Competing photorefractive gratings in organic thin-film devices

$: Competing photorefractive gratings in organic thin-film devices$
2114 J. Opt. Soc. Am. B/Vol. 15, No. 7 /July 1998 Meerholz et al.

Competing photorefractive gratings in organicthin-film devices

Klaus Meerholz, Erwin Mecher, Reinhard Bittner, and Yessica De Nardin

Department of Physical Chemistry, University of Munich, Sophienstrasse 11, D-80333 Munich, Germany

Received September 25, 1997; revised manuscript received February 3, 1998

Recently, amorphous organic photorefractive materials have generated great excitement because of their ex-cellent performance, which permits applications in high-density holographic storage, real-time image process-ing, and phase conjugation. However, the heterostructure of the devices (consisting of glass cover slides,transparent electrodes, and the photorefractive material) and the tilted recording and readout geometry com-monly used result in multiple reflected beams in addition to the normal object and reference beams. Thisresult leads to several photorefractive gratings competing inside the photorefractive polymer device. Weprove the coexistence of these gratings by two-beam coupling and four-wave mixing experiments and demon-strate how to distinguish between them. © 1998 Optical Society of America [S0740-3224(98)04207-6]

OCIS codes: 090.0090, 260.0260, 160.5320, 160.4670, 160.5470.

1. INTRODUCTIONFor more than three decades, photorefractive (PR) mate-rials have attracted a great deal of attention because theyshow promise for holographic applications.1 Photorefrac-tivity in amorphous organic systems, first discovered in apolymer 1991,2 became a rapidly growing field of researchbecause of the excellent performance of this new materialclass, including complete absorption-limited diffractionand large net gain.3,4 In addition to that in polymers,photorefractivity was also discovered in liquid crystals5,6

and in glass-forming low-molecular-weight multifunc-tional compounds.4,7,8 The performance of the latest PRorganic noncrystalline materials competes and in somecases even surpasses the performance of traditional inor-ganic PR crystals.9–12 Potential photonic applications,including dynamic holographic storage,13,14 real-time im-age processing,14,15 and self-pumped phase conjugation,16

have been successfully demonstrated. Their low manu-facturing cost and the excellent reproducibility may per-mit the first widespread use of PR materials in practicalapplications.12

The PR effect is a special holographic recording mecha-nism in which nonuniform illumination leads to the for-mation of a spatially modulated space-charge field, whichin turn modulates the index of refraction of the PR mate-rial. The important feature of the PR effect as opposed toall other holographic recording mechanisms is that the re-corded index grating is phase shifted with respect to thelight-intensity pattern, which is formed by interference oftwo coherent laser beams. This phase shift allows for en-ergy transfer (two-beam coupling) between the writingbeams as a result of dynamic self-diffraction processes.1

The design principles for amorphous organic PR mate-rials have been described in detail previously.9–12 PRmaterials require a combination of several properties:photosensitivity to generate charge carriers, photoconduc-tivity for charge transport, charge trapping, and, finally,an electric-field-dependent refractive index, e.g., by the

0740-3224/98/072114-11$15.00 ©

electro-optical (EO) effect, such as in traditional inorganicPR crystals. Generally one achieves the required proper-ties by combining appropriate functional moieties in anamorphous matrix. One typically fabricates PR deviceson the basis of noncrystalline organic PR materials bysandwiching the PR material between two transparentindium tin oxide (ITO) electrodes to apply an electricfield. This procedure is necessary to break inversionsymmetry in the material to enable one to observe the PReffect by aligning the dipolar EO chromophores, but at thesame time the field also enhances the efficiency of charge-carrier generation and supports charge transport. Align-ment of the chromophores is possible at room tempera-ture because of the rather low glass-transitiontemperature Tg of the composites, providing sufficient ro-tational mobility for the chromophores. As a result of thein situ poling process, the PR properties of noncrystallineorganic PR materials are strongly field dependent, and,most importantly, the index changes originate predomi-nantly from a birefringence contribution that is due to the‘‘orientational enhancement mechanism,’’ 17 unlike in in-organic crystalline materials.

2. OBJECTIVE/PROBLEMHolographic experiments with the devices describedabove are typically performed in a tilted geometry (tiltangle C, defined by the sample normal and the bisectorbetween the write beams, clockwise) to achieve a nonva-nishing projection of the external electric field onto grat-ing wave vector K for carrier migration [Fig. 1(a)]. It hasnot been specifically considered in the literature, so far,that this geometry produces several reflections of the twowriting beams, 10 and 20, respectively, upon the differ-ent optical interfaces of the multilayer heterostructure ofsuch devices (air–glass–ITO–organic layer–ITO–glass–air), as illustrated in Fig. 1(b). Of the six reflections,three occur before the beams actually enter the organiclayer; thus they just reduce the intensity to be considered

1998 Optical Society of America

Meerholz et al. Vol. 15, No. 7 /July 1998 /J. Opt. Soc. Am. B 2115

Fig. 1. (a) Experimental geometry. D’s are detectors. The ro-man numbers mark cases discussed in the text [Eqs. (2)–(5)].(b) Illustration of the multiple reflections for one writing beam inthe multilayer PR polymer device: The interfaces are numbered(1–6) from top to bottom. Black rectangles symbolize an irisdiaphragm. Circles mark contributions relevant for evaluationof the data (see text and Table 1).

for accurate determination of the contrast factor m [Eq.(1) below] of the interference pattern (Table 1).

By contrast, the remaining three reflections may reen-ter the PR polymer layer and cross in the same volumesection of the active PR layer, since the beam diameter(0.5–2 mm) is generally much larger than the thickness ofthe active layer ('100 mm). As a result, the reflectedbeams may interact with one another and also with theprimary beams, leading to competition of numerous PRgratings inside the organic thin layer. By using thickglass slides one can prohibit external reflection 6 from re-entering the active layer. Furthermore, reflections 4 and5 at the polymer–ITO–glass interfaces can be combinedinto one, with the inference of the two components takeninto account. Thus only two secondary beams, 10* and20* , respectively, play a significant role in grating com-petition. For the sake of simplicity we do not considermultiple reflections of the same beam at the different in-terfaces. This assumption is justified because after a fewreflections (see Table 1) the remaining intensities becomenegligibly small.

To distinguish among gratings, we use the notation$a, b%, where a and b are the writing beams that define aparticular grating. The linear combination of four beams(two primary, two secondary) gives rise to possibly six dif-ferent gratings, as illustrated in Fig. 2. Two aretransmission-type gratings, $10, 20% and $10* , 20* %,respectively, and possess an identical grating period L(the beams propagate in the same general direction withrespect to the optical axis; in poled polymers the opticalaxis is defined by the externally applied field, i.e., the zdirection). Note, however, that the gratings have oppo-site tilt angles, C$10,20% 5 2C$10* ,20* % , which meansthat the corresponding gain coefficients have oppositesigns. The $10, 20% grating is typically the only onethat has been considered in the literature on thin-film or-ganic PR devices so far. The other four possible gratings

Table 1. Calculation of Relevant Beam Intensities for l 5 690 nm and l 5 633 nma

Beam Intensity or Reflectivity 10/10* , s Polarized 20/20* , s Polarized 10/10* , p Polarized 20/20* , p Polarized

l 5 690 nmA690 Iout

0(60) @mW# 6 10 810 1120 1500 1500B690 R1 –3(dITO 5 150 nm) 6 0.01 0.85 0.66 0.98 0.95C690 I in

0(60) @mW# 6 10 690 740 1470 1420D690 R4,5(dITO 5 150 nm) 6 0.01 0.027 0.046 0.011 0.009E690 I in

0(60* ) @mW# 6 1 15 27 13 10

l 5 633 nmA633 Iout

0(60) @mW# 6 10 140 200 130 170B633 R1 –3(dITO 5 150 nm) 6 0.01 0.85 0.66 0.98 0.95C633 I in

0(60) @mW# 6 10 120 130 130 170D633 R4,5(dITO 5 150 nm) 6 0.01 0.011 0.023 0.004 0.004E633 I in

0(60* ) @mW# 6 1 1 3 0.5 0.7F633 R4,5(dITO 5 80 nm) 6 0.01 0.103 0.129 – –G633 I in

0(60* ) @mW# 6 1 13 17 – –

a A, Initial light intensity Iout0(60) measured outside the device. B, reflectance R1 –3 of the air–glass–ITO–polymer interfaces calculated from Snell’s

and Fresnel’s laws and the measured refractive indices. The interference of reflections 2 and 3 was taken into account. C, intensity of light I in0(60)

entering the PR polymer layer calculated from R1 –3 and Iout0(60). D, F, calculated reflectance R4,5 of the polymer–ITO–glass interface, with the inter-

ference of reflections 4 and 5 taken into account. E, G, initial intensity of the reflected beams I in0(60* ) calculated from R4,5 and I in

0. Rows C, D andE, F are for ITO thicknesses of 150 and 80 nm, respectively, for the second contact electrode; the first contact had an ITO thickness of 150 nm in all cases[cf. Fig. 1(b)]. The bold-face numbers are those used for evaluation of the data.


Table 2. Tilt Angles Ci Calculated from the External Angles from Snell’s Law and the MeasuredRefractive Index; Grating Periods Li 5 l/(2n)sin(ay 2 ax) Calculated from the Internal Angles;

Grating Contrast Factors a mi for E 5 0 V/mm Calculated According to Eq. (1); and Light Intensity b

Ii 5 (Ix 1 Iy) for the Six Coexisting PR Gratings c

Grating i $x, y% C i [deg] 60.05 L i [mm] 60.005 mi (s) 60.005 Ii (s) [mW] 61 mi ( p) 60.005 Ii ( p) [mW] 61

l 5 690 nm$10, 20% 30.2 3.42 1.00 1430 1.00 2890$10* , 20* % 230.2 3.42 0.96 42 0.99 23$10, 10* % 90.0 0.23 0.29 705 0.9 1482$20, 20* % 90.0 0.24 0.37 767 0.085 1452$10, 20* % 86.6 0.235 0.38 717 0.085 1480$20, 10* % 286.6 0.235 0.28 755 0.09 1432

l 5 633 nm$10, 20% 29.8 3.15 1.00 (1.00) 250 (250) 1.00 300$10* , 20* % 229.8 3.15 0.92 (0.99) 4 (30) 0.98 1$10, 10* % 90.0 0.21 0.19 (0.58) 121 (133) 0.055 131$20, 20* % 90.0 0.22 0.27 (0.64) 133 (147) 0.055 171$10, 20* % 86.6 0.215 0.28 (0.66) 123 (137) 0.055 131$20, 10* % 286.6 0.215 0.18 (0.57) 131 (143) 0.055 171

a Note that the contrast factors m of all gratings (except for the $10, 20% grating) are field dependent (see, for example, Fig. 8 below).b See Table 1 for details.c All values are given for inside the material; dITO 5 150 nm at l 5 690 nm and dITO 5 80 nm at l5633 nm.

are reflection-type gratings; i.e., the two beams propagatein opposite z directions. Two of those gratings,$10, 20* % and $20, 10* %, are a result of the interactionof each of the primary beams with the corresponding re-flected beam. Finally, the remaining two possibilities re-sult from the interaction of one of the primary beams withthe reflected beam of the other: $10, 20% and$20, 10* %. Both gratings possess an identical period Lbut opposite tilt angles, C$10,20* % 5 2C$20,10* % , and thusgain coefficients with opposite sign.

From the general Kukhtarev model, which was devel-oped to describe photorefractivity in inorganic crystals,18

the following equation was derived for the space-chargefield ESC of an $a, b% grating in a PR polymer at fieldshigh enough that the dislocation of charge carriers isdominated by migration and diffusion vanishes (E. 105 V/cm) (Ref. 14):

ESC 5 ms M~I !E0 sin C

1 1 ~iE0 sin C!/Eqexp@i~Kabr 1 j!# 1 c.c.,

(1)

with

m 5 C2@IaIb#1/2

Ia 1 Ib, Eq }

4peNA

uKabuee0, uKabu 5

2p

Lab.

Here m (<1) is the contrast factor of the sinusoidal lightinterference pattern, C 5 1 for s-polarized light, and C5 cos(aa 2 ab) for p-polarized light. E0 sin C is the pro-jection of the external field onto the unit grating vectors [ Kab /uKabu; M(I) is a coefficient that accounts for thecarrier balance in the material and contains, among otherparameters, the photogeneration efficiency s(I) and therecombination rates (see Ref. 14 for details); I 5 Ia1 Ib is the total incident light intensity; e is the elemen-tary charge; NA is the trap density; e is the dielectric con-

stant of the medium; e0 is the permittivity constant; r isthe radius vector; j is the phase difference between thewriting waves; and i is the imaginary unit.

Fig. 2. Six different PR gratings resulting from the linear com-bination of the two primary beams, 10 and 20, and two second-ary beams, 10* and 20* . Thin dotted lines, the x and z direc-tions of the sample; thin dashed lines, bisectors of the beams thatdefine gratings.


The following four factors thus determine the strengthof space-charge field ESC:

(i) Grating spacing Lab ; it follows from Eq. (1) thatwith decreasing Lab (increasing uKabu) the saturation fieldEq becomes smaller, thus rendering the denominatorlarge and reducing ESC . That this is so was confirmedby four-wave mixing experiments in the transmission ge-ometry on a similar PR composite.11

(ii) Contrast factor m; ESC was experimentally foundto increase linearly with m.14 Note that the contrast fac-tors of all gratings, except for the $10, 20% grating, arefield dependent since the reflected intensities are depen-dent on the amount of energy transfer (see, for example,Fig. 8 below).

(iii) Tilt angle C, which determines the projection ofthe external electric field (optical axis) onto the gratingwave vector Kab (E0 sin C); i.e., from the perspective ofcharge generation the tilt should ideally be C 5 90°.9

Note, however, that because of the orientational enhance-ment effect17 a tilt angle different from 90° is beneficialfor optimizing Dn.

(iv) Light intensity I, which is a result of the intensitydependence of the charge generation efficiency containedin M(I). This property is unlike that in inorganic PRcrystals, for which the steady-state performance is gener-ally independent of the light intensity.18

Even though the model developed in Ref. 14 can ex-plain the experimental results qualitatively, a quantita-tive calculation of the relative grating strengths is notpossible at this time because the field-dependent charge-carrier generation efficiency and transport properties arenot known.

For I10 ' I20 [the case studied here experimentally(see Table 1)], one would expect the two transmissiongratings to be the strongest (largest space-charge fieldand, thus, largest index modulation amplitude Dn) be-cause they possess the largest grating period L i of the sixpossible gratings and the contrast factor m is close to theoptimum value 1 for moderate external fields (Table 2).The $10, 20% grating should be stronger than the$10* , 20* % grating because of the reduced light intensityof the reflected beams, with the intensity dependence ofDn taken into account.14 The four reflection gratingsshould all be quite similar in amplitude since the gratingspacings, tilt angles, and contrast factors are similar.They are expected to have reduced Dn compared with thetransmission gratings because of their smaller grating pe-riods and reduced contrast factors (Table 2).

In this paper we verify the existence of the five addi-tional gratings, investigate their interaction, and clarifythe consequences on the PR performance of organic de-vices. Note, however, that the occurrence of non-Braggdiffraction,19 higher-order gratings,17 and beamfanning,20–22 complicates a quantitative discussion. Be-cause of the relatively small thickness of our devices('100 mm) and the large index modulation amplitudesthat can be achieved (Dn . 1023), the Bragg diffractionorders (defined by the write beams) are accompanied byhigher diffraction orders, the so-called non-Bragg orders(they are distinctively different from higher-order diffrac-tion in the Raman–Nath regime).19 These orders are ob-

served in four-wave mixing as well as in self-diffractionexperiments. Because of the occurrence of these non-Bragg diffracted beams (61, 62, etc.), further gratingscaused by the interaction between the higher-order beamsand the 60* beams may have to be considered. Sincethe non-Bragg diffracted beams reach intensities similarto those of the 60* beams only for fields larger thanuEu ' 60 (90) V/mm for s- ( p-) polarized light, perturba-tions that stem from them will become important only forhigher fields. The higher-order diffracted beams (62,63, etc.) can be completely neglected because their inten-sity is so small. The situation is even more complicatedby the fact that, in addition to each $a, b% grating(Lab , Kab) discussed so far, there is always an additionalgrating with half the grating period (Lab/2, 2Kab). Thepresence of these additional gratings is a result of the insitu poling process and cannot be avoided whenever theorientational enhancement mechanism is operative.17

The index modulation amplitude of the 2K gratings,Dn2K , was found to be of the same order of magnitude asfor the fundamental K gratings.17 Finally, it was re-cently demonstrated that light scattered in the polymerlayer can be coherently amplified by the pump beams(beam fanning).20–22 As a result of the fanning, the lightguided in the polymer layer finally exits on the side of thedevice for one field direction, whereas for the other thefanning leads to splitting of the primary beams.22 Theimplications of fanning can be neglected for uEu , 60 (45)V/mm for s- ( p)-polarized light and the field directionwhere no waveguiding occurs (E . 0 for s polarizationand E , 0 for p polarization). For these reasons, anyquantitative discussion must be limited to uEu , 45 V/mm. The convention for the direction of the electric fieldwas defined such that for positive fields the anode facesthe writing beams.

3. EXPERIMENTThe PR polymer composite studied here consisted of theEO chromophore 2,5-dimethyl-4-(p-nitrophenylazo)ani-sole (DMNPAA; 50 wt. %), the photoconducting polymerpoly(N-vinylcarbazole) (PVK; 42 wt. %), the plasticizerN-ethylcarbazole (ECZ; 7 wt. %), and a small amount of2,4,7-trinitro-9-fluorenone (TNF; 1 wt. %). The glass-transition temperature of the composite was determinedby differential scanning calorimetry to be Tg 5 19 °C.The refractive index was determined at 633 (690) nm tobe n 5 1.72 (1.70) 6 0.01. We prepared the devices bysandwiching the composite between ITO-coated BK-7glass slides (thickness, 4 mm; n 5 1.5) at an elevatedtemperature ('160 °C). The active layer thickness wasadjusted by 105-mm spacer beads. Details of the samplepreparation procedure have been described previously.3,14

Unless stated differently, the thickness of the ITO was150 6 5 nm as measured by a Dectac-3 profilometer.The refractive index of ITO was determined to be n' 2.0. Devices of this polymer showed unchanged per-formance for at least 3 months.

The experiments were carried out in the typical tiltedgeometry mentioned above [Fig. 1(a)]. Two equally po-larized coherent writing beams, 10 and 20, originatingfrom either a laser diode (Melles Griot; 25-mW nominal


output power, l 5 690 nm) or a He–Ne laser (MellesGriot; 10 mW, l 5 633 nm) were incident upon thesample at angles a10,ext 5 50° and a20,ext 5 70°, respec-tively. The beams had a diameter of approximately 2mm at normal incidence and could be individuallyswitched on or off by mechanical shutters. Using Snell’slaw, we calculated the internal angles as a10,int 5 26.8°(26.4°) and a20,int 5 33.6° (33.1°) for 690 (633) nm.Table 1 lists the incident and internally reflected intensi-ties for the two beams, calculated with Fresnel’s law andthe refractive indices given above. The individual tiltangles C i , grating periods L i , contrast factors mi , andillumination intensities Ii for the six competing gratingsresulting from this geometry are listed in Table 2 (valuesare given for inside the material).

For the beam-coupling experiments, which were per-formed at l 5 690 nm, the powers of the transmittedpump beams and the reflected beams were simulta-neously monitored by four photodiodes [Fig. 1(a)] as afunction of the applied electric field. Whereas the detec-tion of the transmitted intensities I60 is experimentallystraightforward, for the measurement of the reflected in-tensities I60* the insignificant reflections had to be cut offby iris diaphragms, and only the 60* beams were allowedon the photodetector [Fig. 1(b)]. The experimentallymeasured intensities corresponded well to the calculatedones (Table 2) if multiple reflections are disregarded.The normal field-dependent gain coefficient G$10,20%(E),which describes the energy transfer between the 10 andthe 20 beams, is defined as

G$10,20%~E ! 51d H cos a10 lnF I10~E, II!

I10~E 5 0, II!G2 cos a20 lnF I20~E, II!

I20~E 5 0, II!G J . (2)

Here I(E, II) are the intensities of the beams for an ap-plied electric field E measured on the rear side facingaway from the primary beams, and d is the sample thick-ness. One of the mirrors in the path of the beam 10 wasmounted upon a piezo actuator, which allowed us to de-termine the phase shift f between the light and the indexgrating by the moving-grating technique.23 The actua-tors’s response time was of the order of 1 ms, much fasterthan the response time of the material (t ' 10 s).

Degenerate four-wave mixing experiments were car-ried out in the same geometry at two wavelengths (l5 633 nm and l 5 690 nm) with s-polarized writingbeams and a p-polarized reading beam with reduced in-tensity (IR ' 1 mW). The reading beam was counter-propagating either with the 10 beam, which is the com-monly used (normal) geometry for four-wave mixingexperiments on organic PR devices, or with the 10*beam. We shall refer to the latter readout geometryhereafter as ‘‘crossed geometry.’’ In all cases the appliedfield polarity was negative. It is important to note at thispoint that for both readout geometries three gratings areprobed simultaneously, since they all fulfill the Braggcondition. In the normal readout geometry diffractionoccurs not only from the usually considered $10, 20%grating but also from the $10, 10* % and $10, 20* % grat-

ings (Fig. 2). Similarly, in the crossed geometry the$10* , 20* %, $10, 10* %, and $20, 10* % gratings areprobed at the same time. Therefore, unlike in previousstudies, we used four instead of only two detectors to mea-sure the transmitted probe intensity and the three dif-fracted signals as a function of the applied field. The dif-fraction efficiency of each grating is defined as thecorresponding diffracted light intensity, divided by the in-cident intensity of the readout beam. Note that the situ-ation is further complicated by the possibility of cascadeddiffraction processes; i.e., consecutive diffraction can oc-cur on several gratings.

4. RESULTS AND DISCUSSIONA. Beam-Coupling Experiments with One BeamWe start this section by presenting the results of beamcoupling that was performed at 690 nm only. First, twoexperiments with either of the pump beams incident uponthe sample were performed (one-beam experiments; Fig.3). This allowed us to study gratings $10/10* % and$20/20* % separately from all other possible gratings.For both beams and both polarizations except the 20*beam for p polarization, the reflected beams gain energyat the expense of the primary beams for increasing nega-tive fields, reach a maximum, and finally are reducedagain for the highest fields. We must conclude from thisresult that the index modulations of these reflection grat-ings sensed by the two polarizations have identical signs,unlike for the normal $10,20% grating (see also Fig. 6below).3 This result can be explained by the orienta-tional enhancement model,17 as is shown below. By con-trast, for positive fields the strong primary beams arepumped by the weak secondary beams. The change inenergy transfer direction when the field polarity ischanged is due to the reversed direction of charge-carriermigration. These results unambiguously prove the inde-pendent existence of the two gratings $10/10* % and$20/20* %, respectively, each exhibiting individual beamcoupling. The strong losses in the primary beam inten-sities observed for higher fields (filled symbols, Fig. 3) area result of the above-mentioned beam fanning.20–22

Since the phase relation between the primary and thesecondary beams is constant in the case of internal reflec-tion, these gratings are absolutely insensitive to any per-turbation outside the device. A straightforward determi-nation of the phase shift f between the light and theindex grating in a one-beam experiment is therefore notpossible. Instead, f was measured in a separate two-beam experiment in the reflection geometry(a1 5 2a2).24 The moving-grating technique23 thenyielded f ' 80–90° at uEu 5 45 V/mm, in agreement withearlier results.24 This result was obtained for both polar-izations and independently of the angle of incidence forthe range 20° , a1,ext , 70°. At this rather low fieldvalue the gain is still small enough, and no complicationsare expected in the determination of the phase shift, aswas discussed recently.25

The field-dependent PR gain coefficient G$60,60* %(E) forsuch reflection gratings (referred to hereafter as reflectiongain) was calculated in analogy to Eq. (2):


G$60,60* %~E ! 51d H cos a60 lnF I60~E, II!

I60~E 5 0, II!G2 cos a60* lnF I60* ~E, I!

I60* ~E 5 0, I!G J . (3)

The intensities of the beams are measured either on theside facing the primary beams (labeled I) or on the oppo-site side (labeled II). Since the initial intensity of thesecondary beams 60* at the polymer–ITO interface de-pends on the intensity changes of the primary beams 60,we replaced I60* (E 5 0, I) by AI60(E, II), yielding

G$60,60* %~E ! 5cos a60

d H lnF I60~E, II!

I60~E 5 0, II!G2 lnF I60* ~E, I!

AI60~E, II!G J . (4)

A is a factor that takes into account the intensity ratio be-tween the primary and the secondary beams measured on

Fig. 3. Field dependence of the primary (filled symbols, leftaxis) and the secondary (open symbols, right axis) beam intensi-ties in one-beam-experiments performed at l 5 690 nm onDMNPAA–PVK–ECZ–TNF for (a) s-polarized and (b)p-polarized light: beams 10 and 10* (squares) and beams 20and 20* (circles), respectively. Note that two independent ex-periments are displayed for each polarization.

different sides of the device for zero external field (seeTable 1, values C and E). By setting A ' constant, weneglect field-induced refractive-index changes, which maychange the reflectivities at the ITO–polymer and thepolymer–ITO interfaces. Furthermore, because one canassume that the primary beam intensities are not signifi-cantly affected by their interaction with the secondarybeams for I60 @ I60* , the first term in Eq. (4) can be ne-glected in the first approximation (undepleted-pump-beam approximation):

G$60,60* %~E ! ' 2cos a60

d H lnF I60* ~E, I!

AI60~E, II!G J . (5)

By applying this simplified formalism we can neglect allchanges in the primary beam intensities other thanthrough interaction with the secondary beams.

The absolute values of the reflection gain coefficientsuG$60,60* %u calculated from the data of the one-beam ex-periment with Eq. (5) (squares, Fig. 4) first increase withincreasing field, reach extrema, and finally decrease forthe highest fields. Whereas Gs

$10,10* % , Gs$20,20* % , and

Fig. 4. Field dependence of the reflection gain coefficientG$60,60* % for the 10 beam (filled symbols) and the 20 beam (opensymbols) in one-beam (squares) and piezo (circles) experimentsperformed at l 5 690 nm on DMNPAA–PVK–ECZ–TNF for (a)s-polarized and (b) p-polarized light.


Gp$10,10* % show very similar field dependence, Gp

$20,20* %

shows significantly different values [Fig. 4(b)]. The rea-son for this is unclear.

Because of fanning effects,20–22 interpretation of theabsolute values of the reflection gain coefficients is pos-sible only for fields up to uEu 5 45 V/mm and the field po-larity where no waveguiding occurs (E . 0 for s polariza-tion and E , 0 for p polarization): uGs

$10,10* %u ' 6.2cm21, uGs

$20,20* %u ' 7.6 cm21, and uGp$10,10* %u ' 12.5

cm21. The ratio of reflection gain for the two beams andfor s polarization, Gs

$10,10* %/Gs$20,20* % ' 1.23, corresponds

approximately to the ratio of the grating contrast factors,ms

$10,10* %/ms$20,20* % 5 0.37/0.29 ' 1.29. This is what one

would expect from Eq. (1), because all other factors thatdetermine the strength of the space-charge field except mare at least quite similar (Table 2). The polarization an-isotropy of the $10, 10* % grating is Gp

$10,10* %/Gs$10,10* %

5 12.5/7.6 5 1.64. Because f ' 80–90° for all reflec-tion gratings, Gp

$10,10* %/Gs$10,10* % ' Dnp /Dns . Consider-

Fig. 5. Field dependence of the primary (filled symbols, leftaxis) and the secondary (open symbols, right axis) beam intensi-ties in a piezo experiment (see text) performed at l 5 690 nm onDMNPAA–PVK–ECZ–TNF for (a) s-polarized and (b)p-polarized light: beams 10 and 10* (squares) and beams 20and 20* (circles), respectively.

ing the contrast factors for the two polarizations (ms5 0.29 and mp 5 0.09, respectively; Table 2) and the in-creases in light intensity for polarization, one can esti-mate the real anisotropy ratio to be '4.

B. Piezo ExperimentsThe question arises as to whether these two gratings af-fect each other when they are present at the same time,as in a normal experiment. To answer this question weperformed a piezo experiment during which both primarybeams were present simultaneously but the phase rela-tionship between them was varied in a random fashion bymodulation of the piezo-mounted mirror. In this way theformation of all gratings except the $10/10* % and$20/20* % gratings was prevented, enabling us to studythe interaction between these two gratings. The generalobservations during the piezo experiment are very similarto those during the one-beam experiments (Fig. 5). Thereflection gain G$60,60* % was reduced to approximately60% (80%) for s ( p) polarization (Fig. 4, circles) comparedwith the that in the one-beam experiments (squares). As

Fig. 6. Field dependence of the primary (filled symbols, leftaxis) and the secondary (open symbols, right axis) beam intensi-ties in a normal two-beam coupling experiment performed at l5 690 nm on DMNPAA–PVK–ECZ–TNF for (a) s-polarized and(b) p-polarized light: beams 10 and 10* (squares) and beams20 and 20* (circles), respectively.


two holograms are now present at the same time, the to-tal dynamic range is shared between the two, the ratio be-ing determined by their relative strength. Thus the in-dex modulation amplitude of each single hologram isreduced compared with those in the one-beam experiment(in analogy with the multiplexing of holograms in high-density data storage). The interaction between the indi-vidual holograms is maximum because the grating tiltangles are exactly identical. We attribute the slight in-crease in total Dn to the increased (doubled) light inten-sity.

C. Normal Two-Beam Coupling ExperimentsAs we move on to the normal two-beam coupling experi-ment the situation becomes really complicated, because atleast three additional gratings come into play. Theelectric-field dependence of all beam intensities in suchan experiment is shown in Fig. 6. For positive (negative)fields and s ( p) polarization the 10 beam gains in energyat the expense of the 20 beam. The change in the energytransfer direction for the two polarizations is due to theopposite signs of the index changes Dn sensed by the twopolarizations, as predicted by the orientational enhance-ment mechanism.3,17 The intensities of the secondarybeams follow the general trends of the transmitted inten-sity of the two primary pump beams, although not ex-actly, indirectly indicating the presence of the reflectiongratings. It will be impossible even to qualitatively sepa-rate the individual contributions. The gain coefficientscalculated with Eq. (2) are Gs

$10,20%(145 V/mm)' 111.7 cm21 and Gp

$10,20%(145 V/mm) ' 148.2 cm21;i.e., Gp

$10,20%/Gs$10,20% ' 24. The phase shift between

light and index grating was determined by the moving-grating technique to be f ' 10215° at uEu 5 45 V/mm inboth cases; therefore the gain anisotropy corresponds toDnp /Dns , which is in perfect agreement with the valueobtained from earlier degenerate four-wave mixing ex-periments with the same chromophore.3

D. Comparison between Reflection and TransmissionGratingsComparing the PR gain coefficients obtained for the re-flection gratings $10, 01% and $20,20* % with those ob-tained for the main $10, 20% grating requires that twoaspects be discussed in more detail:

• It was pointed out above that G$10,10* % has the iden-tical sign for both polarizations, unlike for the energytransfer between the primary beams.3 This clearly indi-cates that the index modulation amplitude for these re-flection gratings has identical sign for both polarizations.Such can be the case only if the EO contribution to Dn islarger than the birefringence contribution, unlike for themain grating, which is typically dominated by the orien-tational birefringence.3,17 According to the orientationalenhancement model the anisotropy ratio for the indexmodulation is given by [the square root of Eq. (25) of Ref.17]

Dnp /Dns 5 cos~a2 2 a1!$cos a1 cos a2

1 @~C/A 2 1 !sin~a1 1 a2!tan~p 2 C!#/2

1 C/A sin a1 sin a2%, (6)

where C 5 CBR 1 CEO (A 5 ABR 1 AEO) are constantthat describe the refractive-index changes parallel (per-pendicular) to the poling field direction that are due to bi-refringence and the EO effect. The anisotropy Dnp /Dnsdepends slightly on tilt angle C, and in the limit of smallinterbeam angles (a20 2 a10 → 0) it approaches C/A asa limiting value. C/A was experimentally determined to'24 for the DMNPAA chromophore (see above).3 Notethat for reflection gratings the term sin(a101 a20)tan(p2 C) approaches 2. Using Eq. (6), we ob-tain Dnp /Dns 5 3.89 for the $10, 10* % grating andDnp /Dns 5 2.80 for the $20, 20* % grating, in excellentagreement with the experimentally estimated value forthe $10, 10* % grating ('4). Note, however, that in thelimiting case of normal incidence (i.e., C 5 p/2, a105 0, and a20 5 p) the model predicts that Dnp /Dns5 2 2 C/A, whereas physically Dnp /Dns must be unity,because both light polarizations have the same interac-tion with the medium.

• The gain coefficients obtained for the reflection grat-ings in the one-beam experiments are of the same order ofmagnitude as the normal gain coefficients for the trans-mission grating $10, 20%: uGs

$10,20%/Gs$60,60* %u ' 2 and

uGp$10,20%/Gp

$10,10* %u ' 4 at uEu 5 45 V/mm. This is sur-prising, considering the less favorable grating spacing,contrast factor, and incident intensity of the $10, 10* %and $20, 20* % gratings, which all result in a reducedspace-charge field ESC according to Eq. (1). The reasonfor this result is the much more favorable phase shift be-tween light and index grating for the reflection gratings,which was found to be f ' 80–90, i.e., close to the idealvalue of p/2. By contrast, the phase shift for the maingrating was determined to be only f ' 10–15°.

E. Four-Wave Mixing ExperimentsWhile the various beam-coupling experiments describedabove are unable to unambiguously prove the existence ofthe $10* , 20* %, $20* , 10%, and $10* , 20% gratings,obtaining this proof should be possible by means of four-wave mixing experiments. As we have already men-tioned, diffraction will occur from three gratings simulta-neously. In the normal readout geometry these gratingsare $10, 20%, $10, 10* %, and $10, 20* %. As expected,diffraction from the main $10, 20% grating was by far thestrongest [Fig. 7(a), filled squares]: The typical oscilla-tory dependence of the diffraction efficiency h on the ap-plied field is observed, which is a result of the sin2 depen-dence of h on index modulation amplitude Dn,26 which byitself depends quadratically on the applied electric field aspredicted by the orientational enhancement model.17

The maximum diffraction efficiency is h ' 0.85 and oc-curs at E(hmax) 5 58 (71) 6 2 V/mm for l 5 633 (690)nm. The difference in the field of maximum diffractionat the two wavelengths is due to the dispersion of the mi-croscopic constants of DMNPAA (linear and nonlinear po-larizability) and to variations in photogeneration effi-ciency and photoconductivity. For the other two(reflection) gratings a diffracted signal slightly largerthan the noise level of our setup could be detected only atthe highest fields of uEu 5 105 V/mm, i.e., h ' 5 3 1023

in both cases (not shown). Therefore the upper limit for


index modulation amplitudes of these gratings can be es-timated to be Dn , 7 3 1025.

The analogous experiment on the identical sample inthe crossed-readout geometry proves, for the first time toour knowledge, the existence of the $10* , 20* % grating[Fig. 7(b), filled squares). Surprisingly, its strength isonly slightly reduced compared with that of the usuallyconsidered $10, 20% grating. The maximum of the dif-fraction efficiency occurs near E(hmax) 5 73 6 4 V/mm forl 5 633 nm, which is a 1.25-times-higher field value thanin the normal experiment (see above). Assuming thatDn } E2,17 this means that Dn $10* ,20* % ' (58/73)2

3 Dn $10,20% ' 0.66Dn $10,20% . As for the normal readoutgeometry, the diffraction efficiency of the two reflectiongratings was negligible in the crossed geometry. Notethat the contrast factor for the $10* , 20* % grating is de-pendent on the energy transfer in the $10, 20% grating.However, the changes are small for s-polarized beams(Fig. 8, open circles).

Since the index modulation Dn of the four reflectiongratings is small, one can assume in a first approximationthat the maximum achievable dynamic range Dntot of thematerial is shared between the $10, 20% and the$10* , 20* % gratings only:

Dntot 5 Dn $10,20% 1 Dn $10* ,20* % ' 1.66Dn $10,20% . (7)

Fig. 7. Field dependence of the normalized diffraction efficiencyh in degenerate four-wave mixing experiments performed atl 5 633 nm on DMNPAA/PVK/ECZ/TNF for a p-polarized read-ing beam in (a) the normal readout geometry and (b) the crossedreadout geometry: devices using a 150-nm-thick ITO electrodeas the second contact (squares) and an 80-nm-thick ITO electrodeas the second contact (circles), s-polarized writing beams (filledsymbols) and p-polarized writing beams (open symbols). Thedashed line indicates the expected field of maximum diffractionwhen the reflectivity at the polymer–ITO–glass interface is zero(see text). The field polarity was E , 0.

For E(hmax) 5 58 V/mm we obtain Dntot 5 4.5 3 1023.26

As a result of the grating competition, the relativestrength of the two transmission gratings should be de-termined primarily by the respective light intensities, be-cause all other factors that determine ESC are similar.The intensity dependence of Dn below the saturationlimit14 can be approximated by the following empirical ex-pression:

Dn~E, I ! 5 Dn0~E ! 2 C1~E !exp@C2~E !I#, (8)

where Dn(E, I) is the index modulation for a particularfield value E and light intensity I, Dn0(E) is the satura-tion value for that particular field, and C1(E) (.0) areconstants specific for field E.

The performance of our devices should, therefore, de-pend on the reflectivity of the rear polymer–electrode–glass interface because that interface determines the in-tensity of the 10* and 20* beams. The parameter thatis mainly responsible for the reflectivity of the interface isthe thickness of the ITO electrode, which determineswhether the interference of reflections 4 and 5 [Fig. 1(b)]is constructive or destructive. To study this effect, in ad-dition to devices with two 150-nm-thick ITO electrodes,which were exclusively used so far, we prepared devicesin which the rear contact was replaced with a 80-nm ITOelectrode. The reflectivity for the s-polarized writingbeams is increased in the latter case by approximately afactor of 7 compared with that of the 150-nm devices (seevalues D and F in Table 1 and l 5 633-nm values inTable 2). Considering empirical equation (8), we suspectthat the difference in amplitudes Dn $10,20%

2 Dn $10* ,20* % decreases from the 150-nm devices to the80-nm devices. Assuming that Dntot remains constant,we expect that the field of maximum diffraction will shiftto (2.7/2.48)0.5 5 1.04 larger fields in the normal readoutgeometry, whereas E(hmax) in the crossed geometryshould be reduced. Experimentally we found that in thenormal four-wave-mixing experiment the diffractionmaximum for the 80-nm device (filled circles) was shifted

Fig. 8. Field dependence of the contrast factor m of the $10* ,20* % grating in degenerate four-wave mixing experiments per-formed at l 5 633 nm on DMNPAA–PVK–ECZ–TNF forp-polarized (filled squares) and s-polarized (open circles) beamsfor devices using a 150-nm-thick ITO electrode as the second con-tact. The field polarity was E , 0.


to slightly higher fields @E(hmax) 5 62 6 2 V/mm# com-pared with that for the 150-nm device (58 V/mm); i.e., thefactor in E(hmax) is 1.06 in perfect agreement with the ex-pectations. Unfortunately, the readout error in thecrossed geometry was larger (64 V/mm) than the ex-pected change (3.5 V/mm), and therefore the performanceof the 80-nm devices was the same as for the 150-nm de-vices. Nevertheless, these results support the assumedcompetition between the two transmission gratings.

To improve the performance of the devices rather thanto reduce it, we need to reduce the intensity of the second-ary beams. A first step in that direction is to usep-polarized instead of s-polarized writing beams on thedevices with 150-nm ITO thickness, which reduces the re-flectivity by approximately a factor of 5 (Table 1). Thusthe changes in the maximum fields are expected to occurin opposite directions and should be even smaller thanthe change of ITO thickness for s polarization. However,substantial shifts are observed: The field of maximumdiffraction for the $10* , 20* % grating is shifted beyondE(hmax) . 100 V/mm [Fig. 7(b), open squares]. Thismeans that Dn $10* ,20* % is reduced by at least a factor of 2compared with that in the previous case in whichs-polarized writing beams were used. Correspondingly,the strength of the $10, 20% grating is increased: Forsmall electric fields the diffraction efficiency is larger forp- than for s-polarized writing beams, but the field ofmaximum diffraction is almost identical as for s-polarizedwriting beams [Fig. 7(a), open/filled squares). This is sobecause, unlike in ordinary nondynamic holograms (e.g.,recorded in a photopolymer), in dynamic holograms thesurfaces of equal refractive index may be curved andtilted as a result of the complex nature of the gaincoefficient.18 The imaginary component responsible forthe phase shift becomes strong for small phase shifts fbetween the light and the index grating (as in our case)and large index modulation amplitudes Dn. This condi-tion is fulfilled much more for p- than for s-polarizedwrite beams. When the grating is curved, the probebeam cannot fulfill the Bragg condition for the entiregrating, reducing the maximum achievable diffraction ef-ficiency. Further deviations from the ideal diffractioncurve are caused by the fact that the contrast factor var-ies throughout the material because of the energy trans-fer. Therefore s-polarized writing beams are ultimatelypreferable for four-wave mixing because the photorefrac-tive gain is smaller and both effects are reduced. Theorigin of the strongly reduced amplitude of the$10* , 20* % grating for p-polarized writing beams is thestrongly reduced contrast factor m $10* ,20* % (Fig. 8, filledsquares).

To eliminate the reflections completely it will be neces-sary to match the refractive indices of the PR materialand the substrate to make reflections 4 and 5 [Fig. 1(b)]identical in intensity. Furthermore, the thickness of thecontact electrode has to be adjusted to yield complete de-structive interference and thus zero reflection (;170 nmin our geometry). Note that the adjustment has to bedone for every wavelength and is possible only for one ofthe writing beam angles a i ; the other will still be re-flected somewhat. As a result, the total number of grat-ings will drop to three: for example, assuming that the

ITO thickness is adjusted for a20 , the $10, 20%,$10, 10* %, and $20, 10* % gratings will be present. Inthis case the accessible dynamic range [Eq. (7)] should bealmost entirely occupied by the main grating $10, 20%;i.e., Dn$10,20% 5 4.5 3 1023. This increase of Dn by a fac-tor of 1.66 corresponds to a (1.66)1/2 reduction of the fieldfor maximum diffraction in the normal readout geometryunder identical experimental conditions, assuming thatDn } E2.17 Therefore one would expect E(hmax) to dropto ;45 V/mm (dashed line in Fig. 7) for the material stud-ied here. We are currently working to prove this concept.

5. CONCLUSIONSThe experiments presented here reveal a problem thathas not been considered in the published literature onthin-film organic PR devices, including on polymers,glasses, and liquid crystals. For the first time to ourknowledge, the coexistence of as many as six PR gratings(two transmission, four reflection type) has been demon-strated. The gratings result from the interaction amongfour individual beams, the two original pump beams (10and 20) and two beams reflected at the interface betweenthe PR material and the rear ITO contact electrode (10*and 20* ). Additional gratings should show up when thenon-Bragg diffracted beams19 become strong. The situa-tion is even further complicated by beam fanning20–22 andthe presence of 2K gratings, which are a result of the insitu poling process.17 The coexistence of multiple grat-ings in the thin-film devices may cause image distortionsin optical processing applications such as real-time opti-cal correlation and holographic data storage.

It was demonstrated that the four reflection-type grat-ings show rather small index modulation amplitude (Dn, 1024 at E 5 90 V/mm). Because the phase shift in thereflection gratings is close to the ideal value of p/2, unlikefor the transmission gratings, the reflection gratingscould be unambiguously proved in two-beam coupling ex-periments despite their small Dn. The reflection gain co-efficient has the same sign for s- and for p-polarized light,indicating that the reflection gratings are predominantlyEO in nature, unlike for the $10, 20% grating, for whichmost of the index modulation originates from orienta-tional birefringence,3 as was explained by the orienta-tional enhancement model.17

The two transmission-type gratings possess a muchlarger index modulation amplitude (Dn ' 4 3 1023)than the reflection gratings (Dn , 1024) at E5 80–90 V/mm. It was demonstrated that the$10* , 20* % grating, which was discovered here by use ofa new crossed readout geometry, is only 0.66 timesweaker than the usually considered $10, 20% grating indevices with 150-nm-thick ITO contact electrodes. Themaximum accessible dynamic range of the material isshared between the two gratings in amounts that dependon the reflectivity of the rear polymer–electrode–substrate interface. This finding has important conse-quences for the comparability of results obtained by dif-ferent research teams, since the nature of the ITO slidesused in fabricating the devices can influence the reflectedintensities and ultimately the relative strength of thecompeting PR gratings. By using 80-nm-thick ITO con-


tact electrodes (higher reflectivity), we demonstrated aslightly reduced performance for the main grating$10, 20%; however, this difference corresponds to asmuch as a 12% reduction of Dn in the normal readout ge-ometry. If different materials are to be compared, thesame kinds of ITO slide should be used for all devices, andthe devices should be studied under identical experimen-tal conditions. Possibilities of further improving the per-formance by reducing the reflectivity of the interface werediscussed. A first step to prove the concept was to usep-polarized instead of s-polarized beams, which yielded agreatly enhanced performance at low electric fields. Fur-ther studies are under way.

The results presented were consistent for a number ofsamples and a variety of materials.

ACKNOWLEDGMENTSThe authors thank Christoph Brauchle (University of Mu-nich) and Karsten Buse (University of Osnabruck) forfruitful discussions. This research has been supportedby the Volkswagen Foundation and the German–IsraeliFoundation.

Address correspondence to K. Meerholz (e-mail:[email protected]).

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Competing photorefractive gratings in organic thin-film devices

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