Femtosecond pulsed light polarization induced effects in ......Femtosecond pulsed light polarization...

Femtosecond pulsed light polarization induced effects indirect laser writing 3D nanolithography

Mangirdas Malinauskasa, Sima Rekstytea, Tomas Jonaviciusa, Darius Gaileviciusa,Vygantas Mizeikisb, Eugene G. Gamalyc, and Saulius Juodkazisd

aLaser Research Center, Department of Quantum Electronics, Physics Faculty,Vilnius University, Sauletekio Ave. 10, LT-10223, Vilnius, Lithuania

bResearch Institute of Electronics, Shizuoka University, 3-5-3-1 Johoku, Naka-ku,Hamamatsu 432-8561, Japan

cResearch School of Physics and Engineering, Australian National University,Canberra, ACT 2601, Australia

dCentre for Micro-Photonics, Faculty of Engineering and Industrial Sciences, SwinburneUniversity of Technology, Hawthorn, VIC 3122, Australia

ABSTRACT

We demonstrate how the coupling between (i) polarization of the writing laser beam, (ii) tight focusing and (iii)heat conduction affects the size, shape and absorption in the laser-affected area and therefore the polymerizationprocess. It is possible to control the sizes of 3D laser-produced structure at the scale of several nanometers.Specifically we were able to tune the aspect ratio of 3D suspended line up to 20% in hybrid SZ2080 resist.The focal spot of tightly focused linearly polarized beam has an elliptical form with the long axis in the fielddirection. It is shown here that this effect is enhanced by increase in the electronic heat conduction whenpolarization coincide with temperature gradient along with the absorption. Overlapping of three effects (i-iii) results in the difference of several tens of nanometers between two axes of the focal ellipse. Narrow lineappears when polarization and scan direction coincide, while the wide line is produced when these directions areperpendicular to each other. The effect scales with the laser intensity giving a possibility to control the widthof the structure on nanometer scale as demonstrated experimentally in this work. These effects are of generalnature and can be observed in any laser-matter interaction experiments where plasma produced by using tightfocusing of linear-polarized light.

Keywords: 3D polymerization, femtosecond pulses, heat flow, nanoscale, polarization, super-resolution, voxelaspect ratio, SZ2080.

1. INTRODUCTION

Direct laser writing (DLW) is widely used for three-dimensional (3D) materials processing. One of its realizationvia polymerization enables free-form fabrication of micro-/nano-objects and optical elements down to tens-of-nanometers resolution.1–3 At high irradiance (intensity), the direct laser polymerization is based on curing aresist (resin) via seeding an avalanche ionization by nonlinear absorption at focal volume of a tightly focused highpeak power laser radiation. Only a very small volume, which can be sub-100 nm in cross sections, around the focalspot is affected during the pulse.4–6 After a point-by-point exposure of the resist and subsequent developmentin an organic solvent, only the exposed free standing 3D structure remains on a substrate or can be made as alarger 3D-free workpiece when tight focusing is combined with fast beam scan at a matching high laser repetitionrate.7–9 In order to avoid geometrical distortions occurring during wet developing for the highest resolution 3Dstructures a critical point dryer (CPD) is commonly used.10–12 Pure optical light delivery at tight focusing cannotexplain the final size of the structure due to the threshold effect of laser modification (e.g., polymerization) and

M.M.: E-mail: [email protected], http://www.lasercenter.vu.lt/index.php/en/.S.J.: E-mail: [email protected], http://www.swinburne.edu.au/engineering/cmp/.

Invited Paper

Laser-based Micro- and Nanoprocessing X, edited by Udo Klotzbach, Kunihiko Washio, Craig B. Arnold,Proc. of SPIE Vol. 9736, 973608 · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2207448

Proc. of SPIE Vol. 9736 973608-1

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 07/05/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

thermal effects within the 3D focal volume. Heat accumulation at focus defined by repetition rate and scan speedis used to increase productivity of 3D polymerization and makes thermal issues very important. Polarizationeffects in laser fabrication in 2D and 3D geometries are now explored in polymerization by DLW13,14 and usingstimulated-emission-depletion (STED) control of 3D focal volume,15,16 orientation of deposition of self-organizedmaterials,17 melting and oxidation of thin films,18 laser ablation,19,20 and as self-organized nano-patterns formedon surface by ablation.21

At tight focusing into a spot (volume) comparable in cross section with the wavelength of light, polarizationeffects become dominant. Vectorial Debye theory predicts that lateral cross sections under focusing with objectivelens of numerical aperture NA = 1.4 has a large ∼ 40% difference22,23 (474 vs 654 nm) at full width halfmaximum (FWHM) for the λ = 1030 nm wavelength at typical laser polymerization conditions. In experiments,the difference is only 10% for objects of 1

2λ size under NA = 1.4 focusing.13 What are the key mechanisms whichdefine the final size of photo-modification (polymerization) have to be better understood for nanofabrication taskswhen sub-wavelength (super-) resolution has to be achieved. As for all micro-fabrication tasks, one should answerwhat is (i) light and (ii) temperature delivery (penetration) into 3D focal volume, which is material dependentand defines the final photo-modification popularly referred to as the threshold effect for sub-wavelength (sub-diffraction) features.24,25

So far there was no direct research on polarization induced polymerization peculiarities at nanoscale. Mainlydue to the fact that polymers at nanoscale shrink, wrinkle and tend to show high plasticity, thus loosing theirDLW defined shape and feature rigidness.26–28 At nanoscale dimensions, mechanical properties of polymerizedfeatures strongly depends on degree of crosslinking.29,30 Recently, a circularly polarized light was used to ensurereproducibility of the pattern.31,32

In addition to the polarization effects in light energy deposition, a heat transfer influences the local polymer-ization.33 Recent studies showed that time between bursts of laser pulses influences the ultimate dimensions oflines written in a photosensitive resin. In particular, the photomodified features become smaller with decreasingburst repetition rates explainable by localized heat accumulation.34

Here a systematic experimental study on the influence of polarization on the feature size (resolution) in DLWis presented. The obtained results demonstrate that the orientation of linear polarization in respect to the beamscan (a sample translation direction) affects the resolution by up to ∼ 20%. This is essential for optimizationand high repeatability of 3D fabrication with a sub-wavelength resolution (a super-resolution). The variationof polarization as an exposure parameter enables tuning of the aspect ratio of polymerised volume (a voxel) inprecise femtosecond pulse based 3D material printing. The revealed findings are of utmost importance for themanufacturing of micro-optical and photonic devices.

2. EXPERIMENTAL

Structures consisting of components oriented at various angles in respect to the laser light polarization werefabricated on a well-leveled glass substrate (Fig. 1). SZ2080 organic-inorganic hybrid material was doped with4,4’-bis (ethyl-amino)-benzophenon (BIS) photoinitiator at 1% by weight and was used as a photopolymer (IESL-FORTH).35 A drop of photosensitive material was heated for 20 min at each of 40, 70, and 90◦C temperatures asa prebake prior to laser polymerization. High peak power femtosecond Yb:KGW laser amplifier (Pharos, LightConversion Ltd.) radiation was used at a central wavelength λ = 1030 nm with pulse repetition rate Rrep =200 kHz and pulse duration τ = 300 fs. The whole setup is described in details elsewhere.36 Laser stabilitywas better than 0.7% for pulse-to-pulse energy fluctuation for the used output power. Long term pulse stability> 1 min was not an issue since the resolution bridges were recorded within 1-2 s. A 1.75 mW of average opticalpower corresponds to the 1.16 TW/cm2 intensity/irradiance at the focus of a 100× magnification objective lensof numerical aperture NA = 1.4; transmission of the optical elements was taken into account.

Samples were translated at a 100µm/s linear velocity commonly used in DLW nanolithography. 3D suspendedresolution bridges along one direction of selected stage (x-axis in Fig. 1(a,b)) were fabricated.37

Width and height of 3D suspended bridges was examined using a scanning electron microscopy (SEM)with ±4 nm precision which was higher compared with an experimental error of laser fabrication ±10 nm.After fabrication samples were developed for 30 min in 4-methyl-2-pentanone bath and CPD was used to avoid



a

11

1

structural changes due to capillary forces. All of the samples were coated with 20 nm thick layer of gold usingsputter coater (note, the actual thickness of Au on the 3D suspended bridges was smaller).

3. RESULTS AND DISCUSSION

There are two major closely interrelated effects observed in the experiments: (i) the energy accumulation fromthe consequent pulses hitting the same spot and (ii) polarization direction affecting the size of the polymerizedregion. The observed effect of polarization on the polymerization is the most intriguing and new for the 3Dsuspended polymerized lines made by beam scanning (Fig. 2). There are known effects of polarization on thescalar parameters of laser-matter interaction, such as absorption coefficient and ionization rate.38–40 It is alsoknown that heat conduction flux (vector) in plasma might be depending on the direction of imposed field.41,42

In what follows these effects are considered in succession: (i) the accumulation from the multiple pulses, (ii)effects of polarization under high-NA focusing, and (iii) influence of the external high frequency electric fieldon the electronic heat conduction. The later contribution has not yet been considered in laser fabrication undertight focusing.

Figure 1. (a,b) SEM images of 3D suspended polymerized lines and ”polarization clock” structures made out of SZ2080with 1% BIS photo-initiator. Polarization orientations are marked where applies. Numerical aperture NA = 1.4, pulseenergy Ep = 0.97 nJ at 200 kHz repetition rate and 1030 nm wavelength 300 fs pulsed exposure.



3.1 Thermal accumulation

Focal spot diameter (at 1/e2) equals to df = 1.22λ/NA = 898 nm assuming Gaussian intensity profile forsimplicity. However, at such tight focusing the vectorial Debye theory (Section 3.5) has to be used to estimatetwo lateral cross sections of ellipsoidal focal spot; one would find Wl = 654 nm and Ws = 474 nm for long andshort cross sections, respectively. Width of polymerized 3D bridges 600−700 nm (Fig. 2) is smaller than the focalspot diameter at 1/e2 level for two cross sections 1111 and 805 nm, respectively. Hence, such laser fabrication hasa potential for super-resolution. In these experiments we used middle range pulse energies from an empiricallyestablished fabrication window when 3D suspended bridges without structural damage are retrieved.

The dwell time of each pulse at the focal spot of diameter, df , equals to tdw = df/vscan. Thus the number ofpulses per spot at the repetition rate Rrep = 2× 105 pulses/s equals to Nspot = tdw×Rrep pulses. Heat diffusioncoefficient for cold resist is similar to that in silica, Ddiff = 10−3 cm2/s.43 Thus the cooling time for the heatedarea, tth = d2

f /D, has to be compared with the time gap between subsequent pulses 5µs. The heat transfer tothe surrounding cold material between the pulses results in the average temperature drop at the arrival of thenext pulse and the temperature accumulation can be explicitly calculated for the N pulses as:44

TN = T1(1 + β + β2 + ...+ βN ) = T11− βN

1− β, (1)

where β =√

tthtth+1/Rrep

.

Assuming the same temperature jump, T1 = const, for one pulse regardless polarization the accumulation forthe two orientations of polarization in respect to the scan direction at fixed speed vs = 100µm/s should result insignificant differences of heat accumulation: TN ' 6.39T1 (α = 0◦) along Wl direction and TN = 4.02T1 (α = 90◦

along Ws) due to different number of overlapping pulses N . However, in experiments the expected difference ofthe line widths up to 1.59 times was not observed and was only about 20% at typical polymerization conditionsfor the linearly polarized pulses. Scalar Debye theory for the circularly polarized light would predicts circularfocal spot, Wcirc., with dimensions scaling with the vectorial theory predictions as 1(Ws) : 1.21(Wcirc.) : 1.38(Wl)at FWHM.

For a larger repetition rate (or slower scan) at the same pulse energy Ep when tth � 1/Rrep, a thermal runawaybreakdown occurs even for minute absorption increase inside photo-polymer. Heat accumulation, indeed, has

100 nm 100 nm

620 nm691 nm

E

vs

E

474 nm 654 nm

Figure 2. Top-view SEM images of 3D suspended bridges formed at the same conditions (scanned along the x-axis atvelocity vs) except for light polarization direction: E ‖ vs (or angle α = 0◦) and E ⊥ vs (or angle α = 90◦). The widthdifference is 10.3% for NA = 1.4 and λ = 1030 nm. Ovals shows the FWHM intensity cross section calculated by vectorialDebye formula Wl ×Ws ≡ 654 × 474 nm (see appx. 3.5 for details). Note, the heat accumulation due to difference ofnumber of pulses per diameter is T long

N /T shortN = 1.59 (Sec. 3.1).



2 x 2 m2

|Ey|2 |Ez|

2

E

2 x 2 m2

(a) (b)

E

top view

side view

A

B

C

D

A C B D

E p-pol. p-pol.

Ez

X

Y

|Ex|2

1.0

0.0 0.007 0.0 0.18 0.0

0.0

1.0

Figure 3. (a) Calculated focal intensity distribution of a linearly x-polarized 1030 nm wavelength beam under NA = 1.4focusing using vectorial Debye theory with sin-apodization function inside medium of refractive index of 1.5; normalizedsquares of components of E-field22 (top row). Bottom: an intensity distribution calculated by scalar Debye theory withFresnel reflectivity coefficients for the case when spherical aberration is absent.45 E-field polarization of the incident lightis shown by arrows. (b) Schematic view of polarization under tight focusing which acquires p- and s-polarization andlongitudinal Ez components.

been shown to increase polymerized line width under tight focusing in SZ2080 starting at 200 kHz repetitionrate for picosecond pulses.33

3.2 Contribution of p-polarization

Figure 4 shows data for linear and circular polarization when beam was scanned along direction of one of theaxis (x-direction). According to the the vectorial Debye theory one would expect that the spot size of circularlypolarized beam will be in between the larger and smaller beam cross sections of those for a linearly polarizedbeam. The largest width of a 3D bridge was observed when scan direction was perpendicular to the orientationof linear polarization, α = 90◦ (E ⊥ vs). Variation of up to ∼20% was observed between collinear (‖) andperpendicular (⊥) orientations of the linear polarization in respect to the scan direction. This is much largerthan an uncertainty in measurement of the width of 3D suspended bridges which was < 2% and was determinedby a pulse-to-pulse stability of laser and uniformity of the resist (same refractive index and absorption coefficientalong the scanned line).

The height of bridges or the axial extent of focal region showed that cumulative uncertainly of polymerizationwas smaller than 1.5% (Fig. 4(b)). The height-to-width ratio was dependent on orientation of linear polarizationand was from 3.07 to 3.44, which is close to expectations of aberrations free focusing.

The observed effect of polarization on 3D polymerization (Fig. 4) is the most intriguing. There are knowneffects of polarization on the scalar parameters of laser-matter interaction, absorption coefficient and ionizationrate, which are different for the circular and linear polarizations.38,46 It was found theoretically that polarizationstate affects the shape of the focal spot when the laser beam focuses with high-NA lenses.13,47 Effect starts at



-90 -45 0 45 900.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15W

idth

of

a 3

D lin

e (

m)

Angle (deg)

Width

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

Height

He

igh

t o

f a

3D

lin

e (

m)

side view

height

10 m

1 m

Figure 4. Width and height of 3D suspended bridges at different angles, α, between scan direction and linear polarization.Numerical aperture NA = 1.4, pulse energy Ep = 0.97 nJ (at focus) at 200 kHz repetition rate. The fit line to widthdata is plotted as ∼ sin(ϕ); arrow marks direction of scan. The inset shows a typical SEM image used for determinationof the height of the structures; Height/Width from ≈ 3.07 to 3.44.

NA = 0.2 and at 0.95 it is significant however not quantified.47 The focal spot (the energy density distribution,wen = (E ·E∗)/16π) of linearly polarized beam has an elliptical form with the long axis in the E-field direction.Besides in the central part of the tightly focused beam the polarization state becomes unidentifiable. However,at the outer edge of the focal spot the polarization direction is not affected by the tight focusing.

The high-NA focusing and polarization around the focal spot of p-polarized (parallel to the plane of incidence)beam is considered next (Fig. 3(b)). One can see that in the direction A−C (plane of incidence) across the focuspolarization changed projection with increased contribution of a perpendicular to the sample surface componentand is different from the projection in the B − D cross section. This effect significantly increases for denseplasma for large angle of incidence.48 Figure 8 (Section 3.6) shows skin depth and reflection coefficient as well asrefractive index (n+ ik) at different excitation of resist which initially has index 1.5 + 0i. Dielectric breakdown isdefined as <εD = 0, i.e., when real and imaginary parts of refractive index become equal n = k (<εD = n2−k2).This condition occurs when n = k = 0.6 (Fig. 5 and Fig. 8). P-pol. has always a stronger absorption in aresist at unexcited up to the breakdown conditions while the beam of circular polarization should experience anaverage absorption of typical for the s- and p-polarizations (Fig. 5).

The difference in the energy absorption along the polarization direction ‖ might be significantly higher thanin the perpendicular direction ⊥ resulting in elongation of the absorbing area in the direction of the field as itwas observed in the experiments. It noteworthy that due to presence of both lateral Ex and Ey fields (Fig. 3(a))the p-pol. will be always present at the focal plane (Fig. 4(a)). Since coefficients As,p not defined at the centerof the beam the additional absorption is affected only at the lower intensity regions away from the center of thefocus. This makes the effect less prominent (Fig. 5).

3.3 Heat conduction and polarization cross talk

Following a more general description, the heat conduction flux in plasma placed into external electro-magneticfield has a form:41,42

qα = −καβ∂T

∂xβ= κ1

∂T

∂xα+ κ2eαeβ

∂T

∂xβ(2)

The first term is the conventional heat flow, while the second term relates to the contribution due to the effectof external field. Here e = E/E is the unit vector in the direction of the electric field; κ1,2 are two scalar



1E21 1E22

0.0

0.5

1.0

1.5

2.0

Skin

de

pth

(m

)

Density Ne (cm

-3)

0.00

0.25

0.50

0.75

1.00R

efle

ctivity

1E21 1E22

0

1

2

3

n,k

Density Ne (cm

-3)

0 20 40 60 800.00

0.25

0.50

0.75

1.00

n+ik

1.5 + 0i

0.6 + 0.6is

s

p

As,p =

1-R

s,p

Angle of incidence (deg)

p

(a) (b)

n

k

NA

= 1

.4

Figure 5. Dependence of the Fresnel absorption coefficient As,p = 1 − Rs,p on the angle of incidence for s- and p-polarizations, respectively, at different excitation levels (see appx. 3.6 for details). The arrows mark the 67.5◦ angle forthe focusing with NA = 1.4 objective lens inside material of refractive index 1.5. The dashed lines are for the unpolarizedand circularly polarized light.

functions, which can be obtained from the solution of the kinetic equation. Note that the general form of Eqn. 2is applicable to the constant external field as well as to the high frequency field. The second term contributionholds after averaging over the laser period. Thus it is applicable to the experiments on polymerization by DLW.It follows from Eqn. 2 that the field-related second term equals to zero when the polarization direction is ⊥to the temperature gradient. Let us now consider effects of linear and circular polarizations in laser-plasmainteractions.

3.3.1 Stationary case

Movement of the laser spot creates different temperature gradients ∇T along and across the scan direction vs.It is instructive to consider the most simple case of uniform heated spot and coupling of heat transport withpolarization as follows from Eqn. 2 even without scanning.

Linear polarization. The intense laser beam hitting the solid surface along the normal (z coordinate) producesplasma spot elongated in direction of polarization (x,y plane), surrounded by cold unperturbed resist. Let’ssuggest that the temperature is homogeneous in the interior of the focus. Therefore the temperature gradientsare concentrated at the outer boundary of heated spot directed along the radii from the center to the outside.Let’s consider the linear polarization of the laser with the field direction along x-axis. As it follows from Eqn. 2the field affects the heat flow only along the x-axis, while in the other parts of heated circle the heat flow isunperturbed because temperature gradient and the field are perpendicular to each other. Therefore expectedeffect of the linear polarization is an elongation of the laser-affected spot in the polarization direction turning acircle into oval.

Circular polarization. The electric field vector of the incident beam at any moment of time is collinear to thetemperature gradient directed along the radius of the beam. Thus, the field influence on a heat flow is evenlydistributed along the circle embracing the heated zone leading to the small change of the zone’s radius at thesame absorbed energy density.

3.3.2 Heat diffusion at threshold of breakdown

The conclusion as presented from analysis of Eqn. 2 about elongation of polymerized region along the linearpolarization can be obtained from heat diffusion scaling. See Section 3.7 for details.



1 2400

600

800

1000

1200

Polarisation

lin. 0

lin. 45

lin. 90

circ.

Power (mW)

Lin

e's

wid

th (

nm

)

(a) (b)

1.00 1.25 1.50 1.75 2.00 2.25 2.50

0

10

20

Between α= 0° and:

90°

45°

circ.

Lin

e's

wid

th in

cre

ase (

%)

Power (mW)

Figure 6. (a) Width of line vs average power (at 200 kHz) at different orientations of linear polarized light in respectto the scan direction: E ‖ vs (or angle α = 0◦) and E ⊥ vs (or angle α = 90◦) and for the circularly polarized light.The white region is bound by one- and two photon absorption scaling on incident power, P , (or intensity, fluence, dose,pulse energy P ) W ∝ 420× P [nm] and W ∝ 420× P 2 [nm], respectively. (b) Line’s width increase in respect to E ‖ vs

(α = 0◦). Scan speed was 100 µm/s. The dashed lines in (b) are eye guides for the ∝√P dependence.

Figure 6(a) shows polymerized line width change at increasing pulse energy (power). Polymerization withlinear α = 0◦ and circular polarization result in comparable width of line. This power dependence shows thatthe final polymerization line width is sub-linearly and linearly proportional to the power (intensity, energy).From tight focusing considerations an expectation would be that the circular polarization should produce linewidth in between the two linear polarizations as show above 1(Ws) : 1.21(Wcirc.) : 1.38(Wl) at FWHM. The heataccumulation would scale the same since the largest pulse accumulation occurs for the widest spot Wl. However,in experiment these two predictions are not observed and changes of line width are only 12-20% (shown in (b)).

The predicted in Fig.6 scaling ∆W ∝√I is a recognizable trend. The change of the line width is calculated

in respect to the Wl (α = 0◦), which corresponds to the most of heat accumulation. This can explain negativeslope at small power (b) due to presence of different heat accumulation for experiments carried at the samefrequency and scan speed. This proves that heat diffusion, hence, ∇T is coupled with polarization of light atfocus.

3.4 Different contributions

The effects of the high-NA focusing and field enhanced heat conduction both lead to elongation of the focalspot in the direction of the E-field in the case of linear polarization. Semi-quantitative estimate for elongationof polymerized region could be calculated as the following. Conversion of s-pol. light to the p-pol. along thepolarization direction as described above results in significant (up to 20%; see Fig. 5) increase in absorption andtherefore increasing the temperature gradient at the edges of the spot and promotes polymerization (crosslinking).Simultaneously, heat accumulation is also present due to difference in the number of pulses per spot along thescan (Sec. 3.1). The discussed optical and thermal mechanisms are efficient during the pulse time only. Theelongation of the polymerized region might be estimated as the distance which the heat wave travels during thepulse time transferring the energy to the area unaffected by laser directly, Lheat =

√Dτ ' 5.5 nm per pulse. The

effect from many consecutive pulses then accumulates in a qualitative agreement with observations. It followsthat the additional polymerization length directly depends on the laser fluence, wavelength, pulse duration andrepetition rate.

The width of line for circular polarization was consistently smaller or close to the minimum width for linearpolarization which was at E ‖ vs (α = 0◦. Optical calculations of focal volume, absorption of p-pol component,and heat accumulations due to difference in spot cross sections all would predict that line width should be in



1.0

0.8

0.6

0.4

0.2

0.0-800 -600 -400 -200 0 200 400

Radial coordinate (nm)

600 800

between of the α = 0◦ and 90◦. Also the heat flow direction vs decoupling from the E-pol. due to non-zeroangle among them should place the width of line at circular pol between the other two Wlin(α = 90◦) < Wcirc <Wlin(α = 0◦). In most of experiments, the width of line for circular polarization was the smallest (Fig. 4). Onepossible reason is a lower multiphoton ionization rate for circular polarization which is important for seeding theavalanche ionization.38 This effect is significant at 10 TW/cm2 intensities for multi-photon photon processes. Inour case intensity was 1 TW/cm2 for the resist which absorbs at ∼ 0.5 µm (due to BIS49) implying a two-photonprocess at 1030 nm.

Earlier results on ablation,19 nano-ripple formation (including using relatively low NA = 0.1 − 0.25),50–52

growth of nano-flakes in solution,17 and controlled melting of films18 using short laser pulses clearly showedelongation of fabricated features beyond extent of the focal spot. Even at low-NA = 0.25 focusing and ablationof MgF2 at very high intensity20 there is clear elongation in direction of linear polarized which is comparable insize with ablation pits for the τ = 1 ps duration and λ = 6.25 µm wavelength pulses. This is in agreement witha predicted here scaling ∆W ∝ τ

√Iλ (Fig. 3.7).

It is noteworthy, the same experiments repeated directly on the glass-resist interface (2D lines) corroboratedthe 3D results observed for suspended bridges. Thermal conductivity of glass substrate and reflection at theinterface was not affecting the difference between the polymerized lines width for ‖ and ⊥ orientation in respectto the scan direction. However, the 3D case analyzed here in details is more generic and does not depend onoptical and thermal properties of the substrate.

3.5 Debye focusing

Vectorial Debye’s theory predicts that using a high numerical aperture focusing (NA > 0.7) the cylindricalsymmetry of the focal electric field distribution is broken and (assuming that input beam is linearly polarizedalong x-direction) a corresponding elongation takes place with alteration of the Ey and Ez components.23 Electricfield at the focal point is expressed as:23,53

E(r, ψ, z) =πi

λ{[I0 + cos(2ψ)I2]i + sin(2ψ)I2j + 2i cos(ψ)I1k} , (3)

where i, j and k are the unit vectors in the x, y and z directions, respectively, and variables r, ψ and z arecylindrical coordinates of an observation point. Integrals I0, I1 and I2 are calculated over focusing angle, θ, fora chosen apodization function.22,23 In case of focusing through N media, they have expressions shown in eqn.2–4.

360 nm

500 nm

Figure 7. Calculated point spread functions for various polarizations: 1(Ws) : 1.19(Wcirc.) : 1.39(Wl).



1E21 1E220,0

0,5

1,0

1,5

2,0S

kin

de

pth

(m

)

Density Ne (cm

-3)

0,00

0,25

0,50

0,75

1,00

Re

fle

ctivity

1E21 1E220

1

2

3

n,

k

Density Ne (cm

-3)

0 20 40 60 80

0.00

0.25

0.50

0.75

1.00

n+ik

1.5 + 0i

0.6 + 0.6is

s

p

As,p =

1-R

s,p

Angle of incidence (deg)

p

(a) (b)

n

k

NA

= 1

.4

Figure 8. (a) Skin depth δ = c/(2ω=√εD) ≡ λ/(4π=√εD) (for intensity) and reflection coefficient R =(<√εD−1)2+=√εD

2

(<√εD+1)2+=√εD2

for λ = 1030 nm wavelength at different plasma densities Ne; the critical plasma density is Ncr(λ) = 1.05 × 1021 cm−3.(b) Real and imaginary parts of refractive index calculated by formula given in Section 3.6.

So light is depolarized at the focal region with preferentially elongated focal spot along the direction of linearlypolarized light. Figure 7(a) shows numerical simulation for the sin-apodization function

√cos(θ1), where θ1 is

the focusing cone covering from 0 to α with NA = n sin(α). It is assumed that light is focused through immersionoil (n1 = 1.518), 150 µm thick cover glass (n2 = 1.523) into volume of polymer (n = 1.504), 10 µm from thesurface of the glass. Corrections for the objective’s design parameters (RIs of the immersion oil [n∗1 = 1.518] andcoverglass [n∗2 = 1.5255]; coverglass thickness [h∗1=170 µm]) are included:53

I(N)0 =

α∫0

√cos θ∗1 sin θ1 exp[ik0(Ψ−Ψ∗)](T

(N−1)s + T

(N−1)p cos θN ) (4)

×J0(k1r sin θ1) exp(ikNz cos θN )dθ1,

I(N)1 =

α∫0

√cos θ∗1 sin θ1 exp[ik0(Ψ−Ψ∗)]T

(N−1)p sin θN ) (5)

×J1(k1r sin θ1) exp(ikNz sin θN )dθ1,

I(N)2 =

α∫0

√cos θ∗1 sin θ1 exp[ik0(Ψ−Ψ∗)](T

(N−1)s − T (N−1)

p cos θN ) (6)

×J2(k1r sin θ1) exp(ikNz cos θN )dθ1.

T(N−1)p ir T

(N−1)s are transmission coefficients through N − 1 interfaces for s and p polarizations. Function Ψ

is the initial aberration function and Ψ∗ – initial aberration function calculated for the objective’s parameters,which in our three media case are:

Ψ = −h1n1 cos θ1 + h2n3 cos θ3, (7)

Ψ∗ = −h∗1n∗1 cos θ∗1 . (8)

PSF for a circularly polarised beam was calculated according to formulas given in.53 Figure 3(a) showsnormalized squares of components of E-field revealing strong depolarization together with total focal intensitydistribution calculated by the formulas presented in this section (calculated in the point of maximum intensityof the focussed beam, which was found to be 0.941 µm before the Gaussian focus).

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3.6 Optical properties at high excitation: from solid to plasma

The SZ2080 resist has refractive index close to that of glass n+ ik = 1.5 + 0i at the laser fabrication wavelengthλ = 1030 nm. Fresnel reflection coefficients for intensity are54∗:

Rs(θ) =(a(θ)− cos(θ))2 + b(θ)2

(a(θ) + cos(θ))2 + b(θ)2, (9)

Rp(θ) = Rs(θ)(a(θ)− sin(θ) tan(θ))2 + b(θ)2

(a(θ) + sin(θ) tan(θ))2 + b(θ)2, (10)

where

a(θ) =1

2

(√(n2 − k2 − sin(θ)2)2 + 4n2k2 + (n2 − k2 − sin(θ)2)

), (11)

b(θ) =1

2

(√(n2 − k2 − sin(θ)2)2 + 4n2k2 − (n2 − k2 − sin(θ)2)

). (12)

Dielectric permittivity is taken in the form of Drude:

εD(λ) = ε0 −ω2p

ω(ω + i/τd), (13)

where the plasma cyclic frequency ωp =√Nee2/(mε0) with the electron density Ne, electron charge and mass,

e,m, respectively, τd = 1.6 fs is electron ion momentum relaxation time similar as in glass;55 ε0 is the dielectricconstant in unperturbed medium, c is speed of light.

Figure 8 shows absorption skin depth, reflectivity and refractive index evolution of the resist which is initiallydefined by n + ik = 1.5 + 0i for λ = 1030 nm excitation wavelength at different free carrier concentrations(corresponds to different excitation levels).

3.7 Heat diffusion at threshold of breakdown

The effect of external field polarization on the heat conduction process during the laser-matter interaction. Thethermal diffusion in the absence of field occurs due to the electron-electron (e-e) collisions averaged by thescattering angle (transport cross section and transport mean free path). The heat conduction in the presenceof external field looses its scalar character and becomes anisotropic with the electric field vector being thepreferential direction for the electron motion. Increase in the electron temperature, Te, results in the decreasein the electron-electron collision rate, νee, responsible for the heat conduction νee ≈ T−3/2, and corresponding

increase in the diffusion coefficient D = v2e/3νee ∝ T

5/2e /Ne.40 The collision rate decreases from its value at

the dielectric breakdown threshold for the larger light intensities and gradually becomes lower than the opticalfrequency of 1.83× 1015 Hz (at λ = 1030 nm).

In the case when e-e collision frequency is less than imposed laser frequency after each e-e collision laserfield turns the scattered electron along the direction of the electric field. The imposed oscillating field forceselectrons to move preferentially in the direction of the field. The oscillation field does not change significantlythe electrons velocity (the oscillation energy at the average intensity per pulse is smaller than the temperatureof ablation). The heating and accumulation processes determine the electron temperature. It is reasonable toassume that in the diffusion process the electron temperature determines the electron’s velocity while collisionsoccur preferentially in imposed high frequency (∞) field. Then the diffusion coefficient in the high frequency fieldis D∞ = v2

e/3ωl ≈ Te/meωl. It follows that the thermal diffusion in the presence of the external high frequencyfield significantly decreases in comparison to that in plasma in the absence of the field.

∗Corrected expression shown here. courtesy Prof. Andrei Rode.

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As a result the heat conduction becomes asymmetric in the focal plane: heat diffusion along the polarizationdirection is suppressed in comparison to that in the direction perpendicular to polarization line. Suppressionof heat conduction leads to the local overheating. In the part of the overheated region the temperature mayincrease and in turn significantly enhance polymerization rate. Width of the polymerized line, W , produced bythe linear polarized beam will be larger in the direction of polarization. The size increment is proportional tothe length of the heated region ∆W ∝ Lheat =

√D∞τ ∝

√Teτ/ωl; the effect is taking place during the pulse of

duration τ . In terms of fluence and intensity, F and I, which are proportional to the electron temperature, Te,an increase of the polymerized rod is ∆W ∝

√Fτλ ∝ τ

√Iλ. For typical value D∞ = 1 cm2/s46 and τ = 300 fs

one finds ∆W = 5.5 nm (or 0.6% of the lateral spot size W = 1.22λ/NA ' 900 nm).

4. CONCLUSIONS AND OUTLOOK

The proposed analysis qualitatively explains the difference of the action of linear and circular polarized lighton the width and symmetry of the 3D suspended polymerized bridges under tight focusing. It is shown thatpolarization of incident laser field allows controlling the polymerization process on a scale of nanometers onalready sub-wavelength 3D patterns. These findings might be not of utmost importance for the femtosecondlaser manufacturing of bulky structures56 and tissue engineering scaffolds,57,58 yet are definitely consequentialfor the performance of fabricated micro-optical,59 nano-photonic60 and highly-integrated61 devices operating inVIS wavelengths range.

Using linearly polarized laser pulses, width of polymerized lines increases when the angle between lightpolarization and sample translation directions increases and reaches maximum at 90◦ degrees. Variation ofup to ∼ 20% in the line’s width was observed between E ‖ vs and E ⊥ vs in SZ2080 polymer resist. Heatdiffusion is reduced along the linear polarization and cause local over-heating but does not affect heat flow inthe perpendicular direction during the pulse. Absorption is larger for the p-pol. which contributes to elongationof the polymerized features. These effects are 2-3 times smaller as it would be expected from the elliptical focalspot size due to tight focusing. The heat diffusion and E-field coupling described here have been reported forablation experiments using low-NA.19,20

The observed effect will be more pronounced for longer wavelengths, higher pulse energies, and longerpulses according to ∆W ∝ τ

√Iλ. The performed study demonstrates a possibility of the aspect ratio (line’s

height/width) tuning purely by polarization orientation up to the mentioned 20%.

This study on influence of polarization on 3D polymerization reveals generic mechanisms and is expectedto be applicable to other photo-polymers, glasses, and ceramic materials. The provided insights are relevant tolaser tweezers where Marangoni flows on nano-/micro-scale are driven by minute thermal gradients62 and forlight localization in plasmonic applications. The presence of longitudinal field component, Ez, (Fig. 3(a)) is al-ways present at tight focusing and can open resonant absorption channel as used for the breakdown conditions.63

Control of heat affected zone in laser nanofabrication will benefit from the coupled light-matter interaction in con-junction with heat transport and chemical reactions. Lastly, polarization inevitably contributes to light induceddamage and can be a limiting factor for applications of various micro-optical and nano-photonic components.64,65

ACKNOWLEDGMENTS

S.R. and M.M. acknowledge ECs Seventh Framework Programme Laserlab-Europe IV JRA support BIOAPP(EC-GA 654148). D.G. is gratefull for financial support by ”FOKER” (No. MIP-14459) from the ResearchCouncil of Lithuania. V.M. acknowledges support by JSPS Kakenhi Grant No. 15K04637. S.J. is grateful forsupport via Australian Research Council Discovery DP130101205 and DP120102980 grants.

Proc. of SPIE Vol. 9736 973608-12


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