comparison of parallel-plate and in-plane poled polymer ...hayden/pubs/in-plane poling...

Comparison of parallel-plate and in-plane poled polymerfilms for terahertz sensing

Colin V. McLaughlin, Xuemei Zheng, and L. Michael Hayden*Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA

*Corresponding author: [email protected]

Received 18 May 2007; accepted 29 June 2007;posted 17 July 2007 (Doc. ID 83195); published 23 August 2007

We have performed calculations and measurements of the efficacy of two poling geometries of poledelectro-optic (EO) polymer films for use in sensing terahertz (THz) radiation via EO sampling. Takingreflective and absorptive losses into consideration, we find that a parallel-plate (PP) poled film has asensitivity maximum when oriented at 55° to the incident probe and THz beams. In addition, we showthat our in-plane (IP) poled polymer films are comparable in sensitivity to PP-poled films and discuss thepotential for improving IP-poled polymer devices. © 2007 Optical Society of America

OCIS codes: 160.2100, 160.4890, 190.4360, 190.4400, 190.7110, 250.2080.

1. Introduction

Poled electro-optic (EO) polymers have recentlybeen shown to emit and detect broadband terahertz(THz) radiation [1]. Effective THz sensors operatingin the wavelength vicinity of 3 mm to 30 �m areimportant in applications ranging from semicon-ductor materials characterization to biomedical im-aging [2]. EO crystals [3], photoconducting dipoleantennae [4,5], and poled EO polymer films [1,6,7]have been used as THz sensors. Sensors utilizingEO polymers are desirable because of their broad-band, gap-free response [1,6,8]. To our knowledge, afull analysis of poled polymer devices for THz sens-ing has not been previously presented. In this paperwe provide such an analysis for two different polinggeometries, parallel-plate (PP) and in-plane (IP).We theoretically and experimentally explore angletuning of PP-poled EO polymer sensors to optimizethe detected THz signal. Modeling of the electricfield distribution in the IP-poling geometry is con-ducted for evaluating the poling efficiency and foruse in evaluating the EO measurement. Finally, thedetected THz signals from the IP- and PP-poledpolymers are compared.

Typical EO polymer poling methods employ a PPdesign, where a thin polymer layer is sandwiched

between two electrodes. The electrodes usually con-sist of either indium tin oxide (ITO) and evaporatedgold or ITO–ITO. To use the PP-poled polymer as aTHz sensor, the high reflectivity of metal in the THzregime requires that the one or both of the elec-trodes be removed. The resulting poled, free-standing film makes subsequent poling of thatsample difficult or impossible. In contrast, IP-poledEO polymer devices permit the probe and THzbeams to pass through the polymer without ob-struction from the electrodes, allowing for subse-quent or in situ poling. Recent studies show that EOglasses can exhibit considerably higher EO coeffi-cients ��250 pm�V� than the poled polymers pre-sented here ��30 pm�V� [9]. However, because oftheir fragility, these EO glasses are not currently wellsuited for PP poling in a thick-film ��100 �m� form.IP poling, which requires fewer processing steps thanPP poling, can be used with these EO glasses. Itshould also be stressed that IP poling allows for op-timal overlap of the THz electric field with the polingdirection (z axis) of the oriented chromophores in thepoled film, increasing the detected signal in THzsensing. An IP-poled polymer sensor is oriented suchthat the incident THz beam is normal to the polymersurface, fully aligning the polymer z axis with theTHz polarization. As will be shown, this optimalalignment leads to more efficient THz sensing. Incontrast, utilizing a PP-poled EO polymer sensor re-quires rotation of the polymer film with respect to the

0003-6935/07/256283-08$15.00/0© 2007 Optical Society of America

1 September 2007 � Vol. 46, No. 25 � APPLIED OPTICS 6283

incident THz beam to allow an appreciable compo-nent of the THz electric field to be aligned with thefilm’s poled z axis.

2. Theory

The sensitivity of an EO sampling sensor is directlyproportional to the phase retardation induced by theexternal THz electric field. To compare IP poling toPP poling for use in THz sensing, the THz-inducedretardation [10], due to the EO effect, between the sand p polarization of the optical probe beam needs tobe determined for both cases. For both the IP- andPP-poled sensors we utilize a half-wave plate to ro-tate the probe beam polarization such that the s andp components are of equal amplitude [Figs. 1(a) and1(b)]. The PP-poled sensor is aligned such that theTHz beam, which is collinear with the optical probe,is purely p-polarized, with a projection along the zaxis (poling axis) of the polymer [Fig. 1(b)]. For thePP-poling case, the change in the optical path differ-ence of the p-polarized �lp� and s-polarized �ls� compo-nent of the optical probe beam within the polymer isgiven by

��lp � ls� �dPP

cos ��np � �ns�, (1)

where dPP is the PP polymer thickness and � is therefracted angle. The modulated indices for the s andp polarization are, respectively, �ns and �np. To de-rive Eq. (1), we have used the fact that without thepresence of the THz electric field the static refractiveindex and refracted angle of the s and p componentsare approximately equal ��ns � np � n�, ��s � �p

� �� within the polymer. The probe beam is incidentupon the polymer at an angle �, leading to sin �� 1�n�sin � [Fig. 1(c)]. The applied THz electricfield is

ExTHz � ETHz cos �THz,

EyTHz � 0,

EzTHz � ETHz sin �THz, (2)

where �THz is the refracted angle of the THz beamwithin the polymer. The poled polymer has a symme-try of � mm, which has an EO coefficient tensor of theform [11]

rIk �

0 0 r13

0 0 r13

0 0 r33

0 r51 0r51 0 00 0 0

. (3)

The resulting associated index ellipsoid for the poledpolymer affected by the presence of the THz field is

� 1

no2 r13Ez

THzx2 � 1

no2 r13Ez

THzy2

� 1

ne2 r33Ez

THzz2 �2r51ExTHz�xz � 1. (4)

To remove the cross term associated with xz, we per-form a coordinate system transformation into x�, y�,and z� in which the principle x and z axes are rotatedthrough an angle � [Fig. 1(c)], such that

x � x� cos � z� sin ,

y � y�,

z � x� sin z� cos . (5)

Elimination of the cross term �x�z�� in the new coor-dinate system requires that

tan 2 �2r51Ex

THz

�1�no2 r13Ez

THz� � �1�ne2 r33Ez

THz�. (6)

It is characteristic of poled polymers that the ratio ofr13 and r51 to r33 is approximately one-third [11]. Tak-

Fig. 1. (Color online) Schematic of the PP-poled polymer THzsensor. (a) The probe beam is polarized at 45° to the THz beam and(b) both are incident at an angle, �, and (c) copropagate through thepolymer at an angle, �. The poling direction is the z axis. Theprinciple axes are rotated by � about the y axis in the presence ofthe THz electric field.

6284 APPLIED OPTICS � Vol. 46, No. 25 � 1 September 2007

ing no � ne � n and combining Eq. (2) and Eq. (6), wearrive at

tan 2 � �Ex

THz

EzTHz �

�cos �THz

sin �THz . (7)

In the new coordinate system we obtain

1

nx�2 �

1

n2 r33Ez

THz

3 2r33Ez

THz sin2

3

2r33Ex

THz sin cos

3 ,

1

ny�2 �

1

n2 r33Ez

THz

3 ,

1

nz�2 �

1

n2 r33Ez

THz

3 2r33Ez

THz cos2

3

�2r33Ex

THz sin cos

3 . (8)

From Eq. (8), we can derive indices along the newprinciple x�, y�, and z� axes. Taking �1�3�n2r33Ez �� 1,the induced modulated index in the s-polarized stateis given by �ns � �ny� � �1�6�n3r33Ez. The index forthe p-polarized state is

1

�np�2 �sin2� � ��

nz�2

cos2� � ��nx�

2 , (9)

where propagation relative to the z� axis is given bythe angle � � ��. The resulting modulated index inthe p-polarized state is given by

�np �n3r33

6 �1 2 sin2 � sin 2 sin�2 � 2��Ez

sin 2 cos�2 � 2��Ex�. (10)

Using the fact that the THz index �nTHz � 1.7� isnearly constant from 1–8 THz and approximatelyequal to the optical index at 800 nm [8], we havesin �THz � sin � � �1�n�sin � and Eq. (1) can be sim-plified using �ns and �np to give

��lp � ls� �dPPn3r33

3 ETHzsin �

�n2 � sin2 �. (11)

This result shows that the maximum THz-inducedretardation occurs when the poling direction (poly-mer z axis) is parallel to the THz polarization and theincident angle is 90° [Fig. 2(a)]. However, this doesnot account for reflective losses of the THz and opticalbeams at the surfaces of the polymer. Including anangle-dependent Fresnel transmission factor, FTHz��,

for the THz field due to reflective loss at the air–polymer front interface and ignoring THz absorptioninside the polymer, the detected signal S�� is repre-sented by

S�� lp � ls�FTHz��, (12)

where

FTHz�� 2nair cos �

nair cos �THz nTHz cos �. (13)

The THz transmission factor causes an amplitudereduction throughout the angle tuning range [Fig.2(b)] and the detected signal maximum is shifted toan angle of � � 60°. The detected signal will be fur-ther modified by probe beam loss at both the frontand rear surface of the polymer. Similarly, absorptionof the probe beam within the polymer will also affectthe detected signal amplitude. The inclusion of an-other factor, FOpt��, to account for these losses istherefore required and is given as follows:

FOpt�� T��exp� �ndPP�

�n2 � sin2 �, (14)

where the transmission intensity term, T��, ac-counts for the total transmission of the probe beamthrough the polymer. The exponential is the absorp-tive loss term corresponding to the actual polymerthickness transected by the optical beam, where �is the absorption coefficient. The transmission in-tensity term, T��, is calculated by separating thes- and p-polarized components of the optical beamand independently calculating their respectivetransmission amplitudes. The two attenuated com-

Fig. 2. (Color online) (a) Detection sensitivity due to THz-inducedretardation for the PP-poled EO polymer THz sensor as a functionof sensor incident angle, �. (b) Inclusion of THz loss due to Fresnelreflection produces a maximum sensitivity at an incident angle of60°. (c) Accounting for optical probe absorption in the polymer andreflective losses at the air–polymer and polymer–air boundariesfurther attenuates the sensitivity and brings the optimal sensingangle to 55°.


ponents are then combined to form the probe beamtransmission intensity:

T�� 12 � 4n2 cos ��n2 � sin2 �

�n2 cos � �n2 � sin2 ��2�2

� 4 cos ��n2 � sin2 �

�cos � �n2 � sin2 ��2�2�. (15)

Including probe beam losses and the THz transmis-sion factor, the detected signal for a PP-poled sam-ple is

SPP�� lp � ls�FTHz��FOpt��. (16)

The optimum angle for THz sensing using a PP-poledEO polymer, accounting fully for optical and THzreflection and optical absorption, is �55° [Fig. 2(c)].

As discussed above, because of the poling geometry,EO sensing with a PP-poled polymer requires thatthe film be rotated, permitting only a partial projec-tion of the THz field to be detected. In contrast, IPpoling aligns the z axis of the polymer perpendicularto the polymer surface normal. This allows for a fullprojection of the THz electric field onto the polingdirection in the case of normal incidence of the THzbeam. The THz-induced retardation between the twopolarization components of the optical probe beam inan IP-poled configuration can be shown to be

�IP�lP � lS� �dIPn3r33E

THz

3 , (17)

where dIP is the IP polymer thickness. As in the caseof PP poling, we need to consider THz amplitudereduction and probe beam reflective loss at the air–polymer interface. Because the poled polymer is notremoved from the IP-poling device, probe beam re-flective loss at polymer–fused-silica-substrate andfused-silica-substrate–air boundaries must also beconsidered. These factors are combined in a total at-tenuation factor given by

FIP �2

nTHz 1� 4n

�n 1�2�� 4nnfs

�n nfs�2�� 4nfs

�1 nfs�2�. (18)

The THz and optical polymer index of nTHz � n �1.7 [8] and optical fused-silica index of nfs � 1.453(at 800 nm) result in an amplitude attenuation andreflective loss factor of FIP � 0.663. Including probebeam absorption in the polymer, we arrive at a gen-eral expression for the detected signal in an IP-poledsensor of

SIP � FIP�IP�lP � lS�exp��dIP��. (19)

The ratio of the detected IP-poled signal �SIP� to themaximum detected PP-poled signal at the optimum

angle �SPP�� 55°��, assuming equal polymer thick-nesses and EO coefficients, is 2.4.

3. Experiment

Our polymer sensor films are guest–host mixturesof 40 wt. % of the dye (3-(2-(4-(N,N-diethylamino)-phenyl)ethenyl)-5,5-dimethyl-1,2-cyclohexenylidene)-propanedinitrile (Lemke) and 60 wt. % amorphouspolycarbonate (APC). The dye molecule was obtainedfrom Battelle Corporation (Columbus, Ohio, USA)and the polymer from Aldrich Chemical (St. Louis,Missouri, USA). The polymer films are made by cast-ing a solution of the dye molecule and host polymer indicholoroethane (12%�88% solid-to-solvent mass ra-tio) onto the substrates through a 0.2 �m filter. Sol-vent removal is accomplished through a soft bake at80 °C for 4 h under normal atmospheric conditions,followed by a hard bake at 105 °C for 12 h in vacuum.

The IP-poling devices consist of 3 �m aluminumelectrodes on a substrate of 1 mm thick fused silica.The electrodes are separated by a gap of 100 �m andhave a parallel face of 1 cm in length [Figs. 3(a) and3(b)]. It should be noted that rounded electrode edgesreduce the high-field fringing effects that are presentwith sharp edges, thereby reducing the occurrence ofpolymer dielectric breakdown during poling. The IPdevice requires only drop casting of the polymer so-lution, with the film thickness controlled by the mass-to-solvent ratio and solution volume applied. The PPdevice is created by casting the polymer solutiononto an ITO-coated substrate. After solvent removal,we press several polymer films between two ITOsubstrates, at approximately 80° above the glass-transition temperature �Tg�, using 75 �m thick poly-imide spacers between the substrates to create auniformly thick film. A nonzero EO coefficient is im-parted to both the IP and PP films through standardelectric field poling [12]. The maximum poling tem-

Fig. 3. (Color online) (a) Top and (b) side views of the IP-polingdevice. The poling electrodes are 3 �m thick and are separated bya 100 �m gap. The arrows within the electrode gap in (a) and (b)denote the poling field. (c) Measurement of the EO coefficient in anIP sample utilizes a modified transmission-geometry setup.


perature for Lemke�APC (LAPC) (40%�60%) is 90 °C,which is 5 °C below Tg.

The EO coefficients of the PP- and IP-poled poly-mers are measured using a transmission-geometrysetup [13]. In both cases, modulation of the incidentbeam �Imod� is a result of polarization rotation due tothe EO effect induced by an externally applied elec-tric field of frequency � and has the form

Imod � �Imax � Imin

2 � sin��t�. (20)

The maximum EO phase shift is given by � . Theterms Imax and Imin are determined through rotationof the Soliel–Babinet compensator and are, respec-tively, the maximum and minimum intensity at thedetector. We let the amplitude of the modulated sig-nal be defined as

A � �Imax � Imin

2 � , (21)

where the EO phase shift is given by

� �2�d

� � �np

cos �p�

�ns

cos �s, (22)

for a polymer of thickness d. The wavelength is � and�np and �ns are the modulated indices in the p and spolarizations, respectively. A polarizer placed beforethe sample provides linearly polarized light at 45° tothe polymer z axis. The PP-poled sample requiresrotation with respect to the incident beam, as in Fig.1(b) [13]. However, because of the poling geometry,the IP setup utilizes normal incidence, leading to�s,p � 0 [Fig. 3(c)]. For clarity, we define np � ne andns � no, where ne is the index in the polymer z axis.The resulting phase shift for the IP case is

� �2�dIP

� ��ne � �ns�. (23)

Recalling that r13 � �1�3�r33 [11], the modulated in-dices are, respectively,

�ne �12 n3r33Ez,

�no �16 n3r33Ez, (24)

where n is the optical index of the polymer. Unlike aPP-poling configuration where the applied electricfield �Ez� is highly uniform and is expressed as theapplied voltage divided by the polymer thickness, inan IP-poling configuration Ez is highly nonuniformdue to fringing effects. Therefore, we modeled theelectric field distribution of our IP device using acommercially available finite-element analysis pack-age [14]. The results of these simulations (Fig. 4) are

in excellent agreement with previous studies [15] andshow that the average Ez in the polymer (across andabove the electrode gap) is proportional to the appliedvoltage and is a function of the polymer thickness.For a first approximation, we assume uniform illu-mination of the electrode gap by the incident laserbeam and replace Ez in Eq. (24) with the averageelectric field within the polymer, Eeff. Using Eq. (24)with Eqs. (21) and (23) and solving for r33, we arriveat a detected EO coefficient for an IP-poled polymer of

r33 �3�

�dIPn3

1

�Imax � Imin�� AEeff

. (25)

Because of the Eeff factor, the reported EO coefficientsfor our IP-poled polymers are an averaged value forthe full width and thickness of the polymer in theelectrode gap.

We used both types of poled polymer geometry asEO sensors in a standard THz setup (Fig. 5). A 1 kHz,

Fig. 4. (Color online) Simulation of the poling field through a90 �m thick polymer in an IP device. This is a model of 7 kVapplied to 3 �m thick electrodes with a 100 �m wide gap on afused-silica substrate. The extremely high fields surrounding theelectrodes limit the poling efficiency through the rest of the poly-mer. The average field �Eeff� in this simulation is 36.5 V��m.

Fig. 5. Schematic of the THz setup. A pellicle beam splitter splitsthe probe and pump beams. The pump generates THz in an EOcrystal or poled polymer film. The half-wave plate is used to rotatethe probe beam polarization 45° with respect to the THz polariza-tion. Both the THz and probe are focused onto the polymer sensorand a balanced detection scheme records the THz electric field.


800 nm centered, 45 fs FWHM pulse train from aTi:sapphire laser is split by a pellicle into a probe andpump beam, after which the pump beam is used togenerate THz in either a poled polymer or EO crystal.Off-axis parabolic mirrors collimate and focus theTHz beam onto the poled polymer sensor. Col-linearly propagating with the THz beam, the probebeam is also focused into the poled polymer sensor.When using a PP-poled sensor, the polymer isplaced such that the incident THz beam electricfield is p-polarized at an incident angle, �, withrespect to the polymer [Fig. 1(c)]. An IP-poled poly-mer sensor is oriented so that the probe and THzbeams are incident normal to the polymer surface.For both cases, the optical probe beam is polarizedat 45° with respect to the THz polarization. EOmodulation of the probe beam by the THz electricfield is then recorded through a balanced detectionscheme. Fourier transformation of the detected THzelectric field yields the THz amplitude spectrum.

4. Results and Discussion

We obtained lower values of the EO coefficient �r33� inan IP-poled polymer film than that obtained in aPP-poled sample with an equivalent applied voltageand electrode separation. This is consistent with ourmodeling and is expected due to the fringing effects ofthe thin electrodes of the IP device resulting in anonuniform electric field, as discussed above. The an-alytically derived electric field at the center of theelectrode gap for an IP geometry with an infinitelythin electrode is reported to be Ecenter � �2��*�V�g�[15], where V is the applied voltage and g is theelectrode gap. Our simulation accurately recoversthis value at the midpoint of the gap but rises sharplynear the electrode edges as expected. We calculate Eeff

by averaging the value of the electric field at each gridpoint between the electrodes up to the thickness ofthe polymer.

Modeling of our IP device yields an average ef-fective electric field in the z direction of Eeff �36.5 V��m for a 90 �m thick polymer, a 100 �melectrode gap, 3 �m thick electrodes on fused silica,and an applied voltage of 7 kV (Fig. 4). An IP-poledfilm corresponding to the above specifications had ameasured EO coefficient of r33 � 12.4 pm�V. Previ-ously, we studied the relationship between the polingfield and the measured r33 in PP-poled LAPC [16].Using these results, we predict that LAPC poled at36 V��m should have an EO coefficient of r33 �12 pm�V.

After EO measurements, we conducted THz exper-iments with both sensors. To compare the angle-dependent sensitivity of a PP-poled sample with ourtheory, angle tuning of an 82 �m thick PP sensor�r33 � 29.7 pm�V� was conducted using the THz setuppreviously described. The THz emitter for this studywas a PP-poled polymer film. THz electric field traceswere taken at various sensor angles, �, between 20°and 85°. Four traces were recorded at each angle andthen averaged. The averaged electric field traceswere Fourier transformed to allow comparison of am-

plitudes at specific frequencies. Figure 6 shows theTHz amplitude as a function of sensor angle at thefrequencies of 1 and 1.5 THz. Equation (16) was usedto fit the data by adjusting only the overall ampli-tude. The incident angle, �, was measured in the THzsetup, and experimentally determined values for �, n,r33�PP�, and dPP were held as constants in the fit.There is good agreement between the frequency am-plitude measurements and their associated fits.

We also compared the IP- and PP-poling geometryfor EO THz sensing. A 1 mm thick ZnTe (110) crystalwas used as the THz emitter. The PP-poled film hada measured thickness of 75 �m and an EO coefficientof r33 � 27.5 pm�V and was placed as a THz sensor atan angle of � � 60°. The IP-poled polymer film was90 �m thick with an average effective EO coefficientof r33 � 12.4 pm�V. According to our theory [Eqs. (16)and (19)], the sensing ratio for the two sensors de-scribed above should be SIP�SPP�� 60°� � 1.3. Ex-perimentally, we are able to measure the ratiobetween 0.4 and 2.4 THz, as limited by the ZnTeemitter. The measured ratios over the detectablerange fall within 15% of the predicted ratio of 1.3(Fig. 7). The THz time domain traces (Fig. 7, lowerinset) have a similar shape for both sensors, indicat-ing that the IP electrodes do not lead to a time inte-gration of the incident THz field [7].

Improvement upon the IP device is possiblethrough several methods. According to our simula-tions, thicker IP electrodes will lead to a more uni-form electric field, translating to more efficient polingof the EO polymer, a higher EO coefficient (r33), andbetter THz sensing. For a 90 �m thick polymer, ourmodel shows that electrodes 30 �m thick would pro-vide a 40% higher average poling field than the cur-rent 3 m thick electrodes, thereby increasing theTHz sensing efficiency by 40%. Also, our current THzexperiment does not allow tight focusing of the probebeam. As a result, 70% of the probe beam intensity is

Fig. 6. (Color online) The amplitude fits above use the full ex-pression for angle-dependent THz sensing of a PP-poled EO poly-mer [Eq. (16)]. The two frequencies reported were simultaneouslyretrieved from Fourier-transformed THz electric field traces.


blocked by the small �100 �m� gap of the IP elec-trodes, resulting in a low probe beam intensity at thedetectors and a decrease in the signal-to-noise ratiofor the IP device. Therefore, it is reasonable to as-sume that a 70% increase in the detected signal ispossible through tighter probe beam focusing.

5. Conclusion

In conclusion, we have studied the application of EOpolymers for THz sensing. Two geometries of polymerpoling, IP and PP, are studied and compared withregard to their sensitivity as EO sensors. Measure-ments and calculations show the optimum sensingangle for a PP-poled EO polymer sensor to be �55°with respect to the incident probe and THz beams.Our modeling of the electric field distribution for anIP-poled polymer concurs with previous studies andthe measured EO values using this model are consis-tent with previously developed poling and measure-ment methods for polymers poled in a sandwichgeometry between two electrodes (PP). The modelalso provides a base for design improvements of theIP device. The current IP-poled polymer film showscomparable THz sensing properties to the PP-poledfilm and has potential for improvement.

We thank Warren Herman at the Laboratory forPhysical Sciences for his assistance in fabrication ofthe IP-poling devices and James Browning of the Bat-telle Corporation for supplying the Lemke dye. Thiswork is partially supported by the National ScienceFoundation Center on Materials and Devices for In-formation Technology Research, DMR-0120967.

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comparison of parallel-plate and in-plane poled polymer ...hayden/pubs/in-plane poling...

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