Photorefractive Media Research Articles

A numerical approach to nonlinear propagation of light in photorefractive media

The article presents a new approach to the analysis of light propagation in photorefractive materials. The discussed numerical method can be used for an analysis of the dynamics of nonlinear effects taking place in those media in which an analytical approach requires the use of approximations or is impossible. As an example of how the method works, the results of simulation are shown, illustrating the process of spatial solitary wave formation in two materials: a photorefractive semiconductor and a ferroelectric crystal.

Optical induction of 3D rotational symmetry refractive lattices by combined interferometric-mask method in doped LiNbO3 crystals

A novel combined interferometric–mask method for the formation of micro- and nanometric scale three-dimensional (3D) rotational symmetry quasi-crystalline refractive lattice structures in photorefractive materials is demonstrated experimentally. The method is based on micrometric scale spatial modulation of the light by amplitude mask in the radial directions and along the azimuthal angle and the use of counter-propagating beam geometry building up Gaussian standing wave, which defines the light modulation in the axial direction with half-wavelength periodicity. 3D intensity pattern can be represented as numerous mask-generated 2D quasi-periodic structures located in each anti-node of the standing wave. The formed 3D intensity distributions of the optical beams can be imparted into the photorefractive medium thus creating the micro- and sub-micrometric scale 3D refractive index volume lattices. The used optical scheme allows also the formation of 2D lattices by removing the back-reflecting mirror. 2D and 3D refractive lattices were recorded with the use of 532 nm laser beam and rotational symmetry mask in doped lithium niobate crystals and were tested by the probe beam far-field diffraction pattern imaging and direct observation by phase microscope. The formed rotational symmetry 3D refractive structures have the periods of 20–60 μm in the radial directions, 60 μm along the azimuthal angle and half-wavelength 266 nm in the axial direction.

Properties of optical spatial solitons in photorefractive crystals with special emphasis to two-photon photorefractive nonlinearity

We have reviewed recent developments of some aspects of optical spatial solitons in photorefractive media. Underlying principles governing the dynamics of photorefractive nonlinearity have been discussed using band transport model. Nonlinear dynamical equations for propagating solitons have been derived considering single as well as two-photon photorefractive processes. Fundamental properties of screening and photovoltaic solitons have been considered. For each type of solitons, three different configurations i.e., bright, dark and gray varieties have been considered. Mechanisms of formation of these solitons due to single as well as two-photon photorefractive processes have been considered and their self bending discussed. Vector solitons, particularly, incoherently coupled solitons due to single photon and two-photon photorefractive phenomena have been highlighted. Existence of some missing solitons have been also pointed out. In addition, incoherent solitons and discrete spatial solitons in optically-induced photorefractive lattices are also discussed.

Slow and stored light by photo-isomerization induced transparency in dye doped chiral nematics

Decelerating and stopping light is fundamental for optical processing, high performance sensor technologies and digital signal treatment, many of these applications relying on the ability of controlling the amplitude and phase of coherent light pulses. In this context, slow-light has been achieved by various methods, as coupling light into resonant media, Brillouin scattering in optical fibers, beam coupling in photorefractive and liquid crystal media or engineered dispersion in photonic crystals. Here, we present a different mechanism for slowing and storing light, which is based on photo-isomerization induced transparency of azo-dye molecules hosted in a chiral liquid crystal structure. Sharp spectral features of the medium absorption/dispersion, and the long population lifetime of the dye metastable state, enable the storage of light pulses with a significant retrieval after times much longer than the medium response time.

Optical data encryption using time-dependent dynamics of refractive index changes in LiNbO_3

We present a method for optical encryption of information, based on the time-dependent dynamics of writing and erasure of refractive index changes in a bulk lithium niobate medium. Information is written into the photorefractive crystal with a spatially amplitude-modulated laser beam which when overexposed significantly degrades the stored data making it unrecognizable. We show that the degradation can be reversed and that a one-to-one relationship exists between the degradation and recovery rates. It is shown that this simple relationship can be used to determine the erasure time required for decrypting the scrambled index patterns. In addition, this method could be used as a straightforward general technique for determining characteristic writing and erasure rates in photorefractive media.

Ground-state counterpropagating solitons in photorefractive media with saturable nonlinearity

We investigate the existence and form of (2+1)-dimensional ground-state counterpropagating solitons in photorefractive media with saturable nonlinearity. General conditions for the existence of fundamental solitons in a local isotropic model that includes an intensity-dependent saturable nonlinearity are identified. We confirm our theoretical findings numerically and determine the ground-state profiles. We check their stability in propagation and identify the coupling constant threshold for their existence. Critical exponents of the power and beam width are determined as functions of the propagation constant at the threshold. We finally formulate a variational approach to the same problem, introduce an approximate fundamental Gaussian solution, and verify that this method leads to the same threshold and similar critical exponents as the theoretical and numerical methods.

Generation of linear and nonlinear propagation of three-Airy beams

We report the first experimental demonstration of the so-called three-Airy beams. Such beams represent a two-dimensional field that is a product (rather than simple superposition) of three Airy beams. Our experiments show that, in contrast to conventional Airy beams, this new family of Airy beams can be realized even without the use of truncation by finite apertures. Furthermore, we study linear and nonlinear propagation of the three-Airy beams in a photorefractive medium. It is found that a three-Airy beam tends to linearly diffract into a super-Gaussian-like beam, while under nonlinear propagation it either turns into three intensity spots with a self-defocusing nonlinearity or evolves into a self-trapped channel with a self-focusing nonlinearity.

Surface waves formed at the interface between a metal and a photorefractive crystal

The formation conditions and the energy variation of surface waves at the interface between a metal and a photorefractive crystal are investigated by using the particle oscillator model and numerical techniques. Our analysis indicates that the positive and negative values of the propagation constant affect the type of surface waves and the energy distribution: formation surface waves are nonlocal surface waves for negative values of the propagation constant and are oscillating surface waves and localized surface waves for positive values of the propagation constant, and the energy of localized surface waves in photorefractive medium increases monotonically with the propagation constant value increasing. In a given physical system, one can control the different orders and the waveforms of localized surface waves by regulating the variable parameter determining the strength of nonlinear effects.

Self-trapping and periodic modulation of beam propagation in semiconductor photorefractive medium

We have deduced a two-level form of beam evolution in photonic lattices of semiconductor photorefractive medium and its classical canonical form of the two-level equation. We analytically calculate the fixed points of the classical canonical aligns, analyze its stability and calculate the critical value of topology changes. According to the classical canonical form of the two-level equation, we make space phase diagram, further analyze the self-trapping of beam propagation in semiconductor photorefractive medium and find two kinds of self-trapping: 1) Both the population difference and the relative phase in energy levels oscillate near an equilibrium point in the phase space. 2) The population difference in energy levels oscillate near an equilibrium point while the relative phase increases monotonously. From the three aspects of high frequency, low frequency, and intermediate frequency, we investigate how an external periodic field influences the self-trapping and find that the external high frequency periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. It makes the self-trapping occur with small nonlinear effect when the beam propagates in semiconductor photorefractive medium.

Temporal behavior of low-amplitude dark spatial solitons in two-photon centrosymmetric photorefractive media

We investigate the temporal behavior of low-amplitude dark spatial solitons in biased centrosymmetric crystals with two-photon photorefractive effects. The expressions of time-dependent space-charge field and dynamical evolution equation are derived. The temporal behaviors of the intensity profiles and the intensity full width at half maximum (FWHM) of dark solitons are investigated by numerical method. The results indicate that a broad soliton is generated at the beginning, and as time evolves, the intensity width of solitons decrease monotonously to a minimum value toward steady state. Within the same propagation time, the higher the ratio of soliton peak intensity to the dark irradiation intensity is, the shorter the FWHM of dark solitons is.

Reshaping the trajectory and spectrum of nonlinear Airy beams

We demonstrate theoretically and experimentally that a finite Airy beam changes its trajectory while maintaining its acceleration in nonlinear photorefractive media. During this process, the spatial spectrum reshapes dramatically, leading to negative (or positive) spectral defects on the initial spectral distribution under a self-focusing (or defocusing) nonlinearity.

Generation of quadrupoles through instability of dark rings in photorefractive media

We have produced beams with dark rings and studied their propagation through photovoltaic photorefractive media. We observe that dark rings, instead of forming dark ring solitons, break into vortex–antivortex pairs, forming quadrupoles. The experimental results could be taken as a consequence of modulational instability during beam propagation that is revealed through our numerical analysis.

Conservation and transfer of orbital angular momentum of light in optically induced photonic lattices

Using analytical and numerical methods, we elucidate the conservation and transfer of orbital angular momentum of light beams propagating in fully periodic and radially periodic photonic lattices, induced in photorefractive crystals. We consider paraxial beams propagating in both fixed and interacting lattices, in both copropagating and counterpropagating geometries, in photorefractive media with saturable nonlinearity. We also discuss the influence of beam intensity and the finite lattice size on the angular momentum transfer in such photonic lattices.

Theoretical analysis of the effects of frequency detuning dependence of photorefractive two- beam coupling coefficient on gain and phase-shifts of the signal beam for a coupled unidirectional photorefractive ring resonators

Dependence of two-beam coupling gain and phase-shift of the signal beams on the frequency detuning for a coupled unidirectional ring resonators based on non-degenerate two-wave mixing in the photorefractive crystals have been investigated in details. The effects of various parameters characterizing the photorefractive medium such as frequency detuning, absorption strength, two-beam energy coupling strength and pump intensity of the external laser beams, on the two-beam coupling gain and phase-shift of the signal beams for a coupled UPRR have also been studied in details. It has been found that the photorefractive gain of the signal beam in the primary cavity of the coupled UPRR can be enhanced to the higher order by taking the lower value of the frequency detuning of the primary cavity which could exist at much lower value of the absorption strength of the crystal B. This higher value of photorefractive gains in the cavities are responsible for the strong coupling between the modes of the oscillations of the coupled UPRR.

Dynamic study of the gain in two beam coupling in photorefractive materials

Wave equations describing the non-linear two-beam coupling have been solved and expressions for the gain of the two beams in the photorefractive crystals have been derived. In case of the degenerate two-beam coupling, the gain depends upon the crystal thickness, coupling coefficient, absorption coefficient and the input intensity ratio. The effect of these parameters on the gain has been studied in details. In case of non-degenerate two-beam coupling the gain not only depends upon crystal thickness, coupling coefficient, absorption coefficient and the input intensity ratio but also on the response time of the photorefractive medium. This response time is the function of concentration ratio. The influence of oscillation frequency shift, concentration ratio on the gain for the non-degenerate two-beam coupling has also been studied.

Peculiarities of photonic lattices recorded by Bessel beam technique in LiNbO3:Fe crystal

The aim of this work is the investigation of the peculiarities of recording of the refractive photonic lattices by Bessel beam technique in photorefractive Fe doped LiNbO3 crystal. Optical C-axis of the crystal was oriented along the crystal surfaces. The Gaussian laser beam at 532nm wavelength with 17.7mW is transformed into the Bessel beam by an axicon. The intensity pattern of non-diffracting Bessel beam is imparted into the photorefractive medium, being irradiated, via electro-optic effect, thus creating radially modulated refractive index photonic lattices. The annular refractive photonic lattice created inside the LN:Fe crystal has 10 μm period in radial direction. The recorded photonic lattice has been tested by probe beam. The direct observation of recorded lattice by phase microscope was also performed. The azimuthal dependence of created lattice was observed. The qualitative explanation is given.

Multiple-hologram recording with one-beam encoding

This research proposes a method that uses a single object beam to record multiple images in a photorefractive crystal medium without having to use any reference wave. The object beam in this study is modulated using a lenticular lens array sheet to produce a set of sub-object beams. These beams are then angularly separated on the recording plane and their scattered waves overlapped in an iron-doped photorefractive LiNbO₃ crystal. This single-exposure, multiple-holographic-recording method is simple and proven successful via the experiments that recorded four holograms in a 30 x 1 mm³ LiNbO₃:Fe crystal with single exposure.

Nonlinear lattice structures based on families of complex nondiffracting beams

We present a new concept for the generation of optical lattice waves. For all four families of nondiffracting beams, we are able to realize corresponding nondiffracting intensity patterns in a single setup. The potential of our approach is shown by demonstrating the optical induction of complex photonic discrete, Bessel, Mathieu and Weber lattices in a nonlinear photorefractive medium. However, our technique itself is very general and can be transferred to optical lattices in other fields such as atom optics or cold gases in order to add such complex optical potentials as a new concept to these areas as well.

Bright spatial solitons in biased centro-symmetric photorefractive medium under drift as well as diffusion effects

This paper presents an investigation on the propagation characteristics of optical spatial solitons in a biased centro-symmetric photorefractive medium. Unlike earlier attempts on photorefractive solitons, in the present investigation, we have given equal significance to the effects of charge drift and their diffusion. We have obtained dynamical equations for solitons employing paraxial ray approximation and examined criteria for stationary propagation. Trajectories of stationary solitons have been examined.

Enhancement of the diffraction efficiency of the hologram recorded in photorefractive media under the action of external electric field

Diffraction efficiency as a function of the applied electric field for the non-linear regime has been calculated by solving numerically the beam coupling equations. The refractive index variation used in the beam coupling equations was calculated directly from the material rate equations via the total space charge field. The diffraction efficiency of the holograms recorded in photorefractive media is not only a function of the applied external electric field but also a function of crystal thickness, diffusion field, reduced fringe contrast modulation ratio and absorption coefficient of the materials. The effects of these parameters on the efficiency of the holograms have been studied in details. In the absence of the external applied field, it is found that the diffraction efficiency of the holograms could be maximized for a thinner photorefractive crystal having lower absorption coefficient and higher value of diffusion field, which could exist at a much lower value of reduced fringe contrast modulation ratio of the index grating. More efficient holograms can be recorded in the presence of the externally applied electric field as compared to the case of no external field.