Resonant gratings in planar Grandjean cholesteric composite liquid crystals

Resonant gratings in planar Grandjean cholestericcomposite liquid crystals

Alexey Denisov* and Jean-Louis de Bougrenet de la TocnayeDepartment of Optics, Ecole Nationale Supérieure des Télécommunications de Bretagne, Unité Mixte de Recherche

CNRS, Foton, CS 83818, 29238 Brest Cedex, France

*Corresponding author: [email protected]

Received 16 March 2007; revised 27 June 2007; accepted 6 July 2007;posted 6 July 2007 (Doc. ID 81055); published 11 September 2007

We propose to induce a two-dimensional (2D) periodic modulation structure into a planar Grandjeancholesteric liquid crystal (CLC) to demonstrate the intrinsic 2D photonic crystal properties of suchmaterials. The structure combines a thin transmission grating and a Bragg reflective grating. Oneadvantage of using CLC is the intrinsic high quality Bragg structure, which can be modulated by anelectric field: shifting the wavelength band edge by changing the applied field. Another interestingproperty is the polarization dependence. The main difference between using CLC Bragg instead of alinear grating is the need to operate with a circularly polarized light, because the CLC modes are circularin such a regime. We present preliminary results obtained with what we believe to be the first switchablephotonic CLC (PCLC) sample, made up of a polymer CLC gel. © 2007 Optical Society of America

OCIS codes: 050.2770, 160.3710, 160.5470.

1. Introduction

Liquid crystal diffraction gratings have potential ad-vantages over conventional holographic gratings in-cluding large optical anisotropies and the ability toswitch between on and off states under low voltages[1]. Bidimensional diffraction gratings based on cho-lesteric liquid crystals (CLCs) have been studied inthe past [2] and more recently [3] exploiting the in-trinsic formation of thin wave gratings induced by anelectric field, to generate diffractive elements. Herewe propose to induce 2D spatial diffraction patternsinto a CLC bulk, in a planar Grandjean configuration,to achieve resonant gratings. Modulations are ob-tained by an electric field applied parallel or perpen-dicular to CLC layers (respectively, for a positive ornegative dielectric anisotropy). The idea is to exploitthe resonance between two structures: 1D Bragg lay-ers of a CLC and the electric field induced 1D trans-mission grating. Under given conditions it is possibleto obtain a resonance between both gratings, so thatthe maximum in transmission for the CLC coincideswith the resonance in transmission of the thin grat-

ing [4]. This structure could be used as an efficientwavelength filter, with a tuning capability, by chang-ing the CLC pitch and period of the modulation in-duced by an electric field.

2. Optical Properties of Cholesteric Liquid Crystals

As a result of the helical structure of the directors, CLCexhibits unique and attractive optical properties, in-cluding strong optical power (more than several thou-sand degrees�mm), and the selective reflection ofcircularly polarized light. This selective reflection is aresult of the spatially periodic variation of the dielec-tric tensor in a helical structure. For light propagatingparallel to the helical axis, Bragg reflection occurs forwavelengths in the following range:

noP � � � neP, (1)

where P is the CLC pitch and ne and no are the prin-cipal refractive indices of the LC medium. In a CLCstructure, the director completes a full 360° turn in adistance of P. The Bragg reflected light is circularlypolarized if the incident wave propagates along thehelical axis. For a right-handed CLC, only the left-handed circularly polarized (LCP) component istransmitted through the medium, whereas the right-

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20 September 2007 � Vol. 46, No. 27 � APPLIED OPTICS 6680

handed circularly polarized (RCP) component is re-flected.

Exact solutions can be given at normal incidence [5](k parallel to the helix axis). For the wavenumber ofthe normal modes denoted k1 and k2 (with k1 � k2), k2is always real for all frequencies. Modes are ellipti-cally polarized with opposite sense and handedness,with polarization ellipses following exactly the twistof the local principal axes. In a RH-CLC medium, thenormal mode ellipticity for k2 varies from linearly tocircularly polarized with a right-handedness, and fork1 from linearly to circularly polarized with a left-handedness. Various regimes occur as a function ofthe frequency. In the range of Eq. (1), k1 becomespurely imaginary. Thus the normal mode correspond-ing to k1 is an evanescent wave that cannot propagatein the medium, and a stop band exists for a RCPbeam in a right-handed CLC medium. In other words,a beam of RCP light is reflected when the frequencydrops into this spectral regime. This is the so-calledBragg regime when total reflection occurs. This isdifferent from the reflection from a metal mirror forwhich the handedness is reversed. In addition, abeam of LCP light propagates unchanged through anRH CLC medium, for all wavelengths in the trans-parent spectral regime.

The reflectance band of a beam of RCP light from aCLC medium has a finite value �k, a function of theoptical anisotropy. This reflectance approaches unityfor large thickness L (see Fig. 1). The reflectancespectrum is an even function with a main peak witha sharp cutoff and sidelobes. The bandwidth �� of themain peak [4] for a CLC medium with �n �� ne, isgiven by

�� nP. (2)

P is the CLC pitch, n is the average index and �n� ne � no. For �n �� ne, the Bragg condition occurs at� � nP.

A. Manufacturing Efficient Bragg Reflectors at 1.55 �m

The first parameter to adjust is the pitch size thatdetermines the spectral band of the Bragg regime (at1.55 �m). The CLC phase is made up of nematic me-sogenic molecules containing a chiral center that re-sults in a helix formation. The pitch can be adjustedby the chemical compound, since CLC can either con-sist of exclusively chiral molecules or of nematic mol-ecules with chiral dopants dispersed throughout. Thedopant concentration is used to adjust the chiralityand thus the pitch. We note that the pitch varies withthe temperature [6]. The second condition is a largepitch number for a good Bragg reflector efficiency.According to the pitch value (close to 1 �m) it resultsin a minimum cell thickness of L � 30 �m. In a basicfabrication protocol, we use ITO (indium tin oxide)coated glass plates, with a uniaxially rubbed poly-amide layer. Then we assemble cells using spacers;after UV curing of the glue, the cell is filled by cap-illarity. As the number of pitches increases, the effectof surface aligning forces becomes less pronounced,and the basic protocol for LC cell fabrication does notyield a good planar CLC structure. The limiting valuein our case was approximately 15 �m.

This phenomenon is emphasized with the applica-tion of an electric field resulting in a rapid growth offocal conic structures. Removing the electric fielddoes not switch the sample into a planar phase. Fig-ure 2 illustrates the measured transmission spec-trum of a sample before the growth of focal conicstructure and after. We notice a decrease in the trans-mitted intensity due to scattering by the focal conic.The homeotropic to planar relaxation is more com-plex and the director can relax in a one-dimensional(mono-domain) conical fashion to a transient planarstate as explained in [7]. Of course, such a transitionmust be avoided.

Fig. 1. CLC typical bandgap and cutoff frequencies for variouspitch numbers.

Fig. 2. 30 �m CLC sample. Spectrum measured in a planar con-figuration before applying voltage, and after the relaxation into afocal conic state. The bottom curve corresponds to the focal conicstate, with reduced transmission due to scattering.

6681 APPLIED OPTICS � Vol. 46, No. 27 � 20 September 2007

A way to prevent focal conic formation when usinglarge cell thickness is to add polymer to stabilize thestructure. However, the polymer network must notmodify the homeotropic state transparency and theconcentration must be optimized. In practice, a smallpolymer concentration allows us to achieve reversiblebehavior with respect to temperature and voltage cy-cles. The effect of stabilization has been obtained fora polymer concentration greater than 5%. Figure 3shows the effect of an applied field on the spectrum ofa stabilized CLC (with a polymer concentration of6%). We notice that the fluctuation is less pro-nounced, as part of the CLC switches into a homeo-tropic state. A voltage saturation occurs where thepolymer network prevents the CLC from reorienta-tion by the electric field. The most important result isthe homeotropic to planar reversibility. After remov-ing the voltage the CLC returns to planar, and nofocal conic appears. We observe a predictable wave-length drift due to director reorientation with thevoltage value.

However, polymer stabilization does not guaranteesystematically high Bragg quality for large thick-nesses, due to nonuniform stresses in the bulk during

the cell filling. Therefore, a heat treatment has beenapplied after filling to improve the quality of the sam-ples. Then we left the cells for approximately two tothree days at room temperature, to enable stress anddefect lines to relax. After relaxation stops, we heatagain for 2 h at a temperature close to the phasetransition. Heating the cell just after the filling didnot provide good results. We assess the quality of thesamples by looking at the intensity of the oscillationsnear the band edge. For nonhomogeneous samples wedo not see any, whereas for homogeneous, they arerather pronounced. The transmission for one of ourbest samples is presented in Fig. 4.

A simple experiment shows the polarization depen-dence of the transmitted light. Figure 5 shows atransmission maximum for an LCP light and a min-imum for the RCP light (with respect to samplechirality handedness). This diagram demonstratesthe propagation behavior of two orthogonal circularlypolarized modes. Changing the polarization of theincoming light by rotating a quarter-wave plate by anangle � creates a polarization mix that depends on �,corresponding directly to the angle in Fig. 5.

B. Dynamic Behavior and Switching Time

The CLC switching time is mainly limited by therelaxation from the homeotropic to the planar phase(� several 100 �s) [7]. It can be improved by increas-ing the polymer concentration, but with an increasein voltage values needed to create efficient modu-lations in the bulk. In practice, we restrict to thelowest possible concentration of polymer due to thelarge thickness of our sample, resulting in a restric-tion of achievable switching times. The measuredswitching times for our samples vary from sample to

Fig. 4. Circularly polarized light transmission for a 30 �m sam-ple. Gray curve, a 7° incidence angle; black curve, a 14° incidenceangle. We observed oscillations near the band edge.

Fig. 3. Polymer stabilized CLC: black curve, no applied voltage;black dashed, with voltage values of about 2 V��m; gray curve, atthe voltage saturation close to 5 V��m.

Fig. 5. Transmission responses of the PSCLC (polymer stabilizedCLC) as a function of the polarization. Each sector correspondsto 10°.


sample, with a value of �30 ms for the on state (ap-plying a voltage) and 400 �s for the off state (remov-ing the voltage). A typical measurement is presentedin Fig. 6. After an electric pulse is applied we see fastswitching into a homeotropic state (rigorously speak-ing it is not a completely homeotropic state, as a partof the CLC fails to follow the electric field due to theorientational forces of the polymer network), andmuch slower relaxation into a planar state (top blackcurve). Measurements have been carried out as fol-lows: the sample has been illuminated with a He–Nelaser, and we measured the intensity variations whenthe voltage is applied, due to enhanced scatteringresulting from a mismatch between the polymer net-work and the CLC orientation at such a wavelength�633 nm�.

3. Two-Dimensional Photonic Crystal Effect

Transmission gratings are useful for various opticalprocessing purposes. However, due to their smallthickness they operate in the Raman–Nath regimewith several diffraction orders, decreasing the effec-tive diffraction efficiency. Moreover, they are notwavelength-selective enough, which limits their ap-plication to telecommunications. The improvement ofwavelength selectivity has been demonstrated [4] bycombining the Bragg operation of a thin transmissiondiffraction grating with a reflection grating, whereboth orthogonal gratings form a 2D photonic crystal,made up of two orthogonal (or quasi-orthogonal) vol-ume gratings.

Diffraction occurs on the thin transmission grating,which has fringes parallel to the (x, z) plane. For agiven direction of incidence (y, z plane), light is at-tenuated at the band-edge wavelength of the Braggmirror, corresponding to the second grating withfringes parallel to the (y, z) plane (Fig. 7). Multiplediffraction orders diffracted by the thin grating arefiltered by the Bragg mirror when phase conditionsare met. As the incidence angles have the same inci-dence for the read and diffracted beams, at the Braggincidence, diffraction is strongly enhanced for thisdiffraction order unlike for other orders diffracted atdifferent angles. This band-edge property of photonic

crystal is at the origin of the Bragg operation on thethin grating. Moreover, as the band edge correspondsto a small wavelength bandwidth only, the diffractionbecomes wavelength-selective. The sinusoidal indexmodulation can be expressed as a function of bothgratings:

n�x, y� � n0 � �nX cos�2�xX

�� nY cos�2�yY

�, (3)

where the first and second terms correspond to thetransmission and reflection gratings, respectively. Inpractice, the reflection grating should have a rela-tively high reflective index modulation to obtain ahigh reflectivity in the bandgap of the thick Braggmirror. When using a CLC, the phenomenon is morecomplex due to the intrinsic induced anisotropy. Therelative index modulation results from the LC bire-fringence modulation �n and does not have the sim-ple form of Eq. (3). This is the first advantage to usinga liquid crystal for implementing photonic crystals,due to their large birefringence modulations. Accord-ing to Section 2, if we are able to generate a reflectiongrating perpendicular to the intrinsic Bragg struc-ture of a CLC, the photonic crystal effect should occurwhen the grating is illuminated with a CLC Braggmode (let us say the RCP).

A. Principle and Dimensioning of a Switchable PCLCDevice

The idea is to exploit the switching capability of CLCmaterials between planar and homeotropic phases tocreate periodically an index modulation in the bulk.Following this principle the grating should enter intoresonance with the intrinsic planar Bragg structureproviding a photonic crystal effect. CLC phase tran-sition is carried out locally and periodically by usingelectrodes etched on the top of the glass substrate(Fig. 8). If no voltage is applied to the electrodestripes, the device is transparent for a circularly po-larized light, whose handedness does not correspondto the CLC helix and reflective for the other, if the

Fig. 6. Measurement of the response time of polymer stabilizedCLC (top curve). The bottom gray curve is the applied voltage.

Fig. 7. Principle of the 2D photonic crystal by a 2D sinusoidalmodulation of the refractive index.


Bragg condition is verified. By applying a voltage tothe electrodes, a perpendicular electric field is gener-ated locally modifying the planar structure by chang-ing the director orientation from planar intohomeotropic. It is extremely difficult to elaborate on arelevant dynamic model describing the director dis-tribution (including polymer network interactions) asa function of the applied field [8], in particular due tothe 2D periodic structure [9]. Our goal is to show that,under certain conditions, a grating resonance is ob-served. Starting from the planar Grandjean case, forwhich propagating modes are well established, wemodify the bulk structure by modulating weakly andperiodically the director orientation to induce a grat-ing. We assume that there is almost no impact on thepropagating modes (perturbation regime), providedthat voltage value, cell thickness, and grating periodare appropriately chosen. Then we will study whathappens in the bulk (by analyzing the propagatingmodes), when the voltage value is increased and thegrating period is changed. This will be achieved bymeasuring the reflection grating diffracted order (in-tensity and polarization state), until the planar Grand-jean structure is completely destroyed in the bulk.

Based on this principle we realized a first PCLCdevice with a 1 �m pitch. The CLC is confined be-tween two glass plates covered by ITO, the gap be-tween the plates is determined by spacers equal toL � 30 �m. On one glass plate, ITO electrodes areetched to provide parallel long stripes with the period�X. The second plate is a single ITO counter elec-trode. The sample is made up of three successivegratings with different periods (X � 8 �m, 15 �m,30 �m). The electrode size is limited to 3 �m, due totechnological constraints, providing three differentduty cycles (0.4, 0.2, 0.1). Periods have been chosenfor various thickness-to-period ratios. For periodsmuch smaller than the thickness we expect that elec-tric fields created by each stripe overlap, distortingthe planar structure and resulting in a weaker indexmodulation depth. As the period increases the over-lap decreases and the index modulation in the bulk is

closer to the ideal case (i.e., a square wave). Oneimprovement we could make would be to create par-allel stripes on the counterplate, so that the electricfield distribution is more uniform. But it is more tech-nologically demanding, and we decided to start withthis simpler case. For a given grating period we cancalculate the Bragg incidence angle �B as

sin B ��R

2nX, (4)

where �R � 1.55 �m is the resonance wavelength andn is the average refractive index. Simultaneously, tofulfill the resonance condition this value should beclose to the CLC reflection band edge, which deter-mines the pitch value according to Eq. (1). In practice,this value should be finely adjusted by changing thechemical composition of the CLC mixture to satisfythe resonance condition. Estimates according to [10]gave us the following values for the parameters ofinterest: P � 1 �m and B � 1° � 4° depending on thegrating period. We neglect here the error arising fromthe nonsinusoidal variation of modulation of the re-fractive index, as well as the issues that may arise ifwe take into account the polarization dependence ofthe CLC Bragg reflection.

Another critical point is the difference betweenthick and thin gratings. When the sample thicknessis comparable with the grating period, the gratingoperates in the Bragg regime (thick grating) other-wise in the Raman–Nath (thin grating). For�R��nX� �� 1, the ratio of intensity diffracted intothe �1 order with respect to the one diffracted intothe 1 order is given by

I�1

I�1� sin c2��RL

nX2 �, (5)

and the Q parameter gives the transition betweenthin and thick grating regimes [10]:

Q ��RL

nX2 . (6)

In practice, one can consider that for Q � 10 the grat-ing works in the Bragg regime, whereas for Q � 1 inthe Raman–Nath one. With our achievable gratingperiods we obtain Q � 1.4, 0.4, 0.1, for the gratingperiods X � 8 �m, 15 �m, 30 �m. Therefore, we seethat none of our gratings strictly verifies the thickgrating condition. A suitable period should be 3 �m,which was technically difficult to achieve with ourfacilities. However, for all the gratings (in particularfor the smallest one) we expect to observe resonanceeffects due to the existence of an in-bulk Bragg struc-ture, resulting in an improvement of the wavelengthselectivity, compared, for instance, with a pure liquidcrystal grating obtained with the same conditions.

4. Experimental Results

Our CLC sample is a Merck MDA-00-1444 host, andMDA-00-1445 cholesteric mixture, with an ordinary

Fig. 8. Principle of the switchable PCLC device.


index of 1.5 and an extraordinary of 1.68 (valuesprovided by Merck in the visible). The chemical com-position was finely tuned by changing the respectivepercentages. The value we used was close to 30% ofMDA-00-1445 and 70% of MDA-00-1444. For stabili-zation we used polymer RMD-257 (also from Merck),a photoreactive nematic compound with a concentra-tion of 5%. The experimental setup (Fig. 9) allowsmeasurements at different incidence angles and ar-bitrary incident light polarizations. Whereas findinga spectral response at arbitrary angles, i.e., �, �, andinput polarization are free parameters. More specif-ically, we use a tunable laser Tunics-BT with a tun-ing range of 1500–1620 nm. Polarizer and analyzerare made up of a broadband polarizer and a quarter-wave plate that are achromatic in the consideredrange. Quarter-wave plates can rotate providing var-ious input polarizations, and selecting via the outputanalyzer various output polarization states. The spotsize of the incoming light is �1 mm. According tothese parameters a reconfigurable PCLC has beenrealized. As mentioned here, a proof of concept can begiven by measuring the induced reflection gratingdiffracted order (efficiency and polarization state),starting from a planar Grandjean structure, by in-creasing the voltage value and�or decreasing thegrating period, until the Bragg structure is com-pletely destroyed. When a grating is induced in theBragg structure, via etched electrodes, diffraction or-ders appear. To explain the experimental results wehave made simple qualitative assumptions, based oninteractions between grating periods, applied volt-ages, and observed diffraction spectra. We assumethat only RCP light interacts with the CLC Bragggrating, stressing the fact that this phenomenon isdominating (i.e., for the RCP light we observe theresonance spectrum similar to the one predicted forthe sinusoidal modulation case). The modulationscreated by the electric field have two main effects: tocreate diffraction gratings and distort the CLC pla-nar structure, stressing competing effects. When weincrease the electric field, the index modulation in-creases and results in an increase of the diffractionefficiency due to the linear grating, while the CLCBragg grating efficiency decreases simultaneouslydue to the induced distortions.

The first assumption is verified directly by look-ing at the transmission spectrum for RCP and LCPlights (Fig. 10). We see a clear distinction betweenRCP and LCP modes. For LCP we do not see anyeffect on the CLC Bragg grating and only diffractiondue to periodic grating takes place. The higher the

applied field the higher the intensity of diffrac-tion.

Second and third assumptions are verified by look-ing at the transmission spectrum shape, similar toones observed in the 2D sinusoidal modulation case.The spectrum changes as a function of different grat-ing periods and�or voltage values. For RCP we ob-serve the resonance that depends on the applied fieldand grating period. Figure 11 shows the voltage de-pendence and Fig. 12 the grating period one. It goesbeyond a simple filtering effect, where we would justsee the imprint of the transmitted spectrum. Wewould expect the diffraction efficiency at the bandedge to be smaller or equal that far from the bandedge (see Fig. 4). Experiments confirm the interactionbetween the gratings similar to the one we expect inthe 2D periodic sinusoidal modulation described ear-lier.

Fig. 9. Schematic of the measurement setup.

Fig. 10. First diffracted order spectrum (30 �m grating period).Bottom two curves for low applied voltages: 0.25 V��m and or-thogonal polarizations RCP and LCP (no change in intensity forLCP). Top two curves for larger applied voltage 2 V��m, and or-thogonal polarizations RCP and LCP (once again for LCP, no vis-ible wavelength dependence, apart from the random noise).

Fig. 11. Diffracted order spectra, (30 �m grating period). Appliedvoltage changes: from bottom to top (following the left part of thefigure): 0.25 V��m, 1 V��m, 5 V��m, 3 V��m.


We observe a transformation of the spectrum shape,as the voltage increases: the first maximum disap-pears and the second becomes more prominent as weincrease the voltage, until the structure disappears(gray curve). The gray (3rd) curve corresponding to thelargest applied voltage has a lower intensity due to theprobable increase in scattering losses. We observe thatthe resonance spectrum shape deteriorates when volt-age increases. The first visible resonance peak at 1605nm for the lowest applied voltage disappears as thevoltage increases.

In conclusion, for low voltages the spectrum has aresonant shape (Fig. 11), but weak diffraction effi-ciency, corresponding to small index modulation. Inthis case, the modulation does not impact the CLCplanar structure (sharp spectrum shape). When weincrease the applied voltage, diffraction efficiency in-creases and the resonance spectrum shape deterio-rates. Both effects are obviously linked to planar CLCstructure changes due to the electric field. By increas-ing the applied voltage even further we modify sig-nificantly the planar Grandjean structure in the bulkand the resonance no longer exists. It is worth men-tioning that the CLC Bragg structure is still pre-served (we observe polarization dependence withrespect to RCP and LCP modes) due to polymer sta-bilization but with an observable increase in the scat-tering and therefore a reduction of the transmission.

We observe the resonance peak contrast get worseas the grating period decreases. If we compare grat-ings with different periods (Fig. 12), we should expecta similar role for the modulation intensity, spectrumshape, and diffraction efficiency. Fixing the voltageand taking the transmission spectrum for the threegratings we expect a better contrast for the gratingwith the largest period, as the CLC planar structureis less distorted due to greater spacing between theelectrodes and thus a better formation of the Grand-jean structure within the CLC bulk. This is confirmedby Fig. 12.

More generally, the polarization dependence can beobserved for the diffracted orders (�1 and �1) for thethree gratings (Fig. 13). Such a pattern can be easilyexplained assuming that for a chosen wavelength weare in the reflecting CLC band. Then for a polariza-tion corresponding to the CLC reflection (here RCP)we expect that light is fully reflected and there is nodiffraction, whereas for the opposite polarization(LCP) the CLC Bragg grating does not operate andwe see the diffraction. When the measured wave-length is outside the CLC reflection range we do notobserve any polarization dependence for the diffrac-tion orders, i.e., the intensity is constant regardless ofpolarization and only a thin grating operates.

Although gratings exhibit the same behavior withrespect to polarization dependence, significant differ-ences appear. Diffracted intensities, for the same ap-plied voltages, are different for each grating. Thesmaller the period, the lower the intensity. This isdue to a smaller effective modulation for small periodgratings, due to electric field overlap. This is con-firmed by the presence of higher orders for large pe-riod gratings. For instance, for the same appliedvoltage �1.5 V��m�, we observe two diffracted ordersfor the 8 �m grating (with 13 �W in �1 order), fourorders for 15 �m (with 29 �W in �1 order), and morethan six for 30 �m (with 59 �W in �1 order).

This emphasizes the link between grating periodand thickness. Several effects interfere at the sametime. Assuming the same cell thickness and appliedvoltage for all gratings, we confirm that gratings withlarger periods have better modulation depth andhence higher diffraction efficiency. Better modulationis probably due to a smaller overlap of the appliedelectric field. Another effect is the change in modula-tion profiles. For the smallest period grating, the dutycycle is 0.4, resulting in a modulation close to a sine

Fig. 12. Diffracted order spectra for PCLC with different gratingperiods and the same applied voltage �0.25 V��m�. Thin blackcurve (first sharp peak is not fully shown) corresponds to 30 �mgrating, thick black curve to the 15 �m and thick gray curvecorresponds to the 8 �m.

Fig. 13. Diffracted order polarization dependence: Gray curve��1�, black ��1�. Input polarizations vary from LHC (sector 2) to aRHC (sector 6). Each sector corresponds to 20°.


shape, whereas for the largest period grating, theduty cycle is 0.1, and the modulation is rather square-like. The change in profile results in an increase in adiffraction order number (when no Bragg filteringoccurs), according to the modulation type. Finally, itis worth mentioning the change in the Q factor, whichpartially accounts for the weak intensity of high dif-fraction orders, for small period gratings. We shouldmention that higher diffraction orders exist but havevery low intensity due to the small modulation depth.In contrast, we clearly see a resonance effect near theCLC band edge. Diffraction intensity is clearly higherthan in areas far from the band edge, where the CLCBragg grating does not operate.

Device reconfigurability can be obtained more gen-erally by moving resonance conditions and changingboth the Bragg and the thin grating periods, withoutmodifying the wavelength and the incident beam an-gle. This is theoretically possible by varying the pe-riod and the applied voltage values independently. A2D spatial distribution of the electric field can begenerated in the bulk to modify these parametersindependently providing a more appropriate elec-trode implementation (thick electrodes for instance).

5. Discussion

PCLC-based devices present decisive advantagesover other existing solutions, to implement switch-able photonic crystals or wavelength tunable filters.Their large index modulation under reasonable volt-age and their reconfigurability give rise to variousinteresting applications [11–13]. Their main limita-tion is due to the optimization of the in-bulk modu-lation and Bragg mirror quality (related to planarstructure homogeneity) that imposes, for some wave-length ranges, large thicknesses. This results in con-straints on period choice to guarantee a good 2Dgrating formation in the bulk without too complextechnological achievements. In this preliminarywork, we have given a proof of concept and shown theinterest of polymer stabilization combined with con-ventional surface electrode addressing to providephotonic liquid crystals. We have demonstrated grat-ing resonances and in particular the improvement ofthe wavelength selectivity of a thin diffraction grat-ing. We have shown some degree of reconfigurabilityprovided by voltage modulation and the specific in-terest of PCLC due to the use of polarization as acontrol parameter to switch from a thin to a thickgrating. A complete dynamic modeling of the bulkstructure, as a function of the applied voltage, re-mains extremely difficult. We have proposed an un-derstanding of the phenomenon on a qualitativelevel, through the interaction between the modula-tion created by the electric field and the distortion of

the planar CLC structure, which has been confirmedby measurements. In particular, we observed detailsthat will require further investigations (e.g., sidelobeenergy transfer), but at this stage we were mainlyconcerned with a proof of concept of the grating res-onance. However, it is clear that for practical appli-cations a lot of parameters should be improved (e.g.,etched electrodes on the counterplate). For such pur-poses, a theoretical model would be highly useful.

The authors thank K. Heggarty, B. Caillaud, andB. Vinouze for technical assistance in manufacturingPCLC devices, and L. Dupont for valuable discus-sions about the application.

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Resonant gratings in planar Grandjean cholesteric composite liquid crystals