Beams In Photorefractive Media Research Articles

Soliton shedding of Pearcey-Gaussian beams with sidelobes

Taking the fractional Schrödinger equation as the theoretical model, the propagation characteristics of the Pearcey-Gaussian beams in the photorefractive medium are studied. The results show that stable breathing solitons can only be generated under certain conditions. The nonlinear coefficient and the Lévy index will change the maximum peak intensity and the breathing period of the soliton. The maximum peak intensity increases with the increase of the nonlinear coefficient but decreases with the increase of the Lévy index, whereas the breathing period of the soliton decreases with the increase of the nonlinear coefficient and the Lévy index. Besides, the interaction of double Pearcey-Gaussian beams in photorefractive media is also analyzed. By adjusting the beam amplitude, interval parameters and relative phase, the diffraction effect of the beams and the nonlinear effect of the medium are balanced to form a single breathing soliton or the double breathing solitons, so as to control the form and transmission process of the solitons. These properties can be used to manipulate beams, which have broad application prospects in optical trapping and particle trapping.

Temporal behavior of diffusion-trapped Airy beams in photorefractive media

We theoretically examine the temporal behavior of novel Airy beams, their interactions, and their dependence on thermal energy associated with diffusive nonlinearity in photorefractive media. For the first time, it is examined under the time-dependent diffusive-saturable nonlinear Schrödinger equation (DSNLSE). The results show that optical Airy beam propagation is effectively controlled by illumination time. In long propagation distance, the significant illumination time of the thermal energy-independent optical Airy beams associated with diffusive nonlinearity lead to unstable self-deflection soliton beams over the increasingly intense competition between photorefractive nonlinearity and diffusive nonlinearity. Meanwhile, in short propagation distance, optical Airy beams were found to maintain their acceleration over a certain distance as time increased. The temporal behavior of the interaction of optical Airy beams shows that in phase, they are affected by illumination time, while out of phase, they show almost no significant changes. We find that fusion solitons eventually emerge in phases. On the other hand, we also find that this self-trapped wave packets self-bend during propagation with an acceleration rate that depends on the thermal energy associated with diffusive nonlinearity. Finally, we found that the study results agreed well with previous experiments and studies.

Controllable soliton propagation of Airy-Gaussian beams under the fractional effect

Modulated by fractional Schrödinger equation (FSE), we have mainly focused on the transmission of Airy-Gaussian (AiG) beams in photorefractive medium, adopting the split-step Fourier method. Due to the influence of photorefractive effect, solitons will fall off during the transmission, which is easier to achieve when the beam tends to Airy distribution. The characteristic parameters of solitons, including breathing period and maximum intensity, are closely related to Lévy index and photorefractive coefficient, with whose changes, not only the formation and stable propagation of solitons can be controlled, but also the transmission of solitons can be adjusted. Only when the beam amplitude is in a certain range can solitons be generated and propagated stable. And when photorefractive coefficient increases to a certain value, solitons will appear breathing state. In addition, solitons will deflect to the direction of self-acceleration carrying with high beam energy.

Coherent interactions of multi-Airy–Gaussian beams in photorefractive media

We have investigated the interaction properties of multi-Airy-Gaussian beams under the in-phase and out-phase conditions, respectively. For the case of three Airy–Gaussian beams, the breathing solitons with single, two and three components can be observed under certain conditions. The breathing solitons with single, three and four components can be observed for four Airy–Gaussian beams. The types of breathing solitons for out-phase multi-Airy–Gaussian beams are less than that of in-phase multi-Airy–Gaussian beams. Furthermore, the types of breathing solitons can be controlled by adjusting the space interval, nonlinear parameter and self-accelerating direction.

Interaction of Airy beams in photorefractive media

We investigate numerical interactions between two Airy beams with different relative phases in photorefractive (PR) nonlinear media in one transverse dimension. It is shown that solitons and soliton pairs are generated that are not accelerating, although the incident beams exhibit acceleration property. When the relative phase is very small, the attraction between the two Airy beams is strengthened and their propagation behavior is similar to that in in-phase case, where the two Airy beams attract each other and the main lobes can fuse into one single breathing soliton, secondary lobes can generate soliton pairs with symmetric intensity distribution. While the relative phase is close to [Formula: see text], these beams present out-phase propagation with strong repulsive effect. Their interaction properties are sensitive to both the interval and relative phase between the two Airy beams.

Propagation and interaction of finite-energy Airy–Hermite–Gaussian beams in photorefractive media

We investigate numerically the propagation and interaction characteristics of finite-energy Airy–Hermite–Gaussian beams in biased photorefractive media. For the case of first-order Hermite polynomial, two main lobes of the initial input beam can form breathing solitons with two components. The interval between two soliton components in the \(y{\text{-direction}}\) increases gradually with the propagation distance, while the central position of two soliton components in the \(x{\text{-direction}}\) is almost unchanged during propagation. Moreover, in interaction situations, four main lobes of the two Airy–Hermite–Gaussian beams can also form breathing solitons with four components under the in-phase and out-of-phase conditions, respectively.

Interactions between self-accelerating beams in photorefractive media.

We investigate interactions between in-phase or out-of-phase Airy beams and nonlinear accelerating beams in photorefractive crystals by means of direct numerical simulations. Since self-accelerating beams possess infinite energy, we evaluated the propagation of two shifted counter beams by truncating the oscillating tails. The numerical results show that the external bias electric field has a profound effect on the propagation dynamics and the solitons shed from the Airy beam. We also found that during interactions between two nonlinear accelerating beams, single solitons, soliton pairs, and bound breathing solitons were produced. When the nonlinear accelerating beam collides with a soliton beam, the main lobe continues accelerating while the soliton intensity fluctuates with the lobes.

Time Measurement of Local Photorefractive Response of a Medium Using the π Shift of an Interference Pattern

A method for the measurement of the recording/erasing time of dynamic phase gratings that are recorded by phase-modulated beams in photorefractive medium with local response is presented. The method is based on the detection of the intensity modulation of output beams in the course of rerecording of the grating after a shift of the interference pattern by one-half of spatial period. It is demonstrated that a relatively high sensitivity of the method is due to the selective detection of signals at a high frequency and a high efficiency of energy exchange of the recording beams in comparison with the diffraction of the probe beam. The application of the method in dynamic holographic seismographs is discussed.

Modulational instability of optical beams in photorefractive media due to two-wave or parametric four-wave mixing effects

Modulational instability in a photorefractive medium is studied in the presence of two-wave mixing. We then propose and derive a model for forward four-wave mixing in the photorefractive medium and investigate the modulational instability induced by four-wave mixing effects. By using the standard linear stability analysis the instability gain is obtained. In both cases, the geometry is such that the effect of self-phase-modulation self-focusing is suppressed and only the holographic focusing nonlinearity is acting.

Counterpropagating self-trapped beams in photorefractive crystals

A time-dependent model for the formation of self-trapped optical beams in photorefractive media by counterpropagating laser beams is analysed. It is shown that dynamically the beams may form stable steady-state structures or display periodic and irregular temporal behaviour. Steady-state solutions of non-uniform cross section are found, representing a general class of self-trapped waveguides, that include counterpropagating spatial vector solitons as a particular case. Two critical curves are identified in the plane of parameters, the first one separating vector solitons from the stable bidirectional waveguides and the second one separating stable waveguides from the unstable ones. Dynamically stable rotating beam structures are discovered that have no analogues in the usual steady-state theory of spatial solitons.

Propagation and interaction of single and incoherently coupled nondiffracting beams in photorefractive medium with purely diffusion nonlinearity

We have numerically found profiles of (1+1)D single and incoherently coupled nondiffracting beams in the photorefractive medium with purely diffusion nonlinearity. The main features of propagation and interaction of the nondiffracting beams are analysed and it is shown that interactions in the medium with diffusion nonlinearity are accompanied with the energy redistribution processes that can result in the fusion of the nondiffracting beams.

Dipole-mode vector solitons in anisotropic photorefractive media

Stable dipole-mode vector solitons in photorefractive (PR) crystals are studied, both in numerical simulations and in experimental investigation. Numerically exact multi-humped solitary solutions to the propagation equations of two incoherently coupled beams in PR media with an anisotropic nonlocal material response are found. A continuous set of dipole-mode vector solitons, ranging from the solitons with negligible dipole-mode contribution to the solitons with negligible ground mode contribution, is identified. The results are compared with experimental data.

Optical spatial shock waves in photorefractive media

We show that the evolution equations describing the two-wave mixing interaction between two codirectional optical beams in photorefractive media can allow spatial shock-wave solutions. Our analysis indicates that these kink-type wavefronts move together at an angle that falls outside the initial +/-straight theta sector of propagation. The apparent direction of propagation and the spatial widths of these optical shock-wave beams are directly related to their relative intensity.

Simulation of the temporal behavior of soliton propagation in photorefractive media.

We consider the propagation of light beams in photorefractive media in the framework of a (1+1)-dimensional model. The Kukhtarev band transport model is introduced both in a time-dependent differential equation describing the evolution of the space charge field and in a nonlinear wave propagation equation. This latter is then numerically solved with a beam propagation method routine. The evolution in time and space of an initially diffracting laser beam is simulated as a function of initial profiles and waists. The beam is shown to go through a transient overfocused state prior to relaxing to a steady state soliton. Additional features such as the stability condition of the system or effects such as optical branching and soliton interactions are studied.

Photorefractive screening solitons of high and low intensity

We analyze self-trapping of optical beams in photorefractive media for low irradiances that are typical of cw lasers and high irradiances that are typical of short-pulse lasers and obtain bright and dark soliton solutions in one transverse dimension. Whereas in the low-intensity regime photorefractive screening solitons are trapped by the refractive-index change that is related to the electric field associated with ionized donors or acceptors, in the high-intensity regime the index is related to the field that is also associated with free carriers. Since the time necessary to form the soliton scales inversely with the intensity, one expects a very fast response time in the high-intensity regime, and this suggests attractive applications in optical switching and reconfigurable optical waveguides. We show that throughout the entire intensity range dark solitons require lower voltages and less energy per pulse for applications than do bright solitons.

Dimensionality and size of photorefractive spatial solitons

We study experimentally self-trapping of optical beams in photorefractive media and show that the trapping is inherently asymmetric with respect to the two (transverse) trapping dimensions. We also present experimental results that show how the sizes of the resultant photorefractive spatial solitons are independent (within their range of existence) of the amplitude of the externally applied electric field used to generate them.

Propagation of light beams in photorefractive media: Fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries.

We investigate propagation of light beams in photorefractive media by direct numerical simulation. The two dimensional model is based on solution of nonlinear material equations and parabolic equations for the electromagnetic field. We show that this set of equations describes the wealth of complicated spatial structures observed in these media. We present results on fanning of a single beam and on formation of various four-wave-mixing geometries including self-conjugation of a light beam via total internal reflection, mutual phase conjugation, and self-bending of two counterpropagating beams.

Self-trapping of optical beams in photorefractive media

We study the possibility of self-trapping of an optical beam in a photorefractive medium under the combined influence of diffraction and self-scattering (two-wave mixing) of its spatial frequency components. We investigate the spectrum of solutions for the resulting photorefractive spatial solitons and discuss their unique properties. Design considerations and material requirements for experimental realization of these solitons, together with specific examples, are given.

Phase conjugation involving incoherent counterpropagating beams in photorefractive media

We propose and analyze a new type of phase conjugation between counterpropagating beams in photorefractive materials based on diffraction from transmission gratings only. This effect does not require temporal coherence between the counterpropagating beams and may occur spontaneously, with no external seeding, even with wide (frequency) band light sources.

Diffraction properties of multiple-beam photorefractive gratings

We have analytically solved the problem of N mutually incoherent pairs of beams in photorefractive media, each pair of which shares a common grating. The results are applied to study simultaneous read–write of dynamic photorefractive holograms with beams of comparable intensity. The diffraction efficiency is shown to be a nonlinear function of the read-beam intensity and is nonreciprocal with respect to readout from the two input ports. A complete energy transfer between the two write beams occurs in a finite thickness of the photorefractive crystal, in contrast to the infinite thickness required in the standard two-beam coupling case.