Light diffraction from the volume holograms in electrooptic birefringent crystals

Light diffraction from the volume holograms in electrooptic birefringent crystals

Volume 29, number 1 OPTICS COMMUNICATIONS April 1979 LIGHT DIFFRACTION FROM THE VOLUME HOLOGRAMS IN ELECTROOPTIC BIREFRINGENT CRYSTALS M.P. PETROV,...

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Volume 29, number 1

OPTICS COMMUNICATIONS

April 1979

LIGHT DIFFRACTION FROM THE VOLUME HOLOGRAMS IN ELECTROOPTIC BIREFRINGENT CRYSTALS M.P. PETROV, S.I. STEPANOV and A.A. KAMSHILIN A. I:. loffe Physico-Technical Institute, Academy of Science of the USSR, 194021. Leningrad, USSR Received 27 December 1978

Angular bandwidth of the image reconstructed from the volume phase hologram at a wavelength different from that of the recording beams has been analysed. An optimum holographic scheme on the basis of anisotropic diffraction uniting maximum bandwidth of the Gabor's scheme and advantages of the Leith-Upatnieks scheme has been proposed for nondestructive readout of the volume hologram in birefringenl photorefractive crystals. The main results of the theoretical analysis leading to the optimum holographic arrangement for electrically controlled retrieval of information from the volume of the electrooptic crystal are presented. Demonstrating experiments has been performed with LiNbO3 : l:e crystals.

1. Introduction Photorefractive electrooptic crystals of LiNbO 3 type are of great practical interest due to the possibility of the volume phase hologram recording and realisation of the mass memory on holographic principles [1]. As distinct from other photosensitive storage media these materials allow also electrical control of hologram retrieval by means of an external electric field applied to the crystal [2]. But unfortunately there are several drawbacks preventing the materials in question from wide applications in memory systems, for instance: destruction of information upon readout because of the photosensitivity of the crystals, difficulties with selective erasure of information and so on. The problem of nondestructive readout of holograms appears to be one of the most important and there were different attempts to solve it (thermal [3] and electrical [4] fixing, two-photon recording [1]). But the present state of the art does not allow to consider this problem as a solved one. In this paper we present a new approach to the problem of non-destructive readout of the volume phase hologram in the birefringent crystal by means of a light beam with the wavelength essentially different from that of the recording beams. In addition to that we consider theoretically and present some new expert44

mental results on optimum conditions for electrically controlled retrieval of the volume holograms in electrooptic materials.

2. Nondestructive readout in birefringent media Up to now readout of a hologram at a wavelength different from that of the recording beams was considered to be not applicable for thick media (including photorefractive crystals) because of too high selective properties of the volume holograms [1,5]. It may be shown that the angular bandwidth 60, of the object beam reconstructed at )'2 from the volume hologram recorded at X1 for the usual Eeith-Upatnieks scheme in isotropic medium (fig. l a ) c a n be estimated in the following way

1

)t~

~501 = sin 01 dn(X 2 - ) t l ) '

(1)

where d and n are thickness and refractive index of the medium, 01 is the Bragg angle at X1 in tile volume of the crystal. For the case of LiNbO 3 " Fe is X1 ~ 0.5 /am (the usual wavelength of holographic recording in these crystals), X2 ~ 1.0/xm (at this wavelength LiNbO 3 • Fe is practically nonsensitive), tl ~ 2.3,

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April 1979

versa). The effectiveness of such diffraction accompanied by the rotation of the polarisation plane was demonstrated by the authors earlier for LiNbO 3 crystals [7]. Upon readout of the volume hologram at ?'2 that type of diffraction can provide both selection of zero-order maximum from the reconstructed image and maximum value of 601 (2) simultaneously (fig. lc). So the advantages of the Leith-Upatnieks and Gabor's schemes are united. For the most simple case when the C axis of the uniaxial crystal is perpendicular to the plane of incidence (fig. lc) the reference light beams angles 201 (at Xl) and 202 (at ?`2) resulting in the maximum value of 601 are the following:

IE

e

nl?` 2 sin(202) = n ~ 1 sin(201)

Fig. 1. Drawings illustrating the reconstruction of the volume hologram at the wavelength X2 different from that of recording light beams: (a) Leith-Upatnieks scheme, isotropic medium. (b) Gabor scheme, isolropic medium. (c) Optimum scheme on the basis of anisotropic diffraction, anisotropic medium. d ~ 1 mm, 01 ~ 0.1 ; 601 is about 2 X 10- 3, that provides the effective spatial resolution in the image reconstructed from the hologram about 20 lin/mm. Eq. (1) shows expansion orS01 at the decrease of 01 and 801 reaches its maximum magnitude in the Gabor's scheme [5] (fig. lb) 601 max = 2 [?`;/dn(?`2 -- ?`1 )] 1/2.

(2)

For the conditions mentioned above 801max is about 3 × 10 - 2 , that is sufficient for some practical applications. But unfortunately due to the intense zeroorder of diffraction in the center of the reconstructed pattern and high level noise Gabor's scheme practically can not be used. Eqs. (1,2) are also correct for the usual technique of the image reconstruction from the volume hologram in photorefractive crystals [1]. But for the birefringent photorefractive crystals there is another possibility to reach the maximum value of 601 ( 2 ) b y means of so called anisotropic diffraction [6] where the reconstructing light beam has ordinary and the reconstructed one extraordinary polarization (or vice

t-C-

J

(3) '

where n 1 is the refractive index at ?`1, n2 the ordinary refractive index for the positive and extraordinary one for the negative uniaxial crystal (as in the case of LiNbO3) at X2, and An 2 the crystal birefringency at the same wavelength ?`2" To verify the correctness of eqs. (2,3) we have performed some experiments with the typical birefringent photorefractive crystal LiNbO 3 : Fe (0.05 tool%) of 1.5 mm thickness with the Caxis in the plane of the sample. The volume hologram of the usual optical mira was written with a He-Cd laser (X 1 = 0.44 tam) and reconstructed with He-Cd and He-Ne (X2 = 0.63 tam) lasers. As it follows from theoretical analysis image reconstructed at ?`2 = 0.63 tam by the usual technique (diffraction without rotation of the polarization plane) exhibits quite poor resolution in the plane of incidence (fig. 2c). For the case of focused image hologram (the scheme used in our experiments) it is impossible even to reconstruct the image as a whole. The quality of the image reconstructed from the same hologram at ?`2 = 0.63 tam by means of anisotropic diffraction is much higher (fig. 2d) and comparable with that of the image reconstructed at ?`1 = 0.44 tam (fig. 2b). For the thickness of the crystal about 1.5 mm resolution in the center of the reconstructed pattern was higher than 100 lin/mm both in the plane of incidence and in the orthogonal one. 45

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OPTICS COMMUNICATIONS

t

2

'

??

April 1979

4

' ' '~5

c l:ig. 2. (a) Original image as it is seen through the crystal (X1 = 0.44 #m). (b) Image reconstructed at the wavelength of the writing beams (X1 = 0.44/am). (c) Image reconstructed at 2,2 = 0.63/~m (traditional Leith-Upatnieks scheme). (d) Image reconstructed at X2 = 0.63 ~m (optimum scheme on the basis of anisotropic diffraction).

So we have shown practical possibility o f reconstruction of the volume phase ho!ograms in the birefringent crystals at the wavelength essentially different from that of the recording beams. That enables (choosing the wavelength X2 outside tile sensitivity band of the crystal as a reconstructing one) nondestructive readout of the volume hologram without any additional technological treatment.

2. Electrically controlled readout of the volume holograms in electrooptic media So long as application of the bias electric field C to the electrooptic crystal results in the change of the 46

refractive index n it results also in the change of tile propagation direction and the wavelength of the readout light beam in tile volume of the crystal. That leads to the violation of Bragg condition and because of the high selective properties of the volume holograms can result in total disappearance of light diffraction from the given hologram. Analogously if the volmne hologram was written in the electrooptic crystal under bias electric field ~ 0 the nlaxinlum of" diffraction from the hologram upon readout by the original reference plane light wave is reached under the same value of gO- That enables recording of the w~lume holograms series under different electric voltages U applied to the crystal and subsequent retrieval of the necessary page of information by

Volume 29, number 1

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electric field g0 is applied perpendicular to the direction of light beams propagation. In accordance with the rule such holographic scheme needs application of Denisjuk's technique of the hologram recording [5] and U0. 5 =

U:-0,5

kV

U--1,5 kV

U

- 2 , 5 kV

[J + 0 . : ]

!/

kY

+ I . 5 kV

U = +2.5

kV

Fig. 3. Electrically controlled retrieval of a series of the volume phase holograms written in LiNbO3 crystal at the corresponding voltages. means of application of corresponding voltage. It is possible to formulate the following simple general rule for valuation of U0. 5 - the voltage resulting in reduction of intensity of the reconstructed light beam to half its maximum value: "The difference between the phase shift for the reconstructing and the reconstructed light beams caused by UO.5 is to be equal n". Here both shifts are to be measured from one of two parallel crystal surfaces: front or back. One can see from that rule that the value of 2Uo. 5 necessary to suppress the diffraction from the given hologram is nearly equal to the controlling voltage of the usual electrooptic modulator operating in analogous geometry. That is why one can expect the lowest controlling voltage Uo.5 in transverse holographic schemes where bias

Ux/2 d/2L, U~,/2is tile halfwavelength

(4)

where voltage of the crystal used in experiment, L, d dimensions of the crystal along direction of light propagation and long ~ 0" That arrangement was experimentally investigated in LiNbO 3 : Fe crystals (see also [8] ). To demonstrate the electrically controlled retrieval of information a series of the holograms at different voltages on the crystal was performed. The results of the reconstruction under application of corresponding voltages are presented on fig. 3. The orientation of LiNbO 3 : Fe crystal and the value Lid = 3 used in our experiment provide the value of 2U0. 5 about 600 V. That is why the middle voltage between the values at which the holograms were written no one of two neighboring holograms was reconstructed. It is worth also to mention tTlat when the interelectrode space was not totally irradiated by the recording or reconstructing light beams, a shift is observed between the voltages at which the hologram was recorded and reconstructed. This effect can be explained by an additional internal electric field arising due to the charges trapped at the boundaries of the illuminated region (see for example [9]). Comparing our results with that obtained by other authors it is worth to note that as a rule all experiments known from the current literature both on electrically controlled retrieval of holograms (see for example [10] ) and on switching or modulation of the plane light beam [1 1] were performed with holographic schemes far from optimum what resulted in comparatively high values of controlling voltages.

References ll] D. yon der Linde and A.M. Glass, Appl. Phys. 8 (1975) 85. [2] R.P. Kenan, C.M. Verber and E. van Wood, Appl. Phys. Lett. 24 (1974) 428. [3] D.L. Staebler, W.J. Burke, W. Phillips and J.J. Ametani, Appl. Phys. Letl. 26 (1975) 182. 47

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[4] F. Micheron, C. Mayeux and J.C. Trotier, Appl. Opt. 13 (1974) 784. [5] R.J. Collier, C.B. Burckhardt and L.H. Lin, Optical holography (New York, London, Acad. Press, 1971). [6] E.G.H. Lean, C.F. Quate, H.J. Shaw, Appl. Phys. Lett. 10 (1967) 48. [7] S.I. Stepanov, M.P. Petrov and A.A. Kamshilin, Piz'ma v .IFT, 3 (1977) 849 (in russ.).

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[8] M.P. Petroc, S.I. Stepanov and A.A. Kamshilin, Proc. IV Intern. Conf. on Ferroelectricity, Leningrad 1977, to be publ. in Ferroelectrics. [9] I.'.S Chert, J. Appl. Phys. 40 (1969) 3389. [10] T. Yasuhira et al., Appl. Opt. 16 (1977) 2532. [11] O. Mikami, Optics Comm. 19 (1976) 42.