “for-bidden gaps” for certain frequencies in a study on laminar structures[17]. He presented a photonic band calculation showing both a gap caused by the periodic structure as well as a gap originating from one of the materials. The concept of photonic stop bands was also adapted by Yariv and Yeh[16]

In 1987 two reports[1, 2] were published in the same volume of Physical Review Letters about controlling electromagnetic wave propaga-tion/spontaneous emission from electronic levels, in man-made periodic structures of dielectric matter. This new type of structure was eventually named a photonic crystal (PhC)[18-22] and the idea was to extend the photonic gap from one to two and three dimensions. As for the one-dimensional case and x-rays in crystals, discussed above, the periodicity of the structures should be of the same order of magnitude as the wavelength corresponding to photon energy where the gap is wanted. The major differ-ences between these structures and the multilayers were the way of describ-ing propagating modes, which adopted its nomenclature from solid state physics[13], where band diagrams are used for describing electron states in solids, and the possibility of localization of photons in three dimensions.

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This had not been possible for one dimensional structures since propagating modes are allowed in the plane perpendicular to the periodicity. Another difference was that air typically is one of the dielectric “materials” used in the multi-dimensional periodic structures. The “solid-state way” of describ-ing mode propagation was extended to one-dimensional structures [23, 24].

Different methods have been used to analyze optical properties of photonic crystals. Mostly it is done by transmission and reflectance meas-urements (for gap determination) but the obvious similarity between three-dimensional photonic structures and atomic crystals has lead to similar methods of analysis where the diffraction of light is investigated[25-27]. A more complete picture of the optical behavior of the photonic crystal is thereby achieved.

As mentioned above, the authors of the first two first reports argued that a band gap (BG), should be possible to accomplish in two and three dimen-sions by the use of a multi-dimensional periodic structures. The possibility to have a complete, or omnidirectional, gap, no allowed photonic states in any direction for a certain frequency range was also introduced. The existence of such a gap was verified by Ho et al[28] who showed that dielectric spheres put in a diamond lattice would create an omnidirectional gap if the refractive index ratio was ~2. It is somewhat intuitive that an as spherical BZ as possi-ble is wanted in order to have a complete gap. If so, the gap does not have to be as wide, for overlap in all directions.

From the knowledge of X-ray diffraction and multilayers, it should not be a surprise that if a periodic structure of two, or more, materials with different dielectric functions is prepared, one might end up with a photonic band gap. As already discussed, the periodicity of the material can be 1-, 2- and 3-dimensional. The number of principal axis along which the dielectric func-tion is periodic, determines the dimension of the photonic crystal. Figure 6 contains schematic pictures of all three cases where the different colors rep-resent materials with different dielectric functions[18].

Figure 6. Schematic picture of a 1-, 2- and 3-dimensional photonic crystal. The number of principal axis that exhibits a periodicity determines the dimension of the crystal. From [18].

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The way a photonic band gap is created by a periodically varying dielectric function has a clear relationship with electronic gaps in ordinary crystals. The ion cores in a crystal create a periodic potential, giving rise to an energy gap for electrons. For photonic crystals the difference is that the periodic potential is replaced by a periodicity in the dielectric function, = (r +R), if R is a lattice vector, and on a length scale that is about 103 times as large. Even calculations for photonic crystals appear very similar to calculations made for electrons with Schrödinger’s equation. Joannopoulos et al. present a good review how to handle EM waves in mixed dielectric media. They also list the equations for photonic band gap calculations together with their corresponding quantum mechanical expressions[18].

Within a gap, there are no allowed states for photons in the photonic crys-tal. This means that the wave vector, k, is purely imaginary for the frequen-cies in the gap and the waves are strongly attenuated. In the same way as for metals and polaritonic materials, corresponding frequencies will exhibit high reflectance.

To give a more illustrative description of the origin of the photonic gap, three band diagrams, = (k), for three configurations of a 1-D photonic crystal are shown in figure 7.

Figure 7. Schematic pictures of band diagrams for a one-dimensional photonic crys-tal. Left: All layers have the same dielectric function, centre: a small difference in the dielectric function between the layers, right: Large difference between the di-electric functions. After[18].

The leftmost plot is for a periodic structure where all layers have the same dielectric constant. This is a virtual periodic structure. Here one can see that the light line is folded back into the first Brillouin zone with no resulting gap at the boundary. We could by analogy with the electronic structure name it “The free photon band structure”. The center plot shows the band diagram for a case with a small difference between the two constant dielectric func-tions. One can see that a small gap has opened up at the Brillouin zone boundary. This is a photonic gap. We have chosen to specify it with the name structural gap, since it originates from the structure, i.e. the periodic length, of the material and we wish to separate it form bulk photonic gaps, such as the polaritonic gap. In the rightmost plot the difference between the

25

two constant values of the dielectric functions has been increased. As seen in the figure the width of the gap has increased considerably. This is again analogous with gaps in electronic band structures that grow with the strength of the crystalline potential [5]. Yet, one may wonder why the width of the gaps can increase so much, in the optical case, with the difference between the dielectric functions. By studying the shortest interesting wave, with wavelength 2a, one can see that the electric field can be placed in two ways in the crystal without disturbing the symmetry of the unit cell about its cen-ter. One way is to place the nodes in the high index material and another with the nodes in the low index material, as shown in figure 8 a, b. The darker material represents the high index material.

Figure 8. Illustration showing that two waves with the same wavelength can be placed in a one-dimensional periodic structure (a & b) and the corresponding local-ization of the energy associated with the mode (c & d). From [18].

If the effective dielectric function (the average of the dielectric function of where the energy, in figure 8 c & d, is located) for each wave is considered and inserted in equation 10, it becomes obvious that two waves with the same wavelength (same wave vector) will have different frequencies, and the difference will be bigger for larger refractive index ratio. This means that for the frequencies between the two just mentioned, there will be no allowed states, i.e. a photonic gap. The variational theorem can then be used to show that high-frequency modes concentrate their power to low- regions and that low-frequency modes concentrate their power to high- regions[18].

This description of the principles according to which a photonic crystal should be manufactured may make it sound very simple. However, in a prac-tical case it is not straightforward to obtain a photonic gap, in particular not a

26

complete gap. To succeed, the periodicity has to be close to perfect and the parameters have to be right. If the lattice constant, a, the symmetry and the packing fraction is right, and most importantly, the refractive index ratio nh/nl is large enough, it is possible to end up with a photonic gap. Different symmetries have different requirements for the refractive index ratio[18, 28].

One way of finding possible new optical structures is by studying nature, which has had millions of years of time to develop functional structures. Micro-optical structures, including photonic crystal structures, have been found in stones, flowers, birds and insects[29-33]. The function of the struc-tures varies from thermal control to enhanced/minimized reflectance and focusing of light.

The prospects of a new kind of components for control of light raised high expectations within the opto-electronics industry, and therefore im-mense worldwide development efforts to produce/analyze photonic crystals have begun since the 1990’s. The possibility of strong localization of pho-tons in two or three dimension has been the driving force because the oppor-tunity for wave guiding and lasing applications. These features are possible to have by introducing defects in the crystal where the mode can propa-gate/have a resonance. The analogue to defects in a photonic crystal is dop-ing levels in a semiconductor.

Because of the difficulties with large scale fabrication of three dimen-sional periodic structures, most optical components have been two-dimensional photonic crystals. By sticking to 2-D structures the well devel-oped fabrication tools within the micro-electronics industry can be used and no new machines need to be made. But even though the prospects look good for 2-D optical components, where the signal is propagating in the plane[34-36], the most successful application yet has been for photonic crystal fi-bers[37, 38]. In these fibers the signal is guided parallel to the two-dimensional periodic structure and it has been shown that the signal can be guided both in air[39] and silica.

Another area in which photonic crystals may be of interest is for negative refraction. This optical phenomenon has been showed for two-dimensional photonic crystals [40]. Berrier et al. presented in 2004 an experimental veri-fication of negative refraction for infrared wavelengths[41].

The field of photonic crystals is growing and since 1987, when the field was initiated, the number of yearly publications has increased exponentially. According to accessible bibliographic information[42], the total number of publications at the end of this year (2006) is predicted to be around 2800. A majority of the publications concern dielectric photonic crystals, but work has also been made for metallic[43, 44] and polar materials, which will be discussed in more detail in the next section.

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3.2 Polaritonic photonic crystals So far we have discussed three different origins of stop bands for photons: a strongly varying dielectric functions with a negative real part, metals and photonic crystals made of purely dielectric materials. Two bulk material properties and one originating from the structure. The possibility to combine two stop bands and make them interact has caught the interest of some re-search groups with the hope of finding new applications and new optical behavior. In this section the combination of polaritonic and structural gaps will be discussed as mentioned above. Bloembergen et al. [17] presented in 1970 experimental and calculated results for the one-dimensional case, where he showed the co-existence of structural and polaritonic gaps. The first results for more than one dimension were due to Sigalas et al. [45, 46], who presented transmission calculations for a two-dimensional photonic crystal made of a polar material, GaAs. Their calculations were made by transfer matrix technique and showed that the position of the structural gap changes when it is located close to the polaritonic gap, compared to a purely dielectric photonic crystal. We will call this type of photonic crystals, where one of the materials has a polaritonic gap, a polaritonic photonic crystal, PPC. The first calculated band diagrams for PPC’s where made by Zhang et al [47, 48]. They showed by plane-wave calculations that the photonic band gap can be enhanced in a PPC and that nearly dispersionless bands occur in the vicinity of T. Both phenomena have later been confirmed by different reports[49-51]. Optical behavior related to the dispersionless bands for PPC’s is the change of the symmetry of the EM field patterns and the reloca-tion of the light into and out of the polaritonic material, studied by Huang et al [50]. Calculations showing gap maps for a two-dimensional PPC has been published by Rung et al.[52]. Their gap maps concern four different configu-rations: the polaritonic material is placed in the cylinders or the matrix, and it is the high or low index material. A destruction of the polaritonic gap has also been demonstrated[53]. Recently Huang et al also proposed that PPC could be used to create metamaterials with both negative permeability and permittivity (mentioned above) in the infrared part of the electromagnetic spectrum [54]. Even though most studies have been made for two-dimensional polaritonic photonic crystals, some recent calculations have been made for the three-dimensional case [51, 55, 56].

Published experimental results for PPC’s have, to our knowledge, only been shown for the one-dimensional case [17, 57, 58]. It has been shown that the structural and polaritonic gap can co-exist, the polaritonic gap can be both strengthened and enhanced, but also eliminated. In figure 9 calculated results for a finite one-dimensional photonic crystal (7 Si layers with 6 inter-vening SiO2 layers, all layers have the same thickness) show all three cases.

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Figure 9. A color graph, consisting of 40 separate spectra, showing the reflectance by different colors for a finite one-dimensional PPC with seven Si layers and six intervening SiO2 layers. All layers have the same thickness which is marked on the x-axis and vary from 0.1 to 4.0 µm. The wavelength for the spectra is on the y-axis. The color scale indicates the reflectance. The horizontal line shows the position of the polaritonic reflectance and the three vertical lines indicates where the polaritonic reflectance is strengthened and widened (a), un-affected (b) and erased (c). From paper I.

Figure 9 is a color graph put together of 40 separate reflectance spectra where each one is for a different lattice constant. The reflectance spectrum for each “lattice constant” (layer thickness) is represented on the x-axis and indicated by the color. The wavelength is represented on the y-axis. Since SiO2 is the polaritonic material in figure 9 the polaritonic reflectance is lo-cated at wavelengths around 9 µm (see figure 22). The polaritonic reflec-tance causes a horizontal stripe in red/yellow when it is not affected by the structural reflectance. For such a case please consult paper 1. The position is indicated by the horizontal line. In the graph three vertical lines have been inserted to highlight the positions where the polaritonic reflectance is strengthened (a), stands by itself (b) and extinguished (c).

Since the origins of the photonic gaps in a one-dimensional polaritonic photonic crystal are different there is also a difference in the angular de-pendence. The peaks originating from the structure will shift to shorter wavelengths with increasing angle. This behavior is not a surprise. The po-laritonic reflectance is widened with angle in both directions for s-polarized light and is decreased for p-polarized. If the polaritonic material is thin enough the longitudinal mode can be excited[59]. In figure 10 a calculated color graph is shown which summarizes the angular behavior for both struc-

29

tural and polaritonic reflectance. The structure was designed that the polari-tonic and structural reflectances do not interact, line b in figure 9. Paper III contains a more detailed discussion and the corresponding experimental color graph.

Figure 10. A color graph summarizing the angular dependence for structural and polaritonic reflectance. The polaritonic reflectance band is located at ~0.15 eV.

In figure 11 normal incidence IR reflectance spectra for four three-dimensional PPC’s, with different lattice constants are shown.

Figure 11. Normal incidence reflectance spectra for four PPS’s with different lattice constants. The crystals are made by sedimented silica spheres of different sizes, indicated in the inset. The four peaks to the left are gaps originating from the peri-odic structure and the peak to the right is the polaritonic reflectance. From paper V.

The crystals were made of sedimented silica spheres of different size: d = 0.49, 0.73, 0.99 and 1.57 µm. In the spectra two types of reflectances can be seen, structural and polaritonic. To the left the structural reflectance shifts to longer wavelengths with increasing sphere size, while the polaritonic reflect-ance stays at the same spectral position. The polaritonic reflectance is sur-prisingly robust for structures as small as /20. For details see paper V. Op-

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tical measurements on crystals made of larger spheres, where the structural gap overlaps the polaritonic gap, would be of great interest, but have not been possible to acquire.

Park et al have presented related results for a three-dimensional photonic crystal with a frequency dependent component [60]. They sedimented doped 215 nm polystyrene spheres into an opal structure. The gap originating from the periodicity was overlapping the absorption peaks for the dopant, Oil Blue N, which resulted in an enhanced photonic gap. Their results verified ex-perimentally the gap enhancement for multidimensional structures. The dif-ference between figure 11 and the results presented by Park et al is that his frequency dependence does not originate from the bulk optical behavior.

A potential application for PPC’s is as a selective low emittance coating in the thermal infrared. This will be discussed in more detail in section 6 and paper II.

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4. Surface polaritons

In sections 2.2, 2.3 and 3.1 in this thesis, different origins of a complex wave vector for an electromagnetic wave have been discussed. Metals, dielectrics and polar materials can all cause a complex wave vector. The difference is that metals and polar materials create it as a bulk property, while dielectrics need to be periodically structured such that a photonic band gap is achieved. The intervals, regardless the material, where the wave vector is complex do not just have high reflectance in common, they can also support bound sur-face waves, i.e., surface polaritons. These surface excitations can be used within many different fields and different applications: biosensing[61, 62], biophotonics[63], thermal emission control[64], data storage[65], micros-copy[66], optical filters[67] and waveguiding [68, 69]. Because of the nature of surface polaritons they are suitable in interconnects in electro-optic de-vices, and for nano-imaging and spectroscopy.

Most of the work within the field has been made for metals[70, 71], but work has also been published for non-conducting materials [64, 72-74] and photonic crystals[18, 75, 76].

4.1 General theory It has been known for a long time, that a propagating quasi particle com-posed of a photon and a polarization wave is possible along the interface of two materials if the optical conditions are right[71]:

0)Re()Re(0)Re(

III

II (21 a, b)

where I and II indicate the two media, forming the interface along which the surface polariton travels. is the complex frequency dependent dielectric function ( ( )). Equations 21 a and b state that one of the materials must have a negative real part of the dielectric function at some frequency and the absolute value for that frequency must be larger than the corresponding value for the other medium. As mentioned earlier, a negative dielectric func-tion causes a complex wave vector, which is the fundamental physical condi-tion. For metals 1 is <0 when < p[71], i.e. the plasma frequency[5]. For

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polar materials <0 in the Reststrahlen region < < L[7], and for photonic crystals it is for frequencies within the photonic gap(s)[18]. Within these intervals the amplitude of the electric field for the surface polariton will decay exponentially away from the interface. Figure 12 is a schematic picture of the surface excitation in a x-z plane. It displays the propagation of the electromagnetic field in the x-direction, the exponentially decaying fields in the z-direction and the orientation of the magnetic field in the y-direction. The wavelength of the surface polariton SP is also indicated.

Figure 12. A schematic picture showing the propagation in the x-direction of the electromagnetic field along an interface. In the left part the exponential z-dependence of the electric fields are shown in the two media. The magnetic field is oriented in the y-direction.

As mentioned above, the surface oscillation can have different sources. If the polarization wave in the material is composed of electrons they are named surface plasmon polaritons, in case of phonons they are named surface pho-non polaritons (SPP). If the surface excitation is located on a photonic crys-tal it is called a surface state[18].

The wave vector for surface polaritons can be derived from Maxwell’s equations by using the correct boundary conditions [71], one obtains

III

IIISP c

k (22)

where kSP is the surface polariton wave vector, c the speed of light, the angular frequency. kSP is, as most EM waves in a medium, composed of a real and imaginary part (kSP=k’SP+ik’’SP). The real part describes the propa-gation of the polarization wave and the imaginary part gives the damping. The propagation length, LSP, of surface polaritons is given by:

1'' )2( SPSP kL (23)

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In figure 13 the real and imaginary part of the dispersion curve for a SiC/air interface is presented together with the light line for vacuum. In the figure the negative side of the x-axis displays the imaginary part of kSP. If calcula-tions are made with these values the absolute value of k’’SP should be used.

Figure 13. The real part and imaginary parts of the dispersion relation for surface phonon polaritons on an air / SiC interface calculated according to (22) together with the vacuum light line. The negative values display the imaginary part and the abso-lute value should be used for calculations. The imaginary part is here presented on the negative side of the x-axis for convenience. The oscillator parameters for SiC used for the calculation are[8]: L=969cm-1, T=793cm-1, =4.76cm-1, e =6.7.

For surface polaritons to be tied to the interface, i.e. called non-radiative, the frequency interval where they can exist is where the dispersion relation is located to the right of the light line for the dielectric medium. In figure 13 this is where < < L, i.e. between 793 and 969 cm-1. It can be seen in the figure that for < T the dispersion relation is located to the left of the vac-uum light line and therefore are the states here not bound to the interface. For metals the dispersion relation is located to the right of the light line for

< P.Equation (22) and figure 13 explains why surface polaritons can become

sub-wavelength and be used for nano-imaging at optical frequencies: the wavelength of SP’s kSP goes to infinity when I+ II 0, which implies that the wavelength goes to zero (the surface polariton resonance frequency).

Since the light line is located to the left of the dispersion relation the sur-face states can not be excited by just shining light onto the surface. The dif-ference between the two curves indicates a momentum mismatch. This im-plies that the momentum mismatch between SP’s and the incoming light must be added. Coupling of incoming light to the surface states can be done in three ways: grating coupler[71], attenuated total reflection (ATR)[71] and coupling by nanostructures[77]. Surface plasmons can also be excited by electrons that are accelerated into a metal foil and when hitting the material

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the momentum is transferred to the electrons in the metal[71]. This excita-tion method will not further be discussed.

4.1.1 Coupling by periodic structure If light hits a surface with an angle , the parallel component of the wave vector, kx, will be:

sin1 ck (24)

If the material is structured periodically with a lattice constant a, the added parallel component, g, will be: g=2 /a. So, when light hits a periodically structured surface the total parallel component will be:

ngc

kx sin (25)

where n is an integer and ng is k in figure 14. If the geometrical setup is correct the momentum mismatch will be overcome, i.e. kx=kSP, and a surface polariton can be exited. The process is schematically illustrated in figure 14, with labels according to (24) and (25). Light hits the structured surface under an angle , and will then have a parallel wave vector component k1. The structure adds k to the incoming light and thereby the momentum mismatch is satisfied, i.e. surface polaritons can be excited. If the light hits the surface at normal incidence there will not be any parallel component, i.e. k1=0, and the entire momentum has to be added by the periodic corrugation.

Figure 14. A schematic picture showing the dispersion relation for a surface polari-ton (SP), the vacuum light line (LL), the vacuum light line for an angle ( with its parallel wave vector component (k1), and the added momentum from the periodic structure ( k). (after [71])

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In figure 15 three reflectance spectra are shown: a calculated reflectance for an infinite hole array, an experimental reflectance for a finite hole array and the bulk SiC reflectance.

Figure 15. Three reflectance spectra showing the calculated reflectance for an infi-nite hole array, the experimental reflectance for a finite hole array and the bulk re-flectance for SiC.

In the calculated and experimental reflectance spectra, in figure 15, two dis-tinct dips can be noticed. These dips are associated with the excitation of surface phonon polaritons which can be launched in the high reflectance interval, where 1<0. The long wavelength dip is associated with the geomet-rical parameters of the periodic structure, lattice constant 11µm and hole radius 6 µm. The short wavelength dip is the result of surface polariton exci-tation at the polariton resonance frequency, i.e. at the frequency for the as-ymptote in figure 13. At that frequency almost any wave vector can excite a surface state. For a more detailed discussion and pictures of the periodic structure, please consult paper IV or the cover of this thesis.

Periodic structures can also have another effect on surface polaritons. Bozhevolnyi et al. have shown that in the same way as light can be totally reflected for a range of frequencies by a photonic crystal (section 3), surface plasmons exhibit the same effect by a periodic array of scatterers made by gold nanoparticles[78]. By removing some rows of scatterers in the periodic structure, surface plasmons are localized to the unstructured surface and wave guiding is possible through the array.

4.1.2 Coupling by ATR and nano structures When light travels through a dielectric medium ( >1) the light line will be shifted to the right compared to the vacuum light line. If the dielectric con-stant is large enough the dielectric light line will be placed to the right of the dispersion relation for surface polaritons (for a <0/air interface) for a range

36

of frequencies. This means that if light comes from the dielectric material and hits the <0-material it can excite surface polaritons on the air interface side of the <0 material. This is done by tunneling of the electric field through the <0 material. This way of launching surface polaritons is called the Kretschmann configuration and used for bio-sensing[61]. The excitation of surface polaritons will be noticed as a strong dip in the reflectance just as in figure 15. The frequency at which the dip appears varies with both film thickness and angle of incidence.

Figure 16. A schematic figure showing the coupling of light to surface polaritons by ATR (after [71]). LL/ is the light line for a dielectric medium, and is for an incidence angle . SP indicates the air/( <0) interface surface polariton dispersion relation and LL the vacuum light line.

The third way of launching surface plasmon by light is by using nano parti-cles. Ditlbacher et.al [77] presented results for cylindrical spots and a wire, fabricated by e-beam lithography on a silver film. Different shapes excite surface plasmons with different lateral intensity distributions, which were imaged by fluorescence.

4.2 Enhanced optical transmission In 1998 Ebbesen et al. published a paper in which extraordinary optical transmission through sub-wavelength hole arrays in optically thick metal films was reported[67]. They showed that even though transmission through apertures, which are smaller than the wavelength, is extremely low[79] they had zero-order transmission peaks for wavelengths as large as ten times the hole-diameter. The position and the spectral appearance of the transmission peak can be shifted by changing the lattice constant[70] and shape of the hole[80]. They suggested that enhanced optical transmission (EOT) was associated with the excitation of surface plasmons. The same phenomena was not seen for germanium.

37

Many contributions have since then developed the theory for the en-hanced transmission for hole arrays and one dimensional gratings [73, 81-89] . The authors show that the enhanced transmission is associated with modes on the two surfaces which are coupled by resonant tunneling through the holes, transmission maxima occur at the same wavelength as reflectance minima and absorbance maxima and that transmission minima occurs at the same wavelength as reflectance maxima and absorbance minima. Their con-clusions are that enhanced transmission occurs when excitation of surface polariton plasmons is allowed on one or both surfaces. It has also been theo-retically demonstrated that if the entire system (holes and metal) is consid-ered as one material it will support “spoofed” surface plasmons[82].

However, there has also been reports arguing that surface polariton plas-mons should have no, or even negative effect on the transmission [86-88]. They show by calculations that transmission is nearly zero for frequencies corresponding to the excitation of surface plasmons[88]. According to these reports the EOT is due to a waveguide mode resonance and diffraction. It should be noted that all the contributions claiming the negative role of sur-face plasmons have presented their results for gratings of slits and not for an array of holes. It seems like the field is converging to a physical explanation where light couples to surface polaritons which generate surface waves that couples through modes in the holes/slits to states on the other surface which then re-radiates the light. Several key aspects have been realized concerning EOT, but a more detailed explanation still needs to be presented.

Almost all contributions within the field are dealing with EOT through metallic substrates, but some reports have been published for non-conductors. Laroche et al. showed calculated results for resonant transmis-sion through a photonic crystal in the forbidden gap[76] by launching sur-face states that couples through the 3.5µm thick crystal. Marquier et al. pub-lished a paper showing calculated results for EOT through a grating of slits in SiC[73]. Based on the lack of experimental contributions we shall de-scribe an attempt to accomplish EOT in a non-conducting material in sec-tions 5.1.2 and 5.2.2 in this thesis.

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5. Experimental

5.1 Fabrication of periodic structures 5.1.1 One-dimensional structures The materials we have used in the one-dimensional structures are silicon, as the dielectric material, and silicon dioxide as the polaritonic material. This material combination was primarily chosen for of their optical properties in the wavelength interval of interest. Another important factor was the possi-bility of simple sample preparation. The samples were grown by chemical vapor deposition (CVD) on a 550 µm thick (100) Si-wafer. Both processes are standard techniques used in the micro-electronics industry. The materials obtained by the CVD processes are polycrystalline silicon (poly-Si) and amorphous silicon-dioxide. In figure 17 the electron diffraction patterns for the poly-Si (a) and SiO2 (b) films are presented. The sharp dots, e.g. 220, as marked in the SAED (Selected Area Electron Diffraction) pattern of the poly-Si indicate that the grains are textured. If the film had been truly poly-crystalline, the pattern would only consist of circles. The diffraction pattern for the SiO2 film verifies that the film is amorphous, as assumed in the choice of optical constants.

Figure 17. Selected area electron diffraction image of (a) poly-Si, and (b) amor-phous SiO2. The sharp dot marked in (a) is the [220] direction, which indicates that there is some structure in the film. In (b) there is no structure in the image which verifies that the film is amorphous.

a b

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Polycrystalline Si (poly-Si) is obtained from decomposition of silane (SiH4)[90] gas at a working temperature of 650o C resulting with a deposi-tion rate of 10.4 nm/min. The amorphous SiO2 originates from hydrolyzation of tetra-ethyl-ortho-silicate (TEOS, Si(OC2H5)4)[90] at a working tempera-ture of 710o C and with a deposition rate 5.6 nm/min. The oxide formed is a stoichiometric oxide, i.e., the molecular unit is a tetrahedral structure where one central silicon atom is bound to four oxygen atoms. The bond angle for different tetrahedrae varies between 120o and 180o, centered about 145o[91]. Both processes were carefully calibrated to achieve good thickness control.

Two types of samples were prepared. A finite one-dimensional photonic crystal consisting of three poly-Si layers interspaced with three SiO2 layers, and a double layer of poly-Si and SiO2. The justification for using so few layers for analysis of periodic structures is that the dominant optical features are already present, and will not be changed with an increased number of layers. The difference will be that most interference fringes between the dominant reflectance peaks will disappear.

As mentioned above, both samples were grown on a 550µm thick (100) silicon wafer. In Figure 18 a transmission electron microscope (TEM) pic-ture shows a cross section of one of the finite one-dimensional photonic crystals .

Figure 18. A TEM picture of a cross section of a one-dimensional photonic crystal. The silicon wafer is at the bottom of this image. The bright layers are SiO2 and the striped layers are poly-Si.

It is evident that the SiO2 layers are not perfectly equal in thickness (despite the careful calibration). In figure 19 a) and b) high resolution TEM pictures show the material boundaries between the layers for the structure in figure 18. Figure 19 a) shows the interface between the mono-crystalline Si-wafer and the first SiO2-layer and b) the interface between SiO2 and the poly-crystalline Si.

40

Figure 19. High resolution TEM images of the interfaces between the different lay-ers of the structure shown in figure 18. a) shows the interface between the mono-crystalline wafer and SiO2, and b) the interface between SiO2 and poly-Si. It is pos-sible to see some kind of texture in the poly-Si

In both pictures one can see that Si is more ordered than SiO2, and also that the Si-wafer is more ordered than the poly-Si.

Since the Reststrahlen peak of SiO2 is of particular interest in this thesis, we plot an experimental spectrum together with a calculated spectrum in figure 20. The sample is a 2.9 µm thick silicon dioxide layer, deposited with the same technique as used for the samples, on a silicon wafer. The calcula-tions were made without fitting, for the same system.

Figure 20. Experimental and calculated reflectance spectra for a 2.9 µm thick SiO2layer deposited on a Si wafer.

It can be seen in the figure that the experimental reflectance peak has a small red shift with respect to the calculated. This red-shift of the peak is also pre-sent in the papers included in this thesis. Some claim[92] that this red shift is

a b

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caused by a difference in density. They show that a deposited TEOS-film has lower density, than a thermally grown oxide, because of impurities. Analyz-ing transmittance measurements, they show that there are both OH-ions and free water in the films.

We have also made investigations with electron energy loss spectroscopy (EELS). The results show that besides a measurable amount of O-H bonds, there are also small clusters of phase-separated amorphous silicon in the film. The EELS mapping of Si in a SiO2 matrix was acquired by selecting the Si plasma peak at 17 eV, with a narrow energy window. The analysis shows that the amount of silicon is large compared with the amount of O-H bonds. Figure 21 is an image where the clusters of phase-separated amor-phous silicon are mapped by high intensity.

As seen there are substantial amounts of silicon in the film, and the Si clus-ters with average diameter of 2-3 nm, are clearly shown. The effect of this on the Reststrahlen reflectance is not further discussed in this thesis.

5.1.2 Two-dimensional structures To overcome the momentum mismatch between the vacuum light line and the surface phonon polariton dispersion relation and obtain coupling between incoming radiation and surface states, a square array of circular holes were milled in SiC (the substrates were provided by [93]). The milling was per-formed with a FEI dual beam 235 focused ion beam (FIB) system[94, 95]. A FIB was chosen as tool because of the need for high resolution preparation patterning and the fact that the ions have enough energy and momentum to remove material even in such a hard material as SiC. Most materials can be processed by a FIB, but the milling parameters must be optimized to obtain the best final result.

Figure 21. Small clusters of phase-separated silicon shown by EELS mapping. High intensity represents areas with additional silicon.

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The parameters of importance in FIB patterning are: the type of ions used, ion beam current, ion beam density (ions/cm2), beam dwell time (the time the ion beam stays within a specific spot), overlap (percentage indicating the beam overlap between two adjacent spots) and scan speed. To optimize the milling parameters holes were made with different ion currents, and cross section images were taken to analyze the hole shape. Figure 22 is a graph showing the influence of the ion beam current on the actual hole diameter. The current was varied between 1 and 12 nA and the preset diameter and depth were 6 µm.

Figure 22. Experimental values showing the influence of the ion beam current on the final hole diameter. The preset diameter and depth of the hole was 11 µm.

In figure 22 it can be seen that 3 and 5 nA gives the diameter closest to the preset (6 µm) and that for higher ion currents the diameter is strongly af-fected.

In figure 23 SEM images showing holes made by ion currents 3, 5 and 7 nA, and corresponding cross sections, are presented.

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Figure 23. Six SEM images showing holes produced by FIB with different ion cur-rents. The corresponding cross section is displayed in images d-f. Images a and d, b and e, c and f are made with the ion beam current 3, 5 and 7 nA respectively.

It can be seen from the SEM images, a-c, that the resolution is affected by increased ion-current. For 5 and 7 nA the hole edges are affected and the diameter is also changed as discussed above. Images d-f show cross sections of the holes made with the same currents as the image above. One can see that the holes have a Gaussian hole shape. Holes made with ion currents lower than 3 nA produce holes of good quality, but the time needed makes it almost impossible to produce larger structures than individual holes. At the other end, holes made with currents higher than 7 nA are not of high enough quality for optical structures. Non-uniform holes would cause too much damping and scattering. Our conclusion is therefore that an ion current of 5 nA is optimum for micro hole fabrication in SiC. The optimized parameters are dwell 2µs, the ion beam dose 1018 ions/cm2, 50 % overlap, scan speed 50 µm/s for a serpentine scan. More details concerning the fabrication can be found in paper IV.

The structure fabricated with the parameters mentioned above was a square array of circular holes (21*21) with diameter 6 µm and lattice con-stant 11 µm. The choice of having 21*21 holes was motivated by the calcu-lations. The structured area needs to be large enough so that measurements are possible, and the excitation of surface states is made possible through an interaction between the radiation and the periodic structure which requires that the structure has a minimum area. Details concerning the calculations can be found in [81].

Two types of hole arrays were fabricated: one with surface pits only and one with holes going through the membrane. In figure 24 two SEM images

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are presented showing a hole array where the holes do not penetrate the membrane.

Figure 24. Two SEM images showing a square array of circular holes with diameter 6 µm and a lattice constant of 11 µm. The holes do not go through the sample. The right image is taken at a tilt angle of 52o.

In figure 24 it can be seen that the fabrication process, which takes between 40 and 50 hours, is very stable, i.e., the sample stage has stayed in the right position during the process. One can also see that there are no traces at the top surface of redeposition or other surface structures originating from the fabrication process.

In figure 25 two optical images are presented showing a sample with holes going through the membrane. Both images are taken at the exit side of the sample for the beam.

Figure 25. Two optical images of a hole array with holes penetrating the sample. The left image is taken in transmission mode and the right in reflectance mode.

The left optical image is taken in transmission mode and the right in reflec-tance mode. From the left image it can be seen that the holes penetrate the sample. One can also notice that the beam has not penetrated the sample for all spots. One of these spots is shown in the right image. In the right picture

45

it is also obvious that there is dirt on the sample surface. It is small islands of metal that has been evaporated onto the sample surface. The metal originates from the sample holder on which the membrane was attached with carbon tape. To ensure that no glue from the tape would be on the area of the struc-ture the array was fabricated on a piece of the SiC that had no tape beneath. Instead metal was evaporated to the surface when the beam penetrated and heated the sample holder.

Because of the Gaussian hole shape shown in figure 23 the diameter of the holes was measured on the exit side. The exit side diameter was ap-proximately 5.4 µm, which is 0.6 µm less than desired.

5.1.3 Three-dimensional structures Fabrication techniques for high quality three-dimensional photonic crystals have been developed for several years. The possibility to have a complete photonic bandgap which can guide light in three dimensions[96] and have strong localization of photons is driving the research. During the years sev-eral different techniques have been developed for the preparation of the three dimensional structures [97-99]. In this thesis we choose to work with gravi-tation sedimentation of monodispersed spherical microspheres.

When monodispersed colloids (usually silica or polystyrene) are allowed to sediment slowly, they place themselves in the energetically most favor-able structure, a fcc (face centered cubic) lattice[100]. This structure is called a synthetic opal and has got its name from natural opals, which are formed by close packed silica nanospheres. The structure has one sphere in each of the lattice points of an fcc crystal. The colloids form a crystal with the (111) surface at the top. Figure 26 shows a (111) face of a colloidal crystal made of silica micro spheres with the diameter 1.6µm

Figure 26. A colloidal crystal (the (111) face) made of silica micro spheres.

46

If the connected void volume within the crystal is filled with another mate-rial it forms a structure named an inverse opal is formed. The inverse opal exhibits a complete photonic bandgap if the refractive index ratio is large enough[101]. The opal structure does not have a complete gap.

A range of approaches have been suggested to infiltrate the inverse struc-ture including sol-gel[102], chemical vapor deposition[103], electrochemical growth[104], hot imbibing[105] and atomic layer deposition[106].

Problems involved with sedimentation of microspheres into crystals are defect and small mono-crystalline domain sizes. Different sedimentation techniques have therefore proposed [107-109] to overcome the problems.

The synthetic opals discussed in this thesis have been prepared with a technique developed by Lu et. al[109]. The main advantages with this tech-nique are that it is very easy to use, it is inexpensive and does not require clean room environment. The sedimentation of the monodispersed colloids takes place in a rectangular Mylar film gasket between two glass slides (all cleaned with acetone and ethanol). A square hole is cut into the film so that it forms a frame. The glass slides and the Mylar frame create a cavity in which the colloids can sediment. The advantage of using a Mylar film is that it is available in different well-defined thicknesses and by choosing a certain film thickness one can adjust the crystal thickness. The suspension with the colloids is injected in the cavity through a hole in the top glass slide. On top of the hole a glass tube is glued as a tank for the suspension before it has enters the cavity. To create channels in the Mylar frame for the extraction of liquid it is dipped in a dilute suspension of colloids before sandwiched. When the pressure is applied by the paperclips over the sandwich the col-loids attached to the surface of the frame will get pressed into the Mylar creating spacing smaller than the colloidal diameter. Through this spacing the liquid can flow, whilst the colloids are kept in the cavity. When the sus-pension is in the glass tube, a rubber bulb is place on the top. It prevents the solvent to evaporate and applies a small external pressure that helps the sus-pension to enter the cavity. Figure 27 shows photo of the packing cell.

Figure 27. A packing-cell used for sedimentation of colloidal microspheres. The technique was developed by Lu et al.[109]. In the photograph the suspension is just placed in the glass tube. One can see that the microspheres are starting to sediment in the cavity.

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The packing cell is then placed on a vibrating ultra sonic cleaner where it is kept until the colloids have sedimented. The rubber bulb is removed and the crystal is left to dry. After drying the top glass slide, with the glass tube, is removed, and the crystal is out in the open. To prevent sticking to the top surface and cracking of the crystal, the top surface it is made hydrophobic by dipping it into a solution 5 ml dichlorodimethylsilane (Aldrich) and 45 ml trichloroethylene.

Monodispersed silica spheres were used because of their optical proper-ties in the infrared, and the availability of high quality colloids[110]. Crys-tals made of microspheres with four different diameters have been prepared: d= 0.49, 0.73, 0.99 and 1.57 µm.

5.2 Optical analysis A general comment concerning the optical measurements: Because of the wavelength interval of interest discussed in this thesis, around 10 µm, there has been a difficulties finding analyzing equipment. The reason is ironically the scope of this thesis, the strong dispersion. Most often when optical mi-crostructures are analyzed optical fibers are used. This has not been possible since there are no optical fibers working in the thermal infrared. We have therefore been forced to prepare samples which can either be analyzed by normal incidence reflectance measurements with an IR microscope, or large enough samples, 10*10 mm, that they can be analyzed with a spectropho-tometer.

5.2.1 One-dimensional structures The one dimensional periodic structures were analyzed with a Perkin Elmer 983 IR spectrophotometer. For the angular measurements a “Variable angle specular accessory 186-0445” was used permitting measurements between 15o and 75o. Measurements were made for both s- and p-polarized light with a gold mirror as reference. For each angle of incidence, the signal was maxi-mized by adjustments of the mirrors in the accessory.

5.2.2 Two-dimensional structures The optical properties of the hole array was examined by transmittance and reflectance spectra recorded with a IR microscope, Bruker Hyperion 1000 with a MCT-detector. A gold mirror was used as reference for the reflec-tance spectra and spectra were collected both for the hole array and the un-structured surface. The optical images were taken with an Olympus AX 70 microscope.

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5.2.3 Three-dimensional structures The three-dimensional photonic crystals were analyzed by normal incidence reflectance measurements. The spectra were recorded with two IR micro-scopes: a Bruker Hyperion 3000 using an InSb detector and a Bruker Hype-rion 1000 with an MCT detector. The Hyperion 3000 provided reflectance data in the wavelength interval between 0.83 and 2.8µm, and the Hyperion 1000 in the interval 2.8 to 12 µm. A gold mirror was also here used as refer-ence.

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6. Signature management in the thermal infrared

6.1 Black-body radiation All objects emit electromagnetic radiation in the infrared part (IR) of the spectrum. For a blackbody[111] the spectral radiance L, at a certain tempera-ture is given by Planck’s law

)1(

),(2

5

1

KTc

e

cTL , [W / m2 sr µm] (26)

where c1=1.91044*105 [W µm4/m2 sr], c2=14387.69 [µm K] and TK the ab-solute temperature. In Figure 28 the spectral radiances for two blackbodies with different temperature, 60o C and 14o C, are plotted. These temperatures were chosen to represent different objects. 60o is typical for the surface of a car with a running motor and 14o represents the temperature of clothes cov-ering a human body.

Figure 28. The spectral radiance for two blackbodies with the temperature 14 and 60 oC

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As seen, at different temperatures the blackbody curves have their maxima at different wavelengths. This is described by Wien’s displacement law[111]. For all wavelengths, the spectral radiance will be higher for higher tempera-tures, i.e., if T1>T2 then L( ,T1) > L( ,T2). The radiance drops fast on the short wavelength side and has a long tail on the long wavelength side. This explains why iron when is heated it appears red, and when the temperature is increased it looks white (and not blue). The black smiths used this technique for determining the temperature of iron by its’ color.

A unit often used when dealing with radiating objects is the emissivity, e, of a surface/object. It is defined as the ratio of the radiance of a given body to that of a blackbody[112]. The emissivity is a function of temperature, wavelength and polarization. If the emissivity of a certain body is wave-length independent it is called a gray body.

6.2 Atmospheric windows To detect an object one can use different kinds of sensors that work in dif-ferent wavelength intervals. For example there are sensors available in the visual, UV, IR (heat cameras/IR seekers) and radar. Because of the limita-tions of the human vision, that only monitors wavelengths between 380 and 780 nm, we are forced to use sensors if we wish to work in other wavelength intervals. The visual spectrum is an exception, the atmosphere has high transmittance for the wavelengths therein. This is not the case for most of the electromagnetic spectrum. Wavelength intervals with high transmittance are called atmospheric windows. Most parts of the atmosphere are in fact opaque for electromagnetic waves, due to absorbtion in gas molecules and scattering by particles. Both parameters vary with altitude and geographical location. A transmittance spectrum for 1 km of mid-winter atmosphere in the thermal infrared is shown in figure 29. We notice that infrared atmospheric windows exist, one between 3-5 µm (MW) and one between 8-13 (LW). The MW is split into two parts by a strong narrow absorbtion band originating from carbon dioxide

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Figure 29. A transmittance spectrum for 1 km of mid-winter atmosphere according to ModTrans (see paper II)

Consequently, to detect heat radiation through the atmosphere from distant objects at moderate temperature, one is limited to look in these two windows (wavelength intervals). When an object has higher or lower temperature than its’ surroundings it may be detected by a heat camera, working in one or both of the two windows. This is used e.g. in the combat field to detect the enemy or enemy platforms, but also when rescue personnel in helicopters are searching for people e.g. in water.

6.3 Infrared camouflage To avoid detection by a heat camera when an object has higher, or lower, temperature than the surroundings, signature management has to be used. This is achieved by minimizing the contrast between the object and the background, just as a soldier dresses in beige when located in the desert or green in the jungle. Objects used by humans often have considerably higher temperature than the surrounding, e.g. a car engine or the nose cone of an airplane. This means that signature management in the infrared part of the spectrum boils down to reducing the thermal emittance to the same level as the background in the two atmospheric windows. It is important that the emittance does not reach zero. This will cause negative contrast, i.e., the object is easy to detect because it appears cooler than the surrounding. This is also the case when an object is cooler than the surroundings. Then the thermal emittance has to be increased in the two windows.

In this thesis we only consider the most common case, i.e., when an ob-ject has to have a reduced thermal emittance. Kirchhoff’s law states that the emittance, e of a blackbody is equal to the absorbance . In optics it is well

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known that the reflectance, the transmittance and the absorption for an object summarized is equal to one,

1 = R + T + A (27)

If the object has zero transmittance (15) changes to

e = 1 – R. (28)

This means that high reflectance will give low emittance. Intervals with high reflectance located in the two thermal atmospheric windows will then have low emittance in the same intervals. To improve radiative cooling of the object, high emittance is an advantage in the opaque parts of the spectrum.

Earlier in this thesis, two optical phenomena causing high reflectance have been discussed, structural and polaritonic gaps. Structural gaps origi-nate from the periodicity of the material. The position of the gap can be shifted to different wavelengths by changing the lattice constant. Material properties determine the position of the polaritonic reflectance, i.e., the spec-tral position cannot be changed. If the polaritonic material is chosen such that the polaritonic gap is located in one of the two thermal infrared atmos-pheric windows it will reduce the emittance in that interval[113]. The same holds for the structure gap[114]. To achieve simultaneously low emittance in both infrared atmospheric windows the combination of these two optical phenomena is an option. Since there is no material known to have a polari-tonic gap for the MW wavelengths the structural reflectance has to be used there and the polaritonic reflectance in the LW window. By design (materi-als and layer thickness) of a multilayer selective low emittance can be real-ized simultaneously in both windows.

We have worked with the materials combination of silicon and silicon di-oxide. The main reason for this choice is that silicon dioxide has a polari-tonic gap located for wavelengths around 9 µm (which is in the LW) and that silicon is a material with high refractive index that can create a structural gap together with silicon dioxide. It is of course also a major advantage that both materials can be easily deposited with standard clean-room techniques.

The design was made with a multilayer program[9] and the final result was a double layer, placed on a silicon wafer, with silicon as the top layer. An increased number of layers affected the integrated window reflectance behavior negatively. When the structure was made of more than two layers the reflectance peak in the MW was narrowed and did not cover the entire window. In figure 30 both the calculated and the experimental reflectance are plotted together. Also included in the figure is the transmittance of the filters on the heat cameras indicating the wavelength interval where high reflectance is desired.

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Figure 30. Calculated and measured normal incidence reflectance for the designed double layer. No fitting has been performed. The thickness of the layers is 0.9µm (Si) and 2.45µm (SiO2). Also included is the filter transmittance for the heat cameras indicating the two atmospheric windows where high reflectance is wanted.

6.4 Emittance determination The evaluation of the emittance properties of the structure was made with heat cameras (Agema Thermovision 900). The cameras provide a realistic (similar to the combat field) picture of how the improved emittance proper-ties are perceived. The sample was placed, together with other reference samples, as “windows” in a water tank. Figure 31 shows a photograph of the sample holder.

Figure 31. A photo of the water tank used in the emittance analysis. The black hole in the middle is an exit from a spherical hole-roam which represents a black-body radiator.

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In the sample holder the samples were in direct contact with the water, which was heated to 60o C. To ensure a constant water temperature through-out the water tank the water was set in motion by a water pump. Figure 32 shows a schematic picture of the experimental set up. The sample holder is surrounded by a black curtain so that measurements can be made without noise from the surrounding (other objects that are heated).

Figure 32. Schematic figure of the experimental setup. Two heat cameras (Agema Thermovision 900) are placed in a small opening in a cylindrical black curtain.

Heat camera pictures were recorded and analyzed for different angles of incidence, 10o – 60o. Because of the “Narcissus”-effect normal incidence measurements are not possible. In figure 33 a) and b) heat camera pictures are presented for both atmospheric windows.

Figure 33. Heat camera pictures for MW a) and LW b). Bright color indicates high emittance. The circular bright area to the left, in both pictures, is the exit of a black body radiator heated by the hot water. To the right the black area is a curtain sur-rounding the sample holder. In both pictures the samples are the four rectangles. In the upper row: SiO2/Si to the left and Si/SiO2/Si to the right; in the lower row: bulk BeO to the left and a aluminum plate with rough surface to the right.

a b

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The circular area to the left in the pictures indicates a black body radiator and the rough aluminum surface the ideal case. It should be noticed that the sample of interest, the upper right, has almost as good emittance properties (same intensity) as the aluminum plate. An important difference is that alu-minum has high emittance throughout the infrared spectrum whilst, our structure has selective low emittance in the two wavelength intervals where heat detectors are working. This property enables radiative cooling for other wavelengths preventing overheating of the object. It can also be noted that both the BeO and SiO2/Si samples, which both have a reststrahlen band lo-cated in th LW, have low emittance in b) and high emittance in a). By nu-merically analyzing the heat camera pictures one can obtain a value of how much the emittance is reduced. We made angle dependent measurements for both s- and p-polarized emittance. In figure 34 the emittance (mean value of s- and p-polarized light) is plotted as a function of emittance angle. One can see that the emittance at low angles is reduced to 0.37 in the LW and to 0.24 in the MW. Paper II presents a more complete analysis of the emittance properties for both polarizations.

Figure 33 and 34 together evidence proofs that the proposed design can be an alternative for selective emittance control in the thermal infrared. More details are given in paper II[58].

Figure 34. The mean value of the s- and p-polarized emittance for both MW and LW, for angles between 10 and 60 deg.

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7. Summary of papers and conclusions

Paper I H. Högström and C G. Ribbing, “Polaritonic and photonic gaps in Si/SiO2and SiO2/air periodic structures”, Photonics and nanostructures – funda-mentals and application 2, p.23-32, 2004

This paper discusses how the polaritonic gap is affected when it interacts with a structural gap. This is done by multilayer calculations and experi-ments for a one-dimensional photonic crystals made by Si and SiO2, where SiO2 is the polaritonic material. It is shown that a polaritonic and a structural reflectance can: co-exist, have constructive interaction, i.e. the polaritonic peak is strengthened and widened by the structural reflectance, and that the polaritonic reflectance can be destroyed by the periodic structure.

Paper II H. Högström, G. Forssell, and Carl G Ribbing, “Realization of selective low emittance in both thermal atmospheric windows”, Optical Engineering 44(2), 026001, 2005

Here we investigate the possibility of using the combination of a structural and polaritonic reflectance in order to selectively reduce the emittance in the thermal infrared. A double-layer (made of S and SiO2) was designed in such way that the structural reflectance was placed in the short wavelength IR atmospheric window ( = 3-5µm) and an enhanced polaritonic reflectance is automatically positioned in the long wavelength window ( = 8-13µm), be-cause of the optical properties of SiO2. The sample was analyzed by heat cameras in both windows, and for both polarizations, showing a reduction of the emittance to 0.24 in the short, and 0.38 in the long wavelength window.

Paper III H. Högström and C. G. Ribbing, “On the angular dependence of gaps in 1-d Si/SiO2 periodic structures”, Submitted 2006 to Optics Communications

In this manuscript the angular behavior of the polaritonic and structural re-flectance in a periodic structure is investigated by calculations and experi-ments. It is shown that the structural reflectance shifts to shorter wavelengths with increasing angle of incidence. The polaritonic reflectance is sensitive

57

for polarization. For s-polarized light the peak is widened in both directions and for p-polarized it is going through a minimum at the pseudo Brewster angle.

Paper IV H. Högström, S. Valizadeh, C. G. Ribbing, “Optical excitation of surface phonon polaritons by a hole array fabricated by a focused ion beam”, Sub-mitted 2006 to Optics express

Here we show that a FIB can be used for structuring a crystalline SiC surface with deep holes. Optimized FIB parameters for fabrication and the influence of ion current on the final hole diameter are presented. It is also shown that the sensitive optical parameters of SiC, needed e.g. for surface excitations in the wavelength interval between T and L, are not destroyed by the milling. Excitations of surface states by a periodic structure are shown both by reflec-tance calculations and experiments.

Paper V H. Högström and C. G. Ribbing, “Experimental observation of photonic and polaritonic gaps in silica opal”, Submitted 2006 to Applied Optics.

In this contribution we present reflectance measurements on silica opals showing the coexistence of photonic and polaritonic gaps in a three-dimensional photonic crystal. Four different opals were prepared with differ-ent diameters between 0.5 and 1.6µm. It is shown that particles with a di-ameter close to /20 still possess a robust polaritonic gap.

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8. Summary in Swedish, svensk samman-fattning

Den svenska titeln på denna avhandling är ”Optiska studier av periodiska mikrostrukturer i polära material”.

Olika material har olika optiska egenskaper. Ett fönster och ett nypolerat silverfat är ett bra exempel på vardagliga saker som har olika optiska egen-skaper. Fönster har vi på hus för att vi vill släppa in ljus och för att kunna se ut. Man benämner detta som att glaset i fönstret har hög transmittans. Glas reflekterar också en liten del av ljuset, och detta kan bäst ses på kvällarna då det är mörkt utomhus. Om man tittar rakt ned i ett silverfat kan man alltid se en spegelbild av sig själv. Man säger att metallen har mycket högre reflek-tans än glas.

Det som bestämmer ett materials optiska egenskaper är hur elektromagne-tisk strålning (ljuset) växelverkar med olika oscillatorer i materialet. Dessa oscillatorer kan bestå av elektroner (som i det reflekterande silverfatet), joner och molekyler. De två sistnämnda oscillatorerna har sina resonansfrekvenser vid mycket lägre frekvenser än det synliga ljuset, vilket gör att effekten av dem ej kan observeras av ögat.

I denna avhandling har vi jobbat med material som har en oscillator ska-pad av en gitterresonans, en så kallad fononexcitation. Denna excitation finns hos material vars bindning har jonkaraktär och. När ljus, med rätt fre-kvens (våglängd) träffar denna typ av material kommer jonkärnorna att börja oscillera på grund av att de accelereras av det inkommande elektromagnetis-ka ljuset. Resultatet blir ett litet våglängdsintervall där materialet kommer att vara högreflekterande, precis som en metall. I fortsättningen kommer detta intervall benämnas som polaritonreflektans eller polaritongap, efter en quasi-partikel som är en kombination av en foton och fonon. Metalliknande inne-bär i detta sammanhang att de är högreflekterande, lågemitterande samt att de kan hysa ytvågor. De är dock inte goda elektriska ledare, som metaller är. Skillnaden mellan metaller, och material som optiskt beter sig som en metall, är att de sistnämnda endast har dessa egenskaper i ett smalt våglängdsinter-vall, medan metallers egenskaper (som diskuterats ovan) gäller upp till plasmafrekvensen. De polära material som vi arbetat med i denna avhandling är kiselkarbid och kiseldioxid (samma material som vi har i fönster). Kisel-

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dioxid beter sig alltså optiskt som en metall, fast vid våglängder som vi inte kan se med ögat.

Kan man då påverka ett materials optiska egenskaper så att de blir som vi vill, eller måste man nöja sig med de egenskaper som ges av den atomära strukturen? Svaret är man kan styra ett materials optiska egenskaper, och att det låter sig göras på flera sätt dessutom. Ett exempel är att ändra ett material på atomär nivå, som man t ex gör i smarta fönster. Där ändrar man absorb-tionsenergin för materialet, genom att tillföra eller ta bort joner, så att det kan skifta mellan att vara ljust och mörkt. Detta kan vara till stor nytta i t ex skidglasögon, fönster och displayer. Ett annat sätt att ändra ett materials optiska egenskaper är att skapa en periodisk struktur av olika material. Man kan med beräkningar bestämma hur en periodisk struktur ska se ut för att man ska få hög reflektans för en viss våglängd. Hög reflektans för en viss våglängd uppfattar ögat som en färg. Exempel på var en periodisk struktur skapar en färg är den skimrande färgen hos skalbaggar, opal, bensinfilmer på vatten samt färgen hos vissa fjärilar.

Vad finns det då för möjligheter om man kan skräddarsy ett materials op-tiska egenskaper? Man kan t ex skapa lasrar, häftiga solglasögon och även bestämma hur ljuset ska ledas genom ett material, precis som vägarna styr var vi kör våra bilar.

Arbetet som har lett fram till denna avhandling har innefattat två av de ovan beskrivna optiska egenskaperna, en materialoptisk egenskap samt en egenskap kopplad till en periodisk struktur. Materialegenskapen hör till icke ledande material som har en gitterresonans i de termiskt infraröda området (våglängder runt 10 µm). Arbetet har gått ut på är att se hur de material-optiska egenskaperna i det våglängdsintervallet kan användas och förändras genom att tillföra en periodisk struktur.

Papper I-III samt V undersöker hur dessa två skilda optiska fenomenen påverkas om de placeras i varandras närhet på våglängdsaxeln. Resultaten visar att materialreflektansen kan förstärkas, tas bort samt vara oförändrad i en periodisk struktur. Vi visar även, i papper II, att kombinationen av en materialreflektans och en struktur-reflektans kan kombineras så att den ter-miska utstrålningen från ett material kan undertryckas selektivt. Detta är av intresse för t ex militära plattformar där man vill undvika att stråla ut värme eftersom den kan detekteras av IR-sensorer. Papper III visar att reflektansens vinkelberoende skiljer sig hos de två fenomenen. Strukturreflektansen flyttas mot kortare våglängder med ökande infallsvinkel på ljuset, medan polariton-reflektansen vidgas åt båda håll för s-polariserat ljus, och passerar ett mini-mum för p-polariserat.

I papper IV används en periodisk struktur för att excitera ytvågor i ett polärt material. Ytvågor är en polarisationsvåg som är bunden till ett gräns-skikt mellan ett material som beter sig optiskt som en metall, och ett dielekt-riskt material. För att kunna excitera denna typen av vågor måste viss mani-pulation ske för att ”lura” ljuset att binda sig till ytan. Detta kan t ex göras

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med hjälp av en skapad periodisk struktur. De geometriska parametrarna för den periodiska strukturen bestämmer vilken våglängd som kommer att exci-tera ytvågen. Denna typ av ytvågor är av stort intresse för de kan användas till kemiska och biologiska sensorer samt till att leda ljus och skapa möjlig-heten att utföra mikroskopi på nanostrukturer. Det som presenteras i papper IV är resultat som visar att det går att tillverka periodiska strukturer som exciterar ytvågor i kiselkarbid med hjälp av en fokuserad jonstråle. Proble-met med en jonstråle är att den kan förstöra materialet, och då även förmå-gan att excitera ytvågor.

Sammanfattningsvis kan sägas att i denna avhandling har undersökts hur de optiska egenskaperna hos polära material ändras/kan användas, då de får samverka med optiska egenskaper tillhörande en periodisk struktur. För att denna undersökning skall vara möjlig måste periodiciteten vara av samma storleksordning som det våglängdsintervall där de materialoptiska egenska-perna finns, dvs. mikrometerområdet (10-6 m). Periodiciteten är skapad ge-nom kemisk deponering av tunna skikt, sedimentering av mikrosfärer och genom direkt strukturering med en fokuserad jonstråle. Analysen har främst gjorts genom olika typer av reflektansmätningar.

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Acknowledgements

This work was carried out at the Division of Solid State Physics, Department of Engineering Sciences, the Ångström Laboratory, Uppsala University. The project was financially supported by: The Swedish Foundation for Strategic Research (SSF), the Swedish Research Council (VR) and the Swedish Nanotechnology in Defense Applications Program.

Of course there are a lot of people who deserves to be mentioned in this part of the thesis.

I would like to thank...

- Prof. Carl G. Ribbing, who has been my supervisor during my time as a PhC-PhD-student. You have made my time as a student much easier, thanx. Our trips around the world have been great and I’ve really enjoyed: a cold lager when looking at the sunset in California, eating huge steaks and testing what Sam Adams has to offer in Boston, visiting the fish-market in Tokyo and drinking the worst wine ever in Greece.

- Prof. Claes-Göran Granqvist for giving me the opportunity to work at the Division of Solid State Physics, and for showing me what it feels like to wait for a flight in an airline lounge.

- Andreas, my closest co-worker, for being a cool office-mate who shares my passion for music, and sports ;-). Our discussions about different aspects of life will always be remembered.

- Dr. Göran Forssell, my co-author, for interesting discussions

- Dr. Sima Valizadeh, my co-author, for sample preparation and helping me with the FIB.

- Prof. Paul V. Braun and Stephanie Pruzinsky, University of Illinois Ur-bana-Champaign, for having me as a guest and sharing their knowledge.

- Prof. John B. Pendry, Imperial College London, and Prof Francisco Garcia-Vidal, Universidad Autonoma de Madrid, for fruitful discussions

62

- Dr. Stefan Björkert (FOI Linköping) for helping me with sedimentation of microspheres.

- All my present and former colleagues at the Division of Solid State Physics and the Department of Engineering Sciences, for a friendly atmosphere.

- The people at the Dept. of Functional Materials, FOI Linköping, for show-ing interest in my work and providing me with a framework of applications.

- Bengt Nelander, at beamline 73 MAX-lab for helping me with reflectance measurements.

- Anders Heljestrand for all the help with the sample preparation.

- Jun Lu for the TEM analysis.

- My lunch-pals for all the meaningless discussions. No subject has been too stupid or trivial, I have loved it. If everything else fails, we’ll always have our great business plans which will make us filthy rich.

- All my friends around the world, you know who you are and I will never forget what you have done for me!

Slutligen vill jag självklart även tacka

- Anna-Maija & Håkan, dvs mor o far, för allt det stöd ni ger mig. Jag är er evigt tacksam.

- Hanna o Maija, mina systrar… Vad kan jag skriva som på ett rättvist sätt beskriver hur jag känner för er? Ni är mina änglar…

- dig, för att du är den du är!

I think it was John Lennon who said “Life is what happens when you’re making other plans.” Although he also said: “I am the walrus, I am the eggman” so I don’t know what to believe…

Tim in “The office”

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References

1. E. Yablonovitch, Inhibited Spontaneous Emission in Solid-State Physics and Electronics. Phys. Rev. Lett., 1987. 58(20): p. 2059-2062.

2. S. John, Strong Localization of Photons in Certain Disordered Di-electric Superlattices. Phys. Rev. Lett., 1987. 58(23): p. 2486-2489.

3. J. Maddox, Photonic band-gaps bite the dust. Nature, 1990. 348: p. 481.

4. Hecht, E., Optics. 4 ed. 2002, New York: Addison Wesley. 5. C. Kittel. Introduction to Solid State Physics 7'th edition. 1996, New

York: John Wiley & Sons. 6. S. K. Andersson, Single and Multiphonon Interactions with Infrared

Radiation, in Dept. of Materials Science. 1997, Uppsala University: Uppsala. p. 77.

7. C. F. Klingshirn, Semiconductor Optics. 2 ed. 2005, Berlin: Spring-er-Verlag.

8. E. D. Palik, Handbook of Optical Constants of Solids. 1985, Lon-don: Academic Press Inc.

9. M. Theiss, Scout. 2002, M. Theiss Hard- and Software for Optical Spectroscopy: Aachen.

10. A. J. Sievers, The IR vibrational properties of composite solids and particles: the Lydanne-Sachs-Teller relation revisited, in Spectros-copy and Dynamics of Collective Excitations in Solids, D. Bartolo, Editor. 1997, Plenum Press: New York. p. 227-246.

11. C. G. Ribbing and E. Wäckelgård, Reststrahlen bands as property indicators for materials in dielectric coatings. Thin Solid Films, 1991. 206: p. 312-317.

12. L. Brillouin, Wave propagation in periodic structures. 1946: McGraw-Hill Book Company

13. N. W. Ashcroft and N. D. Mermin, Solid state physics. 1976: Brooks/Cole.

14. Lord Rayleigh, On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium en-dowed with a periodic structure. Philosophical magazine, 1887. XXIV: p. 145-159.

15. A. MacLeod, Thin-Film Optical Filters. 1969, London: Hilger Ltd. 16. A. Yariv and P. Yeh, Optical waves in crystals. 1984, New York:

John Wiley and Sons.

64

17. N. Bloembergen and A. J. Sievers, Nonlinear optical properties of periodic laminar structures. Applied Physics Letters, 1970. 17(11):p. 483-486.

18. J. D. Joannopoulos, R. D. Meade, and J.N. Winn, Molding the Flow of Light. 1995, Chichester: Princeton University Press.

19. K. Sakoda, Optical properties of photonic crystals. Springer series in Optical Sciences. Vol. 80. 2001, Berlin: Springer.

20. E. Yablonovitch, Photonic band-gap structures. J. Opt. Soc. Am. B, 1993. 10(2): p. 283-295.

21. S. G. Johnson and J. D. Joannopoulos, Photonic crystals: The road from theory to practice. 2002, Boston: Kluwer.

22. C. G. Ribbing, Photonic structures as interference devices, in Opti-cal interference coatings, N. Kaiser and H.K. Pulker, Editors. 2003, Springer: Berlin.

23. E. Yablonovitch, Engineering omnidirectional external-reflectivity spectra from one-dimensional layered interference filters. Optics let-ters, 1998. 23(21): p. 1648-1649.

24. J. N. Winn, et al., Omnidirectional reflection from a one-dimensional photonic crystal. Optics Letters, 1998. 15: p. 1573-1575.

25. W. L. Vos, et al., Strong effects of photonic band structures on the diffraction of colloidal crystals. Phys. Rev. B, 1996. 53(24): p. 16231-16235.

26. F. García-Santamaría, et al., Optical diffraction and high-energy features in three-dimensional photonic crystals. Phys. Rev. B, 2005. 71: p. 195112.

27. S. G. Romanov and C.M. Sotomayor-Torres, Forward scattering of light in thin opal films. Phys. Rev. E, 2004. 69: p. 046611.

28. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Existence of a photonic gap in periodic dielectric structures. Phus. Rev Lett., 1990. 65: p. 3152-3155.

29. P. Vukusic and J.R. Sambles, Photonic structures in biology. Nature, 2003. 424: p. 852-855.

30. P. Vukusic and I. Hooper, Directional controlled flourescence emis-sion in butterflies. Science, 2005. 310: p. 1151.

31. L. P. Biró, et al., Role of photonic-crystal-type structures in the thermal regulation of a Lycaenid butterfly sister species pair. Phys. Rev. E, 2003. 67: p. 021907.

32. J. Zi, et al., Coloration strategies in peacock feathers. PNAS, 2003. 100(22): p. 12576-12578.

33. O. Graydon, Nature's nanostructures colour wings and stones. OLE, 1998(june): p. 31-36.

34. S. Noda, A. Chutinan, and M. Imada, Trapping and emission of pho-tons by single defect in a photonic band gap structure. Nature, 2000. 407: p. 608-610.

65

35. T. F. Krauss, R.M.D.L. Rue, and S. Brand, Two-dimensional photonic-bandgap structures operating at near-infrared wave-lengths. Nature, 1996. 383(6602): p. 699-702.

36. B-S. Song, S. Noda, and T. Asano, Photonic devices based on in-plane hetro photonic crystals. Science, 2003. 300: p. 1537.

37. J. C. Knight, et al., All-silica single mode optical fiber with photonic crystal cladding. Optics letters, 1996. 21(19): p. 1547-1549.

38. T. A. Birks, J. C. Knight, and P. St. J. Russel, Endlessly single-mode photonic crystal fiber. Optics letters, 1997. 22(13): p. 961-963.

39. R. F. Cregan, et al., Single-mode photonic band gap guidance of light in air. Science, 1999. 285: p. 1537-1539.

40. J. B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett., 2000. 85(18): p. 3966-3969.

41. A. Berrier, et al., Negative refraction at infrared wavelengths in a two-dimensional photonic crystal. Phys. Rev. Lett., 2004. 93(7): p. 073902.

42. http://home.earthlink.net/~jpdowling/pbgbib.html#R. [cited. 43. J. G. Fleming, et al., All-metallic three-dimensional photonic crys-

tals with a large infrared bandgap. Nature, 2002. 417: p. 52-55. 44. C. Luo, et al., Negative refraction without negative index in metallic

photonic crystals. Optics Express, 2003. 11(7): p. 746-754. 45. M. M. Sigalas, et al., Photonic band gaps and defects in two dimen-

sions: Studies of the tranmission coefficient. Phys. Rev. B, 1993. 48(19): p. 14121-14126.

46. M. M. Sigalas, et al., Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials. Phys. Rev. B, 1994. 49(16): p. 11080-11087.

47. W. Zhang, et al., Photonic band structures of a two-dimensional ionic dielectric medium. Phys. Rev. B, 1996. 54(15): p. 10280-10283.

48. W. Zhang, A. Hu, and N. Ming, The photonic band structure of the two-dimensional hexagonal lattice of ionic dielectric media. J. Phys: Condens matter, 1997. 9: p. 541-549.

49. V. Kuzmiak, A. A. Maradudin, and A.R. McGurn, Photonic band structures of two-dimensional systems fabricated from rods of cubic polar crystal. Phys. Rev. B, 1997. 55(7): p. 4298-4311.

50. K. C. Huang, et al., Field Expulsion and Reconfiguration in Polari-tonic Photonic Crystals. Phys. Rev. Lett., 2003. 90(19): p. 196402.

51. O. Toader and S. John, Photonic band gap enhancement in fre-quency-dependent dielectrics. Phys. Rev. E, 2004. 70: p. 046605.

52. A. Rung, C. G. Ribbing, and M. Qiu, Gap maps for triangular photonic crystals with dispersive and absorbing component. Phys. Rev. B, 2005. 72: p. 205120.

53. A. Rung, Destruction of a polaritonic gap in a 2D photonic crystal.Optics Communications, 2005. 252: p. 329-335.

66

54. K. C. Huang, M. L. Povinelli, and J. D. Joannopoulos, Negative effective permeability in polaritonic photonic crystals. Applied Physics Letters, 2004. 85(4): p. 543-545.

55. R. Moussa, et al., Photonic band gaps in highly ionic medium: CuCl, CuBr, CuI. Infrared physics and technology, 2003. 44: p. 27-34.

56. G. Gantzounis and N. Stefanou, Theoretical analysis of three-dimensional polaritonic photonic crystals. Phys. Rev. B, 2005. 72:p. 075107.

57. H. Högström and C. G. Ribbing, Polaritonic and photonic gaps in SiO2/Si and SiO2/air periodic structures. Photonics and Nanostruc-tures - fundamentals and applications, 2004. 2(1): p. 23-32.

58. H. Högström, G. Forssell, and C.G. Ribbing, Relization of selective low emittance in both thermal atmospheric windows. Optical Engi-neering, 2005. 44(2): p. 026001.

59. D. W. Berreman, Infrared absorption at longitudinal optic frequency in cubic crystal films. Phys. Rev., 1963. 130(6): p. 2193-2198.

60. S. H. Park, B. Gates, and Y. Xia, A three-dimensional photonic crys-tal operating in the visible region. Advanced Materials, 1999. 11(6):p. 462-466.

61. B. Liedberg, I. Lundström, and E. Stenberg, Principles of biosensing with an extended coupling matrix and surface plasmon resonance.Sensors and Actuators B, 1993. 11: p. 63-72.

62. C. Nylander, B. Liedberg, and T. Lind, Gas detection by means of surface plasmon resonance. Sensors and Actuators, 1982-83. 3: p. 79-88.

63. G. Raschke, et al., Biomolecular recognition based on single gold nanoparticle light scattering. Nano Letters, 2003. 3(7): p. 935-938.

64. J. LeGall, M. Olivier, and J. J. Greffet, Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton. Phys. Rev. B, 1997. 55(15): p. 10105.

65. H. Ditlbacher, et al., Spectrally coded optical data storage by metal nanoparticles. Optics letters, 2000. 25(8): p. 563-565.

66. M. Specht, et al., Scanning plasmon near-field microscope. Phys. Rev. Lett., 1992. 68(4): p. 476-479.

67. T. W. Ebbesen, et al., Extraordinary optical transmission through sub-wavelength hole arrays. Nature, 1998. 391: p. 667-669.

68. S. A. Maier, et al., Local detection of electromagnetic energy trans-port below the diffraction limit in metal nanoparticle plasmon waveguides. Nature Materials, 2003. 2: p. 229-232.

69. S. I. Bozhevolnyi, et al., Channel plasmon waveguide components including interferometers and ring resonators. Nature, 2006. 440: p. 508-51.

70. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Surface plasmon sub-wavelength optics. Nature, 2003. 424: p. 824-830.

67

71. H. Raether, Surface Plasmons - on smooth an rough surfaces and on gratings. Springer tracts in modern physics, ed. G. Höhler. Vol. 111. 1988, Berlin: Springer-Verlag.

72. N. Ocelic and R. Hillenbrand, Subwavelength-scale tailoring of sur-face phonon polaritons by focused ion-beam implantation. Nature Materials, 2004. 3: p. 606-609.

73. F. Marquier, K. Joulain, and J. J. Greffet, Resonant infrared trans-mission through SiC films. Optics Letters, 2004. 29(18): p. 2178-2180.

74. J.-J. Greffet, et al., Coherent emission of light by thermal sources.Nature, 2002. 416: p. 61-64.

75. E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, Enhanced transmission and beaming of light via photonic crystal surface modes. Phys. Rev. B., 2004. 69: p. 121402.

76. M. Laroche, R. Carminati, and J. J. Greffet, Resonant optical trans-mission through a photonic crystal in the forbidden gap. Phys. Rev. B, 2005. 71: p. 155113.

77. H. Ditlbacher, et al., Flourescence imaging of surface plasmon fields. Appl. Phys. Lett., 2002. 80(3): p. 404-406.

78. S. I. Bozhevolnyi, et al., Waveguiding in surface plasmon polariton band gap structures. Phys. Rev. Lett., 2001. 86(14): p. 3008-3011.

79. H. A. Bethe, Theory of diffraction by small holes. Phys. Rev., 1944. 66(7 and 8): p. 163-182.

80. K. L. van der Molen, et al., Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwave-length holes: Experiment and theory. Phys. Rev. B, 2005. 72: p. 045421.

81. L. Martin-Moreno, et al., Theory of Extraordinary Transmission through Subwavelength Hole Arrays. Phys. Rev. Lett., 2001. 86(6): p. 1114-1117.

82. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Mimicking surface plasmons with structured surfaces. Science, 2004. 305: p. 847-848.

83. W. L. Barnes, et al., Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwave-length holes in a metal film. Phys. Rev. Lett., 2004. 92(10): p. 107401.

84. F. J. Garcia-Vidal, et al., Multiple paths to enhanced optical trans-mission through a single subwavelength slit. Phys. Rev. Lett., 2003. 90(21): p. 213901.

85. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Transmission reso-nances on metallic gratings with very narrow slits. Phys. Rev. Lett., 1999. 83(14): p. 2845-2848.

86. M. M. J. Treacy, Dynamical diffraction in metallic optical gratings.Applied Physics Letters, 1999. 75(5): p. 606-608.

68

87. M. M. J. Treacy, Dynamical diffraction explanation of the anoma-lous transmission of light through metallic gratings. Phys. Rev. B, 2002. 66: p. 195105.

88. Q. Cao and P. Lalanne, Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits. Phys. Rev. Lett., 2002. 88(5): p. 057403.

89. H. F. Schoutten, et al., Plasmon-assisted two-slit transmission: Young's experiment revisited. Phys. Rev. Lett., 2005. 94: p. 053901.

90. S. M. Sze, Semiconductor devices, Physics and technology. 1985, New York: John Wiley & Sons.

91. W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics. 2 ed. 1960, New York: John Wiley & Sons.

92. S. Rojas, et al., Properties of silicon dioxide films prepared by low-pressure chemical vapor deposition from teraethylorthosilicate. J. Vac. Sci Technol. B, 1990. 8(6): p. 1177-1184.

93. www.novasic.com.94. J. Orloff, M. Utlaut, and L. Swanson, High resolution focused ion

beams, FIB and its applications. 2003, New York: Kluwer Aca-demic/Plenum Publishers.

95. L. A. Giannuzzi and F.A. Stevie, eds. Introduction to focused ion beams - instrumentation, theory, techniques and practice. 2005, Springer: New York.

96. S. A. Pruzinsky and P. V. Braun, Fabrication and Characterization of Two-Photon Polymerized Features in Colloidal Crystals. Ad-vanced Materials, 2005. 15: p. 1995-2004.

97. M. Campbell, et al., Fabrication of photonic crystals for the visible spectrum by holographic lithography. Nature, 2000. 404: p. 53.

98. Y. Xia, B. Gates, and Z-Y. Li, Self-Assembly Approaches to Three-Dimensional Photonic Crystals. Adv. Mater., 2001. 13(6): p. 409-413.

99. S. Y. Lin, et al., A three-dimensional photonic crystal operating at infrared wavelengths. Nature, 1998. 394: p. 251-253.

100. H. Míguez, et al., Evidence of FCC Crystallization of SiO2 Nano-spheres. Langmuir, 1997. 13: p. 6009.

101. K. Busch and S. John, Photonic band gap formation in certain self-organizing systems. Phys. Rev. E, 1998. 58(3): p. 3896-3908.

102. J. E. G. J. Wijnhoven, L. Bechger, and W. L. Vos, Fabrication and Characterization of Large Macroporous Photonic Crystals in Tita-nia. Chemical materials, 2001. 13: p. 4486-4499.

103. A. Blanco, et al., Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres.Nature, 2000. 405: p. 437-440.

104. P. V. Braun and P. Witzius, Electrochemical Fabrication of 3D Mi-croperiodic Porous Materials. Adv. Mater., 2001. 13(7): p. 482-485.

105. P. V. Braun, et al., Epitaxial Growth of High Dielectric Contrast Three-Dimensional Photonic Crystals. Advanced Materials, 2001. 13(10): p. 721-724.

69

106. J. S. King, et al., High-filling-fraction inverted ZnS opals fabricated by atomic layer deposition. Appl. Phys. Lett., 2003. 83: p. 2566.

107. H. Cong and W. Cao, Colloidal Crystallization Induced by Cappi-lary Force. Langmuir, 2003. 19: p. 8177-8181.

108. L.Cademartiri, A. Sutti, and G. Calestani, Flux-Assisted Self-Assembly of Monodisperse Colloids. Langmuir, 2003. 19: p. 7944-7947.

109. Y. Lu, et al., Growth of Large Crystals of Monodispersed Spherical Colloids in Fluidic Cells Fabricated Using Non-photolithographic Methods. Langmuir, 2001. 17: p. 6344-6350.

110. www.dukescientific.com.111. Young and Freedman, University Physics. 9 ed. 1996, New York:

Addison-Wesley. 112. W. L. Wolfe and G.J. Zissis, eds. The infrared handbook, revised

edition. 1989, Office of naval research, Deptartment of the Navy: Washington.

113. C. G. Ribbing, Ö. Staaf, and S. K. Andersson, Selective supression of thermal radiation from radomes and materials therefore. Optical Eng., 1995. 34: p. 3314-22.

114. A. Rung and C. G. Ribbing, Calculated photonic structures for in-frared emittance control. Appl. Opt., 2002. 41: p. 3327-3331.

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