Optical Information Processing

PROCEEDINGS •

International

SPIE-The International Society for Optical Engineering

Conference on

Optical Information Processing Yuri v. Gulyaev Dennis R. Pape Chairs/Editors 2-7 August 1993 St. Petersburg, Russia

Sponsored by A. F. loffe Physical-Technical Institute/Russian Academy of Sciences AT & T St. Petersburg Company with Limited Responsibility STACK, Russia Engineering and Construction Corporation CREATION, Russia Financial and Production Company ESTRA, Russia IEEE/Lasers and Electro-Optics Society, USA Institute of Radio Engineering and Electronics/Russian Academy of Sciences Ministry of Science, Higher School Education and Technical Policy of Russia Moscow Scientific-Production Corporation ASTRA Optical Society of America Radar MMS of Leninetz SPIE Russia Chapter SPIE- The International Society for Optical Engineering, USA St. Petersburg Innovation Bank St. Petersburg State Academy of Aerospace Instrumentation

Published by SPIE- The International

Society for Optical Engineering

Volume 2051

SPIE (The Society of Photo-Optical Instrumentation Engineers) is a nonprofit society dedicated to the advancement of optical and optoelectronic applied science and technology.

The papers appearing in this book comprise the proceedings of the meeting mentioned on the cover and title page. They reflect the authors' opinions and are published as presented and without change, in the interests of timely dissemination. Their inclusion in this publication does not necessarily constitute endorsement by the editors or by SPIE.

Please use the following format to cite material from this book: Author(s), "Title of paper," in Optical Information Processing, Yuri V. Gulyaev, Dennis R. Pape, Editors, Proc. SPIE 2051, page numbers (1993).

Library of Congress Catalog Card No. 93-86914 ISBN 0-8194-1310-0

Published by SPIE- The International Society for Optical Engineering P.O. Box ro, Bellingham, Washington 98227-0010 USA Telephone 206/676-3290 (Pacific Time) • Fax 206/647-1445

Copyright 0.3°, owing to the small crossection of fiber end-face. Therefore, after leaving the sample, this beam was split into two beams (transmitted and reflected). Intensities ratio of these beams depends on the angle 2y as it is illustrated by Fig.l (a and b). And only reflected beam could pass through the fiber for specific angle 2t}o (Fig.lb). The value of t}o naturally depends on geometrical parameters of fiber and on the beam diameter. Usually, the energy exchange effect in photorefractive crystals is described quantitatively by gain factor y 7:

y = Is(with pump) / Is(without pump)

0-8194-1310-0/93/$6.00

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where Is is the intensity of transmitted signal beam. But we had to use other definition of gain factor because in our BTO fiber the intensity of transmitted signal beam alone (without pump) decreased 10 times or more after the strong electric field was applied. The reason of such decreasing is the depletion of the signal beam due to fanning effect, which takes place in siIIenite crystal only under applied electric field. Therefore, we defined the gain factor as

(2) where ISE is intensity of transmitted signal beam with pumping when electric field is applied to the fiber, and Iso is intensity of transmitted signal beam without pumping and without electric field.

Transmitted Signal

Si9::I)~2(}8--~- -g- -~~SilI~iEiil~ -01-

'!tIltIIIln!Bn,

Reflected Signal

Fiber

beam (b) Signal beam

Reflected Signal

1"'·.·."·'·/

Fig.i. Propagation of the signal beam through the fiber under different angles of incidence. Dependence of the gain factor y on the spatial frequency of recorded hologram was measured by varying of the 2t'} angle of incidence of the signal beam (the pump beam propagation direction was always kept to be parallel to the [110] axis) and is shown in Fig.2. Experimental data of Fig.2 were obtained for the recording beam ratio p = 0.0027 under applied ac voltage of 3 kV, which corresponds to 23 kV/cm strong electric field. Experimental data marked in the Fig.2 by crosses were measured for transmitted beam, whereas circles correspond to the reflected signal beam measurement. It was noted that there is no pronounced difference of gain factors measured for transmitted or reflected signal beam. For our specific experimental geometry the angle 2t'}o (when there is no more transmitted beam) is 17.4° . That corresponds to the Fo = 480 lp/mm spatial frequency. For spatial frequency higher than Fo the only reflected beam could be measured (see Fig.lb). Gain factor,

f'

100

ETO-fiber

[110]

10

*

Transmitted

o

Reflected

-----------------------------------------------~-, Fo'

FB

0.1+--------,-------.--------r---~~._~

o

150 300 Spatial frequency,

450 lp/mm

600

Fig.2. Gain factor dependence on spatial frequency of recorded hologram in BTO-fiber at A. = 632.8 nm.

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It could be seen from Fig.2 that for our particular fiber the total signal enhancement turns to be signal depletion (y ~ 1) for spatial frequencies higher than FB = 570 lp/mm (21'}B= 19.5°). To explain this experimental fact, let us analyze the peculiarities of energy effect in the photorefractive fiber of the sillenite family. If we choose the polarization of interacting beams to be optimal for energy transferring from the pump to the signal for transmitted signal beam (the beam, painted by dots in Fig.l), then for the reflected beam (the beam painted by net in Fig. 1) the energy is coming back to the pump from the signal. But before the beam being reflected into the fiber, it had been enhanced. Hence, the output result depends on the ratio between the length of enhancement and the length of depletion inside the fiber. Let us note that the boundary spatial frequency FB has a tendency to be decreasing if the higher ratio of the fiber length to its diameter is used. By other words, that means a possibility of selective enhancement or depletion of several fiber's modes. This experimental fact reflects the difference in behavior of photorefractive fiber compare with bulk crystal. The dynamic of the energy exchange effect was also studied in our experiments. After the signal beam had been turned on, its intensity Is increases following to the exponential law with rather good accuracy: IS = Isst [ 1 - exp( - t/'t )]

(3)

where Isst is saturated value of signal beam intensity and ~ is recording time of hologram in the fiber. We calculate 't by fitting experimental data with Eq.3. Dependence of t on the recording beams intensity ratio ~ is shown in Fig.3. To measure this dependence we kept the pump beam intensity and varied the intensity of signal beam by using attenuator. As one can see from Fig.3, the recording time changes more than 5 times while ~ is varying from 5-10-2 to 9-10-4. This result seems to be rather strange from point of view of usual behavior of photorefractive crystal, if the inverse proportionality of recording time to the total intensity of recording beams had been supposed (dashed line on Fig.3 corresponds to this supposition). But if we take into account multi two-wave mixing and the pump beam depletion owing to the strong fanning effect, we could better understand a tendency of response time dependencies, as it follows from theoretical predictions of Ref.8. Recording

time

T,

sec

2.5r-----------------------------------------------------.

* ---- --- -- -- ---. - _.- - - - - - ----.- -------- ------ -- ------ ------------------*---------*

2

Pump

1.5

E

*

= 0.66 W/cm

=

15 kV/cm

F = 398 lp/mm

* *

0.5

*

O~------~---------L--------~------

o

0.01

2

0.02 Signal-to-Pump

0.03

__L_

0.04

beam

ratio

of MUTUALLY

0.05

{3

Fig.3. Hologram build-up time as afunction of Signal-to-Pump 4. DOUBLE PHASE CONJUGATION

~ __~

beam ratio ~.

INCOHERENT BEAMS

High efficient holographic enhancement observed in BTO fiber allowed us to use it for demonstrating of double phase conjugation effect, when two mutually incoherent beams illuminate the fiber from opposite ends to produce phase conjugated waves of each beam. In other words, that means the four-wave mixing inside the fiber: two pumps beams and two


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phase conjugated beams. The experimental configuration is shown in Fig.4. In our set-up, the two mutually incoherent beams are derived from a single He-Ne laser (A.= 632.8 nm, an output power of 24 mW) by using a path-length difference much greater than the laser coherence length. A nonexpanded laser beam, after passing through an optional neutral ~ensity (N.D.) filter and shutter, is then divided into the two beams of equal power with diameter of 0.52 mm by a beam-splitter BS 1. The beam RI is then directed through a second optional N.D. filter, a shutter, a polarizer PI, and mirrors Ml and M2 into the BTO fiber. The beam R2, on the other hand, is directed through the analogous optical elements in the same horizontal plane as beam RI, but from the opposite end of the fiber. The beam-splitters BS2 and BS3 allow us to measure the power of both incident and phase-conjugate beams. The powers of the incident (pump) beams RI and R2 are detected by the photodiodes PDl and PD2 respectively, meanwhile the photodiodes PD3 and PD4 are used for measurements of the powers of the beams which are the phase conjugate (PC) waves of the RI and the R2 respectively. We denote the power of the pump beams as II and 1

,

2

and the power of PC waves as 13 and 14 respectively. The mirrors MI and M2 are attached to a rotation stage, that

provides a precise rotational control of the beams. The fiber is mounted to a precise translation-rotation us to adjust the beam angle incident on the fiber.

N.D. He-Ne

shutter

BS1

P1

N.D.

laser

f==~~~*,",~-==~==.a.. N. D. c:::::jp

support, which allow

Mirror M1

shutter

-u Fig.4. Schematic of experimental setup for the double phase conjugation experiments in photorefractive fiber. The quality of polishing of the fiber end-faces is not very high, and the end-face surfaces are not planes. Therefore, the beam, transmitted through the fiber has a complex, non-plane wavefront, that is additionally complicated by internal reflections from fiber faces. In other words, the fiber end-faces work as aberrators. If only one beam was introduced into the fiber when the a.c. electric field was applied, then the strong fanning effect was observed in the output of the fiber. By fanning effect we mean a self-scattering process in photorefractive media in which a single light beam generates scattering in an asymmetrical way[9]. In the photorefractive crystals of the sillenite family both the direction and the power of the fanning scattering depend not only on the bias electric field, but on the input polarization of the beam as well. When the second pump beam R2 had been introduced into the fiber from its opposite side, the fanning scattering was observed to be diminishing (similarly to the bleachingl'Pl of the fanning effect observed in BaTi03) and simultaneously the PC waves of both RI and R2 were observed to grow up. The PC wave can be easily recognized owing to its plane wavefront and a propagation direction being opposite to the pump beam. The power of the PC wave depends on the polarization state of the pump beams, the angle 1'} between them and their intensity ratio. It was observed that the double phase conjugation effect was maximal when the intensities of pump beams RI and 1'} between the pump beams has a distinct max-

R2 were in the same order. The dependence of the PC reflectivity on the angle

imum for the angle 1'} = 10°. This angle corresponds to the spatial frequency of hologram of 280 lp/mm. Note, that it is just the same angle, when the energy exchange effect is maximal (see Fig.2). This fact cortfinns the holographic nature of the double phase conjugation effect in photorefractive media. It was measured that the halfwidth of the maximum in the angular dependence of PC reflectivity is near to 6° or 160 lp/mm. It means that in our fiber any complex wave or image the highest spatial

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frequency of which does not exceed 160 lp/mm could be successfully phase conjugated. We define here PC reflectivity as a ratio of the phase conjugate beam power to the input beam power. It can be either 13/R1 or I,JR2. The highest PC reflectivity for our BTO fiber was found to be almost 7%. Note that the refractive index of BTO crystal is rather high (no = 2.58 at ').,= 632.8 nm) introducing big losses of light because of Fresnel reflections. Hence, the end-faces coating of the fiber by antireflection layers could increase the PC reflectivity at least two times. Moreover, such an antireflection coating could serve as a protection against the surface damaging by an electric field, that would allow us to apply a higher electric field and thus to increase the reflectivity even more. The dynamic of the double phase conjugation was also experimentally studied during this work. The typical evolution of the PC wave power after both the pump beams had been simultaneously open is shown in Fig.5. At the moment tl one of the pump beam (R2) was shut off, and the power 14 of the PC wave (measured by photodiode PD4 in FigA) was decreasing owing to the hologram erasure process. The broadening of the experimental curve in chosen time scale is due to a modulation in time of the PC wave power with relatively high frequency. The modulation depth was typically (M4)max/I4 == 25% under our experimental conditions. The reason of this modulation is the bias ac electric field applied to the crystal. Indeed, the PC wave can be considered as a result of the pump beam diffraction from the dynamic volume hologram recorded in the photorefractive crystal. The alternating electric field modulates the polarization state of the pump beam owing to the electrooptic effect in the crystal, hence the diffraction conditions are also modulated causing the modulation of the PC wave power. Our high-voltage source has a possibility to control independently both polarities of applied voltage, and we equalize applied voltage of different polarities inside the 5% of their values, however, the PC signal was found to be asymmetrical, and its shape is strongly dependent on the initial polarization state of pump beams. We suppose that it is also because of the complicated nature of diffraction that takes place in an anisotropic optically active electrooptic media as the BTO fiber is. PC reflectivity,

%

8

6

4

2

o~

-L

6

~

~

12

~~=- __~

__~

18

tl

24

,30

time, see Fig.5. Typical evolution of the PC reflectivity. Both beams were simultaneously open at the moment t = 0, and only one pump beam Rl illuminated fiber from the moment tl on. We found that the experimental data of any PC wave evolution can not be fitted well by the exponential law of the form 14 14st( 1- exp[ - tlt] )2, where lit is an average PC wave power in a steady-state, and 't is a recording time constant. The shape of experimental curves are better described by the sum of two exponents with different recording time constants, except the very beginning of the curves. This is not very surprising for the BTO crystal, in which both photorefractive and photochromic holograms can be simultaneously recorded, as it follows from experiments reported in Ref. 1I. The time constants for the build-up and erasure processes of the PC wave are of practical importance, and taking into account the complicated shape of the evolution curve, we define a response time 'tR of phase conjugation as the time taken to rise from 0% to 70%

=

of an average steady-state value of the PC wave power. Similarly, an erasure time 'tE was defined as the time taken to drop


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from a steady-state value of the PC signal to its 30% level. The experimentally measured

'tR

and

'tE

for different intensities of

the pump beams are shown in Table 1. The only RI pump beam was used during the erasure process. As follows from our experiments, for the same intensity of the pump beam, the erasure process is more than four times faster compared to the PC wave building up. The reason of such a big difference is not clear yet, and further experiments are in progress in our laboratory.

TABLE! Intensity of

Intensity of thepumpR2 (mW/cm2)

thepumpRI (mW/cm2)

Response time (0-70%) (see)

1.39 1.10 0.44

2.83 2.24 0.91

3.4 ± 0.1 4.S ± 0.1 8.0:1:0.2

Erasure time (100-30%) (sec) O.66±O.OS 0.96 ±O.OS 2.2 ± 0.1

S. CONCLUSION It is experimentally

shown that single crystal photorefractive

fibers of Bi12Ti020 are novel nonlinear optical elements of good parameters operating with low power cw lasers. High gain factor optical amplifiers and high coefficient noncoherent phase conjugation mirrors can be manufactured on the base of this fibers. These amplifying and phase conjugator elements can be applied in many different ways to the wide area of optical information processing. 6. ACKNOWLEDGMENTS This research is partly supported by the Academy of Finland. The authors are grateful to Hemmo Touvinen and Risto Ravattinen for technical assistence. 7. REFERENCES 1. P. Gunter and J. P. Huignard, editors, Photorefractive materials and their awlications I & II, (Topics in Applied Physics, Vol.61 & 62), Springer-Verlag, 1988 & 1989. 2. L. Hesselink and S. Redfield, "Photorefractive holographic recording in strontium barium niobate fibers", Opt. Lett., V01.13, N.lO, pp.877-880, 1989. 3. H. Yoshinaga, K. Kitayama, and H. Oguri, "Holographic image storage in iron-doped lithium niobate fibers", Appl.Phys. Lett., Vol.S6, pp.I728-1730, 1990. 4. A. A. Kamshilin, R. Silvennoinen, T. Jaaskelainen, C. J. Lima, M. R. B. Andreeta, and V. V. Prokofiev, "Two-wave mixing in photorefractive Bi12Si020 fibers", Opt.Lett, VoLl8, pp.690-692, 1993. 5. J. P. Huignard and F. Micheron, "High-sensitivity

read-write volume holographic storage in Bi12Si020 and Bi12Ge020 crystals", Appl.Phys.Lett., Vol.29, pp.S91-593, 1976. 6. S. I. Stepanov and M. P. Petrov, "Efficient un stationary holographic recording in photorefractive crystals under an external alternating electric field", Opt.Commun., Vol.S3, N.5, pp.292-295, 1985. 7. A. Marrakchi, J. P. Huignard, and P. Gunter, "Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12Si020 crystals", App1.Phys., Vo1.24, pp.131-138, 1981. 8. M. Horowitz, D. Kligler, and B. Fischer, "Time-dependent behavior of photorefractive two- and four-wave mixing", J.Opt. Soc.Am.B, Vol.8, pp.2204-2217, 1991. 9. J. Feinberg, "Asymmetric self-defocusing of an optical beam from the photorefractive effect", J.Opt.Soc.Am., Vol.72, pp. 46-51, 1982. 10. M. Segev, Y. Ophir, and B. Fischer, "Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media", Opt.Commun., Vo1.77, pp.265-274, 1990. 11. A. A. Kamshilin, "Simultaneous recording of absorption and photorefractive gratings in photorefractive crystals", Opt. Commun., Vol.93, pp.350-358, 1992.

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