photorefractive effect

The photorefractive effect was discovered in 1966 by A. Ashkin et al. at Bell Laboratories as an optical damage effect in a LiNbO3-crystal. But soon, scientists became aware that these refractive index inhomogeneities are indeed a phase hologram and can be exploited for dynamic holography. 

When two coherent light beams are superimposed in a photorefractive crystal, an interference pattern results, i.e., a spatial distribution of areas with high and low light intensity inside the crystal (figure a). In the areas of higher light intensity, charge carriers (electrons or holes) are excited. The gradient in the charge carrier density causes diffusion and thus the carriers migrate through the crystal. Eventually, they are trapped, preferentially at donator or acceptor sites in the crystal. The result is a charge carrier distribution as in figure b. This local charge distribution evokes an electric space charge field, as shown in figure c, due to Gauss' law. According to the spatial derivative in Gauss' law, the space charge field is shifted by a quarter of a grating period (equivalent to a phase of pi/2) with respect to the intensity pattern. The electro-optic effect then creates a refractive index distribution proportional to the electric field, as sketched in figure d. This refractive index pattern is a phase volume hologram

holography

Holography is the storage of the information of a light beam in an interference pattern. For recording, an image-bearing beam (=image or signal beam) is made to interfere with a second beam (reference beam) in the recording medium. Via a conventional photographic plate or the refractive index modulation in a photorefractive crystal, the interference pattern can be recorded. The recorded interference pattern is called a hologram. The hologram is read out by illuminating it with the reference beam only, which is diffracted from the extremely fine structures of the recorded pattern and thus reconstructs the image information recorded in the hologram. Holography is a means for the storage of three-dimensional images, because the complete information of the image (amplitude and phase) is recorded in the interference pattern.
(cf. History of holography)

volume hologram

A volume hologram is a holographic grating with a depth that cannot be neglected. Depth is meant here as the direction of propagation of the light beams. Thus, a hologram recorded in a thin photographic emulsion is no volume hologram. Diffraction from a volume hologram obeys the bragg condition. As a consequence, a volume hologram can only be reconstructed by reference beams with certain angles of incidence and wavelengths.

multiplexing

A consequence of the Bragg condition (cf. volume hologram) is the possibility of hologram multiplexing. Due to the fact, that a volume hologram can only be read out by a reference beam with a certain incident angle, several volume holograms can be stored in the same volume of the recording medium. Each of these holograms is read out (and was recorded) with a different incident angle of the reference beam. The reference beam angle is thus the address of the hologram.

Variation of the reference beam angle is not the only possibility of multiplexing. Due to the Bragg condition, this is also achievable by varying the beam wavelengths and the phase distribution in the reference beam (cf. phase encoding).

phase
encoding

Phase encoding ist a multiplexing technique, that was developed in our institute. It is currently utilized for the realization of a high-capacity volume holographic memory. In this technique, the reference beam is split up in several partial reference beams, the number of which is the maximum number of holograms that can be addressed. The address of the volume holograms stored is given by the spatial distribution of the relative phases in the reference beams, the so-called phase code

beam
coupling

Beam coupling is the transfer of energy in a certain direction between two laser beams interacting in a photorefractive crystal. Via constructive and destructive interference, energy is transferred from one of the interacting beams to the other. (This does not necessarily mean, that the energy transfer occurs from the stronger beam to the weaker beam!!!) The main configurations of beam coupling in photorefractive crystals are two-wave mixing and four-wave mixing. Applications of beam coupling include signal and image amplification, phase conjugation and novelty filtering

two-wave 
mixing

In two-wave mixing, two coherent laser beams interact in a photorefractive crystal (BaTiO3 is commonly used). One of the beams donates energy and is thus depleted (in the image this is beam 1), the other is amplified (beam 2). When the image information is imprinted on beam 2, the result is image amplification. Novelty filtering is obtained when the image information is imprinted on beam 1.

four-wave 
mixing

Although only three beams are incident on the crystal in four-wave mixing, it is in fact four beams that interact, because the fourth beam is generated during the interaction. Four-wave mixing can be explained in a simplified way using an analogy with holography:

Pump beam 1 (P1) and the signal beam (S) write a hologram, that is read out by pump beam 2 (P2) from the opposite direction. Thus, a conjugate beam (C) is created, counter-propagating to the incident signal beam. If P2 is the exact conjugate of P1 (which is the case, if both are unmodulated and exactly counter-propagating laser beams), C is also the exact phase conjugate of S. If P2 is chosen to be much stronger than S, beam C is not only phase conjugated with respect to S, but also amplified.

phase conjugation

Phase conjugation is the exact reversal of the phase front of a light wave. After reflection from a phase-conjugating mirror, the wave is propagating back in the direction it came from (exact counter-propagation) with exactly the same wave front. Mathematically (!!!), this is equivalent to a time reversal of the incident wave. Phase conjugation enables one to compensate for phase distortions, if the distorted wave is reflected from a phase-conjugating mirror and then passes the distorting medium again. The most commonly used geometry to obtain phase conjugation is photorefractive four-wave mixing

beam 
fanning

Beam fanning is the asymmetric fanning and deflection of a single laser beam in a photorefractive crystal. First, a very small portion of the incident beam is scattered from inhomogeneities and impurities in the crystal. The remaining part of the incident beam interacts with the scattered parts via two-wave mixing. This leads to an amplification of the scattered light in the direction of the energy transfer.

novelty 
filter

A novelty filter is an image processing element, that selects only the temporally changing parts of an input image sequence and suppresses the static parts. Novelty filters have been realized in different configurations based on photorefractive beam coupling, the probably best one is based on two-wave mixing. In this configuration, the image information is imprinted on the depleted beam. In steady state, (almost) all energy is transferred to the other beam and thus the output image is dark. After a change in the image information (in amplitude or phase), beam coupling needs a certain time to reach the steady state again. During this time, the changed parts of the input image are visible in the output image, fading away as the beam coupling approaches steady state. For example, the result of novelty filtering of an image sequence showing a moving airplane in front of a landscape is only the moving airplane, the rest of the image is dark.

feedback 
system

In general, a feedback system is a system whose output signal is used as its input signal. In optics, a feedback system can be realized using the simplest of optical elements: a mirror. Two exemplary configurations of optical feedback systems are currently used in our group:

In a single feedback system, the laser beam passes the nonlinear optical medium (in our case a photorefractive crystal), is reflected by a mirror and passes the medium a second time, thus leading to two counter-propagating beams in the medium. (cf. Squares and hexagons..., Dynamics of hexagons...)

In oscillators or resonators, the signal is traveling back and forth (or on a round trip) infinitely often. In most cases, an initial input signal is not necessary, because the signal is created by the amplification of noise. Well-known analogues are for example the acoustic feedback produced by a microphone connected with a loudspeaker and the numerous patterns that form when a tv-camera is directed onto its own monitor.

spontaneous
pattern
formation

Spontaneous pattern formation is a manifestation of a self-organization process, occurring in various nonlinear feedback systems. In this process, ordered structures (patterns) are created out of an unstructured (often uniform) input signal due to the feedback. One of the pattern types that seem to be favored by nature is the hexagonal structure (hexagons or honeycombs). Pattern formation can be encountered in various areas of science, thus revealing its universal character. Examples are nonlinear optics (where our research belongs to), hydrodynamics (Rayleigh-Benard-convection), Geology, Biology, Chemistry and Meteorology (cloud patterns).
(cf. Squares and hexagons..., Dynamics of hexagons...) 

solitons

Mathematically, Solitons are solitary solutions of the wave equation. Thus, a soliton is a wave packet that propagates without changing its shape. The first soliton ever observed was a running water wave in a river, maintaining its shape over a long distance. An optical soliton requires a nonlinear optical medium to provide the effect of self-focusing, that compensates for the effects of dispersion and diffraction, which would alter the shape of the wave packet in the regular case. In photorefractive optics, spatial solitons have been discovered only quite recently. 

In photorefractive crystals, soliton-like beams manifest as thin light beams with nearly constant shape. These beams themselves act as waveguides, thus providing a potential for future applications. Photorefractive solitons can interact in various ways and may (approximately) be described by a simple particle model (collision, annihilation, etc.).