PHOTONIC STRUCTURES FROM LC/POLYMER COMPOSITES

PHOTONIC STRUCTURES FROM PHOTONIC STRUCTURES FROM LC/POLYMER COMPOSITESLC/POLYMER COMPOSITES

• Photonic crystals (general properties)• Photonic crystal optical fibers• Photonic quasicrystals

• Switchable diffraction gratings from liquid crystal/polymer (LC/P) composites• Optical amplification in periodic LC/P structures• Switchable photonic crystals and quasicrystals from LC/P composites• Photonic bandgap fibers from LC composites

1µm

12 k

V x

5,00

0

Photonic crystals-general propertiesPhotonic crystalsPhotonic crystals--general propertiesgeneral properties• Photonic crystals are 1D, 2D and 3D periodic structures of dielectric mediawith periodicity (lattice distance) on the scale of visible light.• Multiple optical reflection and refraction phenomena in such structures result in dispersion relations ω(k) similar to electronic band structure E(k) in crystals.

(ρe=je=0; µ=1) + Maxwell equations ⇒tiet ω)(),( rHrH = tiet ω)(),( rErE =

)()(1)( 1 rHrrE ×∇= −εωi

( )[ ] )()()()(ˆ 20

1 rHrHrrH ωµε =×∇×∇=Θ −

⇒ H(r) ⇒

These equations have to be fulfilled taking into account the structural periodicity: )()( 11 rRr −− =+ εε

Due to the periodicity monochromatic EM fields propagating in such medium have the form Bloch waves : )()( ,)()( rRrrrH kk

krkk uueu i =+=

ε1 ε2

with complicated dispersion relation ω(k). If for some interval of ω all possible solutions have nonzero imaginary part of k, waves with these ω can not propagate in the photonic crystal (PC). Such interval of ω is called the photonic bandgap.

EXAMPLE OF 1D STRUCTUREEXAMPLE OF 1D STRUCTUREEXAMPLE OF 1D STRUCTURESinusoidaly modulated refractive index: Propagation of EM field along the z axis: E(z)=eyE(z)

z2

2001

200 , εωεµγεωεµη −=−=

by substitution:

yand Maxwell equations it follows:

0)cos( 22

2

=++∂∂ Ez

zE γη

zz ezBDezADzE µµ −+= )()()( 21

white regions: nonpropagating waves (µ=a+ib)shadowed regions: propagating waves (µ=±ib)

Solutions of this equation have a form

and are known as Mathieu functions.

Stability diagram of Mathieu functions.

BAND STRUCTURE of 1D LATTICESBAND STRUCTURE of 1D LATTICESBAND STRUCTURE of 1D LATTICES

Reduction to the 1st Brillouin zone.

A(z) E(z)

z

sinusoidal lattice

bandgaps

caπω2

GaAs/GaAlAs GaAs/airPeriodic dielectric layers

In 1D periodic dielectric structures complete photonic band-gaps exist for any value of refractive index contrast (ε1/ε2)≠1. In 2D and 3D this happens only in special cases.

2D PHOTONIC CRYSTALS2D PHOTONIC CRYSTALS2D PHOTONIC CRYSTALSExample: quadratic lattice ofdielectric cylinders

Different behaviour for TE and TM modes!

TE

TE modesTE modes

TM modes TM modes

ε=ε(y,z)

Band-gap only for TM modes Complete band-gap

E

J. D. Joannopolos, R. D. Meade, J.N. Winn, Photonic Crystals: Molding the flow of light (Princeton Uni. Press, 1995)

EXAMPLE OF A 2D PHOTONIC CRYSTALEXAMPLE OF A 2D PHOTONIC CRYSTALEXAMPLE OF A 2D PHOTONIC CRYSTAL

A-C:H = Amorphous Hydrogenatedcarbon

Holographic patterning via photoresist coating.

band-gapregions

F. Quinonez et al., Optics Express 14, 4873 (2006).

3D PHOTONIC CRYSTALS3D PHOTONIC CRYSTALS3D PHOTONIC CRYSTALSTo obtain band-gap structures in 3D a very high refractive index contrast is required (ε2/ε1>10) . Besides this only some lattices exhibit complete band-gaps.

One such example is Yablonovitch construction(E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987))

Self-assembled 3D FCC photonic structure from dielectric spheres (artificial opals)

DEFECTS IN PHOTONIC CRYSTALSDEFECTS IN PHOTONIC CRYSTALSDEFECTS IN PHOTONIC CRYSTALSDefects in PC structures provide localization and guiding of optical waves.

g(ω)

ωA cavity (defect) within the PC structure can act as an optical resonator!

New states appear witin the bandgap Such a PC acts as an extremly

narrow band otical filter (dielectric Fabry-Perot filters)

Extended defects in 2D and 3D providewaveguiding effects = bending of light around sharp edges...

Photonic crystal optical fibersPhotonic Photonic crystal optical fiberscrystal optical fibersPC optical fibers are a new technological chalange for improoved optical communication lines.Compared to standard quarz glass fibers they exhibit reduced optical loss, they can transmit higher optical power, they exhibit lower optical nonlinearities, they can be used also out from the conventioanl spectral region (λ~1.5 µm), their dispersion properties can be tuned to the desired needs...

http://ab-initio.mit.edu/photons/tutorial/

corecladding

Basic idea of the PC fibers:Reflection at the surface of an„air core“ is obtained by surrounding it with a cladding of the PC band-gap medium.

Number of guided modes at selected bandgap region (2D): ( )4

222coreLH rN ββ −

≈

EXAMPLES OF STRUCTURESEEXAMPLES OF STRUCTURESXAMPLES OF STRUCTURESa) Bragg reflection

fibers:cladding is made from periodic cylindrical layers of two dielectric materials.

The first example of optical fiber for CO2 laser light. (OmniGuide, MIT)

B. Temelkuran et al., Nature 420, 650 (2002)

J. F. Cregan et al., Science 285, 1537 (1999)

b) PC fiber based on 2D periodic arrangement of air channels in fused silica.

Photonic quasicrystalsPhotonic quasicrystalsPhotonic quasicrystals• Quasicrystals are structures with long-range positional order, but no regular periodicity (no Bloch waves and Brillouin zone concepts, effective Brillouin zones are called (pseudo)Jones zones).• To desribe their structure a basic set of more than 3 lattice vectors is needed (4D, 5D...).• They posses 5, 7, 8, 9 10, 12...fold rotational symmetry axes, which are not possible in regular crystals.• They can exhibit complete photonic bandgaps (actually pseudogaps!!) more readily and at much lower refractive index contrasts than 3D photonic crystals.

Effective „Brillouin zone“ image

Hand-made icosahedral quasicrystal formicrowave radiation

http://www.physics.princeton.edu/~steinh/quasiphoton/W. Man et al., Nature 03977, 2005

PENROSE QASICRYSTAL STRUCTUREPENROSE QASICRYSTAL STRUCTUREPENROSE QASICRYSTAL STRUCTURER. Penrose andR. Ammann Penrose tiling is based on two elements:

1) Thick rombus (angles of (2/10) and (3/10)*360 deg)2) Thin rombus (angles of (1/10) and (4/10)*360 deg)

Basic rule: no two tiles can be touching so as to form a single parallelogram!

Optical structures composed of such tailings can be made by appropriate drilling and/or etching processes of dielectric films.

Example of structurefabricated by electronic-beam litography.M. A. Kaliteevski et al., Nanotechnology 11, 274 (2000).

PENROSE QC – band structure and density of modesPENROSE QC PENROSE QC –– band structure and density of modesband structure and density of modesThe reciprocal wavector space of QC structures in in principle full. Nevertheless, some diffraction peaks have much higher intensity than the others. So in practice we always „see“ only a finite number of diffraction peaks.

Band structure calculation with 2 different sets of RWVsM. A. Kaliteevski et al., Nanotechnology 11, 274 (2000)

Optical diffraction pattern reduced to 3 most intense classes of peaks

b1=(1,0)=(10000)b2 =(cos(π/5), sin(π/5))=(01000) b3 =(cos(2π/5), sin(2π/5))=(00100)b4 =(cos(3π/5), sin(3π/5))=(00010)b5 =(cos(4π/5), sin(4π/5))=(00001)Reciprocal wave vectors of the internal „ring“.

Switchable diffraction gratings from LC/polymer composites

Switchable diffraction gratings from Switchable diffraction gratings from LC/polymer compositesLC/polymer composites

100 µm

Optical diffraction from a H-PDLC transmission grating

Polarization optical microscopy imageof a H-PDLC transmission grating.

gratinggrating ΛΛ=1.8 =1.8 µµmm

Optical grating structures from LC/P media can be obtained by:

• periodic configuration of the external electric field (patterned electrodes)• periodic modification of the alignment layers (patterned alignment layers)• filling of a periodic polymeric host by the liquid crystalline material• periodically modulated photopolymerization induced phase separation process

GRATINGS BASED ON PERIODIC ELECTRODESGRATINGS BASED ON PERIODIC ELECTRODESGRATINGS BASED ON PERIODIC ELECTRODESprobe beam w0<<Λ

Optical microscopy, Λ=50 µµmm, L=5 , L=5 µµmm

0 50 100 1500,00

0,02

0,04

0,06

0,08

0,10

∆nIP

Lateral position (µm)

( )∫ −=∆L

spIP dzzxnzxnL

n0

),(),(1

Field induced in-planebirefringence.

800 V (RMS) 100 V (RMS)

DIFFRACTION PROPERTIESDIFFRACTION PROPERTIESDIFFRACTION PROPERTIES

0.

p polarizationIvp

probe beam w0 >>Λ

0 200 400 600 8000,0

0,2

0,4

0,6

0,8

1,0

0 200 400 600 8000,00

0,02

0,04

0,06

0,08

2nd order 3rd order 4th order

RMS Voltage (V)

I. Drevensek-Olenik at al., Fig. 5

0th order 1st order

Diff

ract

ion

effic

ienc

y

RMS Voltage (V)0 200 400 600 800

0,0

0,2

0,4

0,6

0,8

1,0

0 200 400 600 8000,00

0,02

0,04

0,06

0,08

2nd order 3rd order 4th order

RMS Voltage (V)

I. Drevensek-Olenik at al., Fig. 5

0th order 1st order

Diff

ract

ion

effic

ienc

y

RMS Voltage (V)

I. Drevensek-Olenik at al., J. Appl. Phys. 96, 6207 (2004)

1. 2. 3.

ηN (U)=IN(U)/(T(U)Ivp)Diffraction efficiency:

FORMATION OF HOLOGRAPHIC PDLC GRATINGSFORMATION OF HOLOGRAPHIC PDLC GRATINGSFORMATION OF HOLOGRAPHIC PDLC GRATINGS

I(z)

z

LC+polymer precursorlaser beam 1

Polymer rich regions

LC rich regions

Inhomogeneous phase separationprocess

laser beam 2

z

Spatially inhomogeneous polymerization-induced phase separation process.

1µm

12 k

V x

5,00

0

Λ = 0.8 µm Λ = 1.6 µm Λ = 3.1 µm

Examples of Examples of HH--PDLCPDLC transmission transmission gratings with different values of the gratings with different values of the grating pitch (grating pitch (SEM images)..

H-PDLCs are electrically switchableholographic media with contrast of refractive index (ε1/ε2)≤1.3.

SWITCHING PROPERTIES of H-PDLC GRATINGSSWITCHING PROPERTIES of HSWITCHING PROPERTIES of H--PDLC GRATINGSPDLC GRATINGS

nlc~ npol

s

U+ -

Bragg reflection

nlc ≠ npolp

0 5 10 15 200,0

0,1

0,2

0,3

0,4

0,5

Ukl

onsk

i izk

oris

tek

E (V/µm)

p-polar. s-polar.

Time (s)

Diff

ract

ion

effic

ienc

y

Diff

ract

ion

effic

ienc

y

Switching field Eth~10 V/µm, switching times τ are in the ms region.

Transmission grating

n=n0+n1(r); n1 ≤ 0.1

• switchable 1D photonic band-gap reflectors.• selectively reflect light of specific wavelengths• applications in reflective display devices, color filters...

• switchable deflectors for monocromatic light• voltage controled grating structures for spectral analysis

• applications in beam steering units, opticalinterconnects...

REFLECTION AND TRANSMISSION GRATINGSREFLECTION AND TRANSMISSION GRATINGSREFLECTION AND TRANSMISSION GRATINGS

Reflection grating

Optical amplification in periodic LC/polymer composite structuresOptical amplification in periodic Optical amplification in periodic LC/polymer composite structuresLC/polymer composite structures

• Near band edges cg=dω/dk →0, therefore effective refractive index c0/cg= ng →∞, which results in high reflectivity R at surfaces. • Consequently an optical beam makes many roundtrips in the medium before it escapes out from the structure! • This effect is the basis of Distributed Feed-Back (DFB) laser systems.

k

ωband gap

z

• If in such a structure there exist an atomic transition with inverted population of energy levels (N(E2)/N(E1))>1, optical amplification via stimulated emission will occur. • Due to large reflectivity R at sample surfaces optical gain per round-trip can become stronger than optical losses per round trip, therefore lasing takes place.

N(E2)N(E1)

G= G0/(1+ P/Ps)Gain coefficiet

dP=2GPL-ΛPGain Loss (Λ∝(1-R))

ω=(E2-E1)/h

Optical power

LASING FROM dye-doped H-PDLC GRATINGSLASING FROM dyeLASING FROM dye--doped Hdoped H--PDLC GRATINGPDLC GRATINGSSTo achieve stimulated emission, specific dyes are added to the LC/polymer mixture. The dye molecules are brought to excited state via usual absorption of a VIS or two photon absorption of an IR pump beam. Lasing builds up out from the fluorescence spectrum. noradiative decay

Y. J. Liu et al., Appl. Phys. Lett. 88, 061107 (2006)

absorption lasing

The output wavelenght λ of such a laser depends on the type of the dye and the grating period Λ of the H-PDLC.

SWITCHABLE LASINGSWITCHABLE SWITCHABLE LASINGLASING

V.K. S. Hsiao et al.,Optics Express 13, 3787 (2005)

Laser emission power can be modulated by voltage applied to the H-PDLC grating. Voltage reduces the width of the band-gap and the effective refractive index ng.

Switchable photonic crystals and quasicrystals from LC/P composites

Switchable photonic crystals and Switchable photonic crystals and quasicrystals from LC/P compositesquasicrystals from LC/P composites

• By appropriate orientaion of 4 or more curing laser beams 3D periodic interference patterns can be formed within the H-PDLC structures.• In photopolymerization induced phase separation process LC material concentrates in the intensity minima.• The specific feature of these PCs is that their optical properties can be modulated by low voltage external fields.• The main problem is relatively low contrast of the refractive index

• The feld-induced changes are affected by anisotropy of the droplet shapes.

example of a 2D intereference

pattern

FCC H-PDLC PHOTONIC CRYSTALFCC HFCC H--PDLC PHOTONIC CRYSTALPDLC PHOTONIC CRYSTAL

Optical interference of 4 above described coherent laser beams produces intensity profile with FCC lattice in the 3D space.

p

External voltage modifies the widths as wellas the positions (with respect to k and ω) of the band-gaps.

M. Escuti et al., Opt. Lett. 28, 522 (2003).

PHOTONIC QUASICRYSTALSPHOTONIC QUASICRYSTALSPHOTONIC QUASICRYSTALS

Five beam interference pattern j=1..5)( jjzjyjx zkykxki

jjj eeAE ϕ+++=[ ]))()(cos)(2),(

,

2ljlyjylxjxl

jljjlj

jj ykkxkkeeAAAyxI ϕϕ −+−+−+= ∑∑

>

calculation for • TM polarized beams • wavelength = 532 nm, • angle of incidence with respect to the xy plane θ = 30o.• Ai = A, ϕi = 0, i = 1..5

H-PDLC PHOTONIC QUASICRYSTALHH--PDLC PHOTONIC QUASICRYSTALPDLC PHOTONIC QUASICRYSTAL

Expected refractive index profile n(x,y) for synchronized phases

-200 -100 0 100 200

-200

-100

0

100

200

Ai = A, ϕi = 0, i = 1..5

Calculated Fraunhoffer diffraction pattern.

square=10x10 µm2

H-PDLC PHOTONIC QUASICRYSTALHH--PDLC PHOTONIC QUASICRYSTALPDLC PHOTONIC QUASICRYSTALExpected refractive index profile: n(x,y)

Ai=A, i=1..5, ϕ1 =0.55, ϕ2 =5.99, ϕ3 =1.89, ϕ4 =1.90, ϕ5 =1.82

asynchronized phases(usual case!!)

square=10x10 µm2

Fraunhoffer diffraction

EXAMPLE OF QUASICRYSTAL STRUCTUREEXAMPLE OF QUASICRYSTAL STRUCTUREEXAMPLE OF QUASICRYSTAL STRUCTURESEM-image of broken and etched H-PDLC morphology.The structure is very irregular.Volume fraction of the phase separated LC seems to be very low (small isolated droplets)

Images of diffraction pattern observed on a far field screen: a) E=0, b) E=100 V/µm.

a) b)

IRREGULARITY OF DIFFRACTION EFFICIENCYIRREGULARITY OF DIFFRACTION EFFICIENCYIRREGULARITY OF DIFFRACTION EFFICIENCYnomenclature

1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

1

Diff

ract

ion

effic

ienc

y (1

0-4)

Diffraction peak

2

Sample region 3 4

diffraction efficiency: ηn,N= In,N/Iin

1st order

2nd order 3rd order

4th order

0 100 200 300 4000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3 2.peak

Rel

ativ

e di

ffrac

tion

effic

ienc

y

RMS Voltage [V]

8.peak 6.peak

10.peak

5.peak

Various peaks within the 1st

diffraction order

1st diffraction orderIrregularities are correlated over the entire sample region.

They result not from local sample imperfections, but from the imperfect holographic writing process.

Electric field induced effect are very dispersed.

Photonic bandgap fibers from LC compositesPhotonic bandgap fibersPhotonic bandgap fibers from LCfrom LC compositescompositesIf usual air core in the PC fibers is filled with the LC, fiber properties can be tuned by temperature or external electric and magnetic fields. This property is important for waveguide modulators, couplers, filters, sensors and similar elements...

PC fiber filled with cholesteric LC.Transmitted light at different temperatures.

T. T. Larsen at el., Optics Express 11, 2589 (2003)

CONCLUSIONSCONCLUSIONSCONCLUSIONS

Photosensitive polymer/LC composites provide a simple way to make switchable PC structuresAll the structures reported during the last years are typically very imperfect. Extended work is needed in order to optimize appropriate material compositions, curing parameters and switching properties.

What about other (besides the electrooptic effect) nonlinear optical properties of such structures?These are for the moment completely unexplored and will very probably be the topic of many near future PhD theses....