Photorefractive Media Research Articles

Nonlinear dynamics of two-wave coupling process

We present a closed-form solution for the two-wave coupling process, resulting in a solution with an interesting part, the arbitrary function Lambda(t), not being considered in the previous works. In the photorefractive medium, it has been shown that a moving grating will produce a phase shift in the coupling constant. To our knowledge, this has not been derived directly from the grating dynamic equations. We will also show that the temporal dynamics does not have any asymptotically stable equilibrium points of an exponential form. As an example, we have developed resonance conditions resulting in a new expression for the frequency detuning of a resonator with a photorefractive gain medium.

Incoherently coupled screening soliton pairs composed of spatially incoherent multimode beams

Incoherently coupled screening soliton pairs composed of spatially incoherent mu ltimode beams can be established in biased photorefractive media under steadys t ate conditions, every soliton constituent of which is not only spatially incoher ent with respect to each other, but also to itself. We study that the property o f th ese incoherently coupled soliton pairs in brightbright, darkdark configurati on s by the coherent density approach and get the intensity expression of these sol iton pairs. The propagation characteristics of coherent components that compose each soliton constituent of the coupled soliton pairs are discussed in detail.

Molding and Stretched Evolution of Optical Solitons in Cumulative Nonlinearities

The observation of initial time dynamics of self-trapping in photorefractive media indicates that optical spatial solitons supported by intense cumulative nonlinearities manifest temporally nonlocal signatures in the form of stretched exponential behavior. This general result, supported also by numerical predictions, is triggered by wave shaping in a time-constant buildup map, a consequence of the spatially resolved inertial response intrinsic to the geometrical transition from a diffracting to a self-focused beam, inherent to soliton appearance.

Interactions in large arrays of solitons in photorefractive crystals

Large two-dimensional spatial soliton arrays are generated experimentally and numerically in photorefractive media and their waveguiding properties at red and infrared wavelengths are demonstrated. An enhanced stability of solitonic lattices is achieved by exploiting the anisotropy of coherent soliton interaction and by controlling the relative phase between soliton rows. Manipulation of individual solitonic channels is accomplished by the use of separate control beams.

Solitary beam formation with partially coherent light in an anisotropic photorefractive medium

We report on the stable self-focusing of light for various degrees of spatial coherence. Since the diffraction of a partially spatial coherent light beam is mainly governed by the transverse correlation width, its self-focusing is generally non-trivial. Here, we systematically demonstrate that partially coherent solitons can be generated in a non-instantaneous nonlinear material when the external parameters are properly adapted to the degree of coherence of the light beam.

Stabilization of the interference pattern when recording volume transmission holograms

This paper describes a method of stabilizing the interference pattern when recording threedimensional transmission holograms in photochromic and photorefractive media. The method is based on using the dynamic interaction of the interference field with the recorded hologram.

Mutual spatial-soliton trapping in photorefractive media: experiment versus theory

We investigate the interaction of two-dimensional solitons propagating at small angles in a photorefractive crystal. We observe fusion of the beams when the intersecting angle is lower than some critical value. We measure the critical angle for fusion for different relative phase relations of the beams and demonstrate how this effect can be used to steer and switch the propagation of an additional optical beam.

Spatial optical solitons supported by mutual focusing.

We study composite spatial optical solitons supported by two-wave mutual focusing induced by cross-phase modulation in Kerr-like nonlinear media. We find the families of both single- and two-hump solitons and discuss their properties and stability. We also reveal remarkable similarities between recently predicted holographic solitons in photorefractive media and parametric solitons in quadratic nonlinear crystals.

Self-trapped bidirectional waveguides in a saturable photorefractive medium.

A time-dependent model for the generation of joint waveguides by counterpropagating light beams in photorefractive crystals is introduced. Depending on initial conditions and parameter values, the beams form stable structures or display periodic and irregular dynamics. Steady-state solutions nonuniform in the direction of propagation are found, representing a general class of self-trapped waveguides that include counterpropagating spatial vector solitons as a particular case.

Effect of the photosensitizer on the photorefractive effect using a lowT g sol-gel glass

We prepared the photorefractive sol-gel glass based on organic-inorganic hybrid materials containing a charge transporting molecule, second-order nonlinear optical (NLO) chromophore, photosensitizer, and plasticizer. Carbazole and 2-{4-[(2-hydroxy-ethyl)-methyl-amino]-benzylidene}-malononitrile were reacted with isocyanatotriethoxy silane and the functionalized silanes were employed to fabricate the efficient photorefractive media including 2,4,7-trinitrofluorenone (TNF) to form a charge transfer complex. The prepared sol-gel glass samples showed a large net gain coefficient and high diffraction efficiency at a certain composition. As the concentration of photosensitizer increased, the photorefractive properties were enhanced due to an increment of charge carrier density. Dynamic behavior of the diffraction efficiency was also investigated with the concentration of the photosensitizer.

Stability of screening solitons in photorefractive media.

Normal mode stability of both rectilinear and self-bending photorefractive screening solitons is considered. In each case, the Evans function procedure is used to investigate stability and to search for internal modes. For the rectilinear case, a standard Evans function procedure is applied. However, in the self-bending case the asymptotic form of the eigenvalue problem is a system of Airy equations, instead of the usual system of constant coefficient differential equations. To overcome this difference, a modified version of the Evans function method, using Airy functions rather than exponentials, is implemented and applied. The results confirm stability and give an internal mode pattern in good agreement with full numerical integration.

Simulation of the temporal behavior of one single laser pulse in a photorefractive medium

This paper presents a numerical modeling of the temporal evolution of the refraction index induced by a nanosecond single laser pulse propagating in a biased photorefractive crystal. Assuming particular hypotheses typical for a short pulse illumination, a nonlinear time dependent partial differential equation, which describes the mechanisms of space–charge field build up and evolution, is derived from a mono-dimensional Kukhtarev band transport model. The numerical resolution of this space–charge equation is then coupled to the simulation of the propagation of a beam in a nonlinear medium using a beam propagation method. The results evidence the spatial self-focusing of a single nanosecond laser pulse. A description of the output beam profile evolution during the laser pulse is obtained and the role of different physical parameters such as the carriers mobility and the fluence on self-focusing is investigated. A successful comparison to previous experimental measurements is reported.

Nonuniform dynamic gratings in photorefractive media with nonlocal response.

The amplitude of the phase dynamic grating is a nonuniform space distributed in photorefractive crystals with nonlocal response as a result of energy transfer between the interacted waves. The dynamical process of grating formation in the case of transmission two- and four-wave mixing is described by the damped sine-Gordon equation that governs the soliton propagation. A stationary soliton solution for the grating amplitude profile was obtained. Experiments on observation of a nonuniform distribution of the grating amplitude through the crystal volume are presented. It is experimentally shown that the changes of the grating amplitude profile in dependence of input intensity ratio match the solutions of the damped sine-Gordon equation in steady state. The diffraction efficiency of energy transfer is determined by the value of the integral under the grating amplitude profile. The soliton profile is altered with changing input intensity ratio of recorded beams. It provides the effect of diffraction efficiency management by changing the half-width and the position of the soliton. The theory predicts a multisoliton behavior in reversible media with strong amplification gain that leads to auto-oscillations of output wave intensities.

Spatiotemporal self-organization upon two-wave mixing in a photorefractive medium

Nonlinear dynamics of recording volume holographic gratings upon two-wave mixing in an inertial photorefractive media were studied. It is found that the space-time dependence of the grating diffraction efficiency can be quasi-regular, allowing the understanding of the experimentally observed irregular behavior of the diffracted light intensity.

Waveguides and waveguide arrays formed by incoherent light in photorefractive materials

We report on experimental observations of nonlinear optical waveguides and waveguide arrays formed by incoherent light in photorefractive materials. Such waveguides are made possible by creating partially spatially incoherent solitons in a noninstantaneous self-focusing photorefractive medium. In addition to planar, Y-junction, and circular waveguides, we report the first demonstration of pixel-like spatial solitons from partially incoherent light. An array of as many as 56×56 soliton pixels is readily realized by launching a spatially modulated incoherent beam into the self-focusing photorefractive medium. These solitons are stable and robust, forming a steady-state two-dimensional waveguide array in which optical coupling and control of local waveguide channels can be achieved. These experiments bring about the possibility of controlling high-power laser beams with low-power incoherent light sources as well as the possibility for optically inducing three-dimensional reconfigurable photonic lattices in a bulk medium.

Photorefractive solitons

We present a review of recent works on spatial optical solitons in photorefractive media. We discuss fundamental properties of screening solitons and their interaction.

Observation of the Light Beam Evolution in a Biased SBN Crystal in Pulsed and Continuous Regime

Photorefractive self-focusing and self-trapping has proved, over the past decade, to be an efficient low power method able to provide beam control and steering. Over the years, photorefractive Sr x Ba1 − x Nb2O6 has been shown to be the most promising photorefractive media in this field. Its ability to sustain photorefractive solitons at steady state has been thoroughly investigated. In this paper, the focus is set on the temporal development of self focusing in Sr x Ba1 − x Nb2O6, evidencing a soft transition from self-focusing through self-bending and finally optical-branching. This evolution is shown to occur not only as a function of experimental conditions such as electric field applied or beam intensity, but also as a function of time.

Control of the photorefractive effect using a low T g sol-gel glass

We prepared the photorefractive sol-gel glass based on organic-inorganic hybrid materials containing a charge transporting molecule, second-order nonlinear optical chromophore, photosensitizer, and plasticizer. Carbazole and 2-{ 4-[(2-hydroxyethyl) methylamino]benzylidene}malononitrile were reacted with 3-isocyanatopropyl triethoxysilane and the functionalized silanes were employed to fabricate the efficient photorefractive media including 2,4,7-trinitrofluorenone (TNF) to form a charge transfer complex. The simplest way to vary the composition in the matrix was to mix the desired amount of the functionalized alkoxysilane. The prepared sol-gel glass samples contained a large amount of nonlinear optical (NLO) chromophore compared to that of the charge transporting molecules. They showed a large net gain coefficient and high diffraction efficiency at certain conditions.

Effect of phase shift in shape changing collision of solitons in coupled nonlinear Schrödinger equations

Soliton interactions in systems modelled by coupled nonlinear Schroedinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features : shape changing intensity redistributions, amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable 2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called partially coherent soliton (PCS) solution discussed much in the recent literature.

Photorefractive inorganic–organic polymer-dispersed liquid-crystal nanocomposite photosensitized with cadmium sulfide quantum dots

We report on a new photorefractive medium consisting of a hole-transporting polymer composite matrix, electro-optically active nanodroplets of liquid crystals, and cadmium sulfide quantum dots as photosensitizers. This medium exhibits greater than 90% internal diffraction efficiency and a net two-beam coupling gain of 22.5 cm(-1) with a response time of <1 min . Data on optical transmission are also presented.