Photorefractive Materials, Effects, and Applications

Abstract

The photorefractive effect is a phenomenon in which the local index of refraction is changed by the spatial variation of the light intensity. Such an effect was first discovered in 1966. The spatial index variation leads to the distortion of the wavefront, and such an effect was referred to an 'optical damage'. The photorefractive effect has since been observed in many electro-optic crystals, including LiNbO3, BaTiO3, SBN, BSO, BGO GaAs, InP, etc. Photorefractive materials are, by far, the most efficient media for the recording of dynamic holograms. In these media, information can be stored, retrieved and erased by the illumination of light. In addition to the holographic properties, energy coupling occurs between the recording beams and also between the reading beam and the scattered beam. In this Lecture, we first briefly describe the photorefractive effect. The band transport mode is introduced to analyze the process involved in the photo- induced index variation. This is followed by a more detailed analysis of the dynamics of grating formation. We then describe the interaction between electromagnetic waves propagating inside photorefractive media. Nonlinear optical processes including two-wave mixing, four-wave mixing and phase conjugation are discussed. We also point out some fundamental including two-wave mixing, four-wave mixing and phase conjugation are discussed. We also point out some fundamental properties of grating diffraction. Then we demonstrate the applications of the photorefractive effect including volume holographic data storage, image processing, optical interconnections, computing and neural networks. Finally, we discuss some recent developments in photorefractive materials and applications. As an example, we describe an application of photopolymers in a flat-topped tunable filter for optical fiber communication.

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Photorefractive materials, effects,
and applications
Gu, Claire, Yeh, Pochi
Claire Gu, Pochi Yeh, "Photorefractive materials, effects, and applications,"
Proc. SPIE 4419, 4th Iberoamerican Meeting on Optics and 7th Latin
American Meeting on Optics, Lasers, and Their Applications, (14 August
2001); doi: 10.1117/12.437223
Event: IV Iberoamerican Meeting of Optics and the VII Latin American
Meeting of Optics, Lasers and Their Applications, 2001, Tandil, Argentina
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Photorefractive Materials, Effects, and Applications
(Invited Lecture)
Claire Gu
Department of Electrical Engineering, University of California, Santa Cruz, CA 95064
claire@cse.ucsc.edu
Pochi Yeh
Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106
ABSTRACT
The photorefractive effect is a phenomenon in which the local index of refraction is changed by the spatial variation
of the light intensity. Such an effect was first discovered in 1966 [1]. The spatial index variation leads to the distortion of the
wavefront, and such an effect was referred to as "optical damage". The photorefractive effect has since been observed in
many electro-optic crystals, including LiNbO3, BaTiO3, SBN, BSO, BGO, GaAs, InP, etc. Photorefractive materials are, by
far, the most efficient media for the recording of dynamic holograms [2-4]. In these media, information can be stored,
retrieved and erased by the illumination of light. In addition to the holographic properties, energy coupling occurs between
the recording beams and also between the reading beam and the scattered beam. In this Lecture, we first briefly describe the
photorefractive effect. The band transport model is introduced to analyze the processes involved in the photo-induced index
variation. This is followed by a more detailed analysis of the dynamics of grating formation. We then describe the
interaction between electromagnetic waves propagating inside photorefractive media. Nonlinear optical processes [5]
including two-wave mixing, four-wave mixing and phase conjugation are discussed. We also point out some fundamental
properties of grating diffraction [6, 7]. Then we demonstrate the applications of the photorefractive effect [8-18] including
volume holographic data storage, image processing, optical interconnections, computing and neural networks. Finally, we
discuss some recent developments in photorefractive materials and applications. As an example, we describe an application
ofphotopolymers in a flat-topped tunable filter [19] for optical fiber communication.
I. Photorefractive Effect
Although there are several models for the photorefractive effect [20-23], Kukhtarev-Vinetskiis transport model [21]
provides a comprehensive description of the process. In the model, the photorefractive materials are assumed to contain
donor and acceptor traps (see Fig. 1). These traps, which arise from the imperfections or impurities in the crystal, create
intermediate electronic energy states in the bandgap of the insulators. When photons with sufficient energy are present,
electronic transitions due to photo-excitations take place. As a result of the transitions, charge carriers are excited into the
conduction band and the ionized donors become empty trap sites. As a result of the presence of the space-charge field, a
change in the index ofrefraction is induced via the linear electro-optic effect [24](Pockels effect).
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Consider now the illumination of a light beam with an intensity I=10(l+cosKz) in a photorefractive medium. In the
bright regions near cosKzl and I=2I, photoionized charges are generated by the absorption of photons. These charge
carriers can diffuse away from the bright regions leaving behind positively charged ionized donor impurities. If these charge
Figure 1 Model ofPhotorefractive effect.
4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers,
and Their Applications, Vera L. Brudny, Silvia A. Ledesma, Mario C. Marconi, Editors,
Proceedings of SPIE Vol. 4419 (2001) © 2001 SPIE · 0277-786X/01/$15.00 9
Invited Paper
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carriers are trapped in the dark regions, they will remain there because there is no light to reexcite them. This leads to a
charge separation as depicted in Fig. 2. As a result of the illumination with periodic intensity in the photorefractive medium,
the dark regions are negatively charged and the bright regions are positively charged (see Fig. 2). The electric field due to this
charge density distribution has a rt/2 phase shift according to Poisson equation. This space-charge field will induce a change
in the index of refraction via Pockels effect. Fig. 2 illustrates the spatial variation of the light intensity, space-charge density,
space-charge field and the induced index change. We note that the index grating has a spatial phase shift of rc/2 relative to
the intensity pattern.
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2.Wave Mixing and Phase Conjugation in Photorefractive Media
When two beams of coherent electromagnetic radiation intersect inside a photorefractive medium, the periodic
variation of the intensity due to interference will induce a volume index grating. The presence of such an index grating will
affect the propagation of these two beams. In fact, these waves are strongly diffracted by the index grating because Bragg
scatterings are perfectly phase-matched. One beam scatters into the other and vice versa in a process known as two-wave
mixing (TWM). If a third beam is brought in to read the index grating, Bragg diffraction occurs which yields a fourth beam.
These four beams interact inside the photorefractive medium to form a set of index gratings. The index gratings will then
affect the propagation of these beams via Bragg diffraction. This process is known as four-wave mixing (FWM). Four-wave
mixing is a convenient method for the generation ofphase conjugate waves.
In TWM, two laser beams interact inside a photorefractive medium [25]. As a result of the phase shift between the
index grating with respect to the light interference pattern there is a nonreciprocal steady-state transfer of energy between the
beams [21,26-28]. One beam gains energy from the other beam. This is referred to as nonreciprocal energy transfer. If this
two-wave mixing gain is large enough to overcome the absorption loss, then the beam gaining energy is amplified. Such an
amplification is responsible for the fanning of laser beams in photorefractive crystals [29], and the oscillation of
photorefractive resonators [30]. There are other configurations of TWM, such as contradirectional coupling and cross-
polarization coupling in cubic crystals [25]. In addition, the wavelength of the two waves can be different and the coupling
process is known as non-degenerate TWM. Details ofvarious types ofTWM processes are discussed in Ref. 25.
Four-wave mixing in photorefractive media can be employed to generate phase conjugated waves. The mechanism
can be understood in terms ofreal-time holography. Referring to Fig. 3, A2 and A3 are two counter-propagating plane waves.
A1 is the object beam which contains spatial information. The pump beam A2 and the object beam A1 write a hologram
inside the photorefractive crystal. The counter-propagating pump beam A3 satisfies the Bragg condition and, therefore, reads
out the hologram. The diffracted beam A4 propagates in the reversed direction of the object beam A1 and has the same wave
INTENSITY
Figure 2 The spatial variation of the light intensity, space-
CHARGE charge density, space-charge field and the induced index
DENSITY change.
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front as that of A1 . In FWM, the recording and readout happen simultaneously. The net result is that an object beam A1
incident upon a photorefractive crystal pumped by two counter-propagating beams is retro-reflected back with the same wave
front. The combination of the photorefractive medium and the two pump beams is, therefore, a phase conjugator.
A 2 4
Figure3 Schematic drawing offour-wave mixing.
z=O z=L
Phase conjugate waves can also be generated in configurations that do not require external pump beams. The most
commonly used phase conjugators include Self-Pumped Phase Conjugators (SPPC), Mutually Pumped Phase Conjugators
(MPPC) and Stimulated Brillouin Scattering (SBS). Details of these phase conjugators can be found in References 30.
Phase conjugators are optical devices that can generate a time-reversed replica of an incident electromagnetic wave.
These devices play an important role in many optical systems that require the transmission of waves through distortion media
such as atmosphere. They are also used in optical information processing.
3. Applications of Photorefractive Materials
Photorefractive media provide a promising candidate for optical information processing because of their unique
properties, such as low intensity operation, massive storage capacity, directional energy transfer, and real-time response.
These features make them attractive materials for volume holographic data storage, image processing, optical
interconnections, computing and neural networks. Various applications can be found in Refs. 2-10.
In recent years, the research on the applications of photorefractive materials has been focused on volume
holographic data storage. Volume holographic data storage (VHDS) is becoming increasingly important [3 1-36] due to its
large storage capacity (TBits/cm3) and fast access rate (GBits/sec). Multiple holograms can be recorded in a photorefractive
crystal or a polymer sequentially by using an exposure schedule which equalizes the diffraction efficiency or the bit-error
rate. Different reference beam angles, or wavelengths, or phase distributions can be chosen for different exposures; known as
wavelength multiplexing, angle multiplexing, and phase multiplexing respectively. Once information is stored in a volume
holographic medium, it can be retrieved and serve as a library for pattern recognition or other processing. A unique benefit of
such a system is the parallel nature of the readout where an input reference beam can read out an entire page of information,
or alternatively, an input object can be compared with all the stored images simultaneously to achieve high speed pattern
recognition.
4. Recent Development
The general definition of the photorefractive effect is that a phenomenon in which the local index of refraction is
changed by the spatial variation of the light intensity. However, the word "photorefractive" has been traditionally used to
describe the effect in electro-optic crystals. Recently, other materials such as polymers and photosensitive glasses have
attracted much attention because of their improved optical quality and large dynamic range. Photopolymers emerge as one of
the most promising classes of materials for holographic recording media.
In our research, we have designed a flat-topped tunable filter for wavelength division multiplexing (WDM) optical
networks. A photopolymer can be employed in the implementation of such a filter. As we know, WDM is one of the most
promising technologies for increasing the information capacity of optical fiber communications. With WDM, multiple
channels at closely spaced wavelengths are sent simultaneously over the same fiber. One of the essential components for
WDM is a wavelength selective filter. Previously, several WDM filters have been proposed and discussed. However, these
filters do not simultaneously satisfy the two important requirements of a WDM filter: wavelength tunability and flat-topped
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pass band. In our design [19], we used a Fabry-Perot etalon with multiple reflection gratings as the distributed Bragg reflector
(DBR) mirrors. The DBR mirrors lead to the flat-topped line-shape and the Fabry-Perot etalon reduces the interaction length.
An electro-optic material inside the cavity gives the tunability of the filter. The filter has a flat-topped pass band with about 1
nm linewidth and its wavelength can be tuned over the 40 nm range provided by Er-doped fiber amplifiers (EDFA).
In order to implement our design, we need to 1) tune the index of refraction both inside the cavity and in the grating
region, 2) fabricate the DBR mirrors with multiple gratings. The required large tuning range for the index of refraction (An
0.04) suggests the use of a liquid crystal material. On the other hand, the required interaction length for gratings (100 tim)
suggests a holographic medium for the DBR mirrors. Our idea to implement a filter that satisfies all the above requirements
is shown in Figure 4. It consists of a liquid crystal waveguide, whose index of refraction can be tuned by an applied electric
field. On top of the liquid crystal waveguide is a layer of holographic material (e.g., photoconductive polymer,
photorefractive liquid crystal/polymer, or photopolymer) which can be used to fabricate the DBR mirrors optically. Multiple
exposures in the grating regions can be performed to record multiple holographic gratings. The gratings in the polymer will
reflect light waves travelling in the liquid crystal waveguide, therefore serve as DBRs. By applying an electric field across the
liquid crystal waveguide, both the index of refraction inside the cavity and the background index of refraction of the grating
regions can be tuned simultaneously.
4DBRMirror DBR Mirror
-I
VLiquid Crystal
waveguide
Figure 4. Schematic of a flat-topped tunable WDM filter based on a liquid crystal waveguide with external gratings,
recorded in a layer ofphotopolymer, as DBR mirrors.
5. Conclusion
We have described the photorefractive effect, the band transport mode, and the dynamics of grating formation. We
have also discussed the interaction between electromagnetic waves propagating inside photorefractive media, including two-
wave mixing, four-wave mixing and phase conjugation. Furthermore, we have reviewed the applications of the
photorefractive effect including volume holographic data storage, image processing, optical interconnections, computing and
neural networks. In addition, we have discussed some recent developments in photorefractive materials and applications. As
an example, we have described an application of photopolymers in a flat-topped tunable filter for optical fiber
communication. Worldwide efforts in the research of photorefractive materials and applications are beyond the discussion in
this lecture.
6. Acknowledgement
The authors wish to acknowledge helpftul discussions and collaborations with Drs. Demetri Psaltis, Fai Mok, John Hong,
Arthor Chiou, Scott Campbell, Miao Yang and many others who worked with us over the years.
7. References
1. A. Ashkin, GD. Boyd, J.M. Dziedzic, R.G. Smith, A.A. Ballman, J.J. Levinstein and K. Nassau, App!. Phys. Left. 9,72,
(1966).
2. P. Yeh and C. Gu, eds. Landmark Papers on Photorefractive Nonlinear Optics, World Scientific Publishing Co., (New
Jersey, 1995).
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