Photorefractive Media Research Articles

A modified Snyder–Mitchell model and its optical soliton solutions in nonlocal photorefractive media

A modified Snyder–Mitchell model and its optical soliton solutions in nonlocal photorefractive media

The control for multiple kinds of solitons generated in the nonlinear fractional Schrödinger optical system based on Hermite-Gaussian beams

In this paper, we investigate the control for Hermite-Gaussian (HG) solitons in the nonlinear fractional Schrödinger equation (FSE) by sequentially applying power function modulations, cosine modulations, parabolic potentials, and quadratic phase modulations (QPM). In the photorefractive media, the HG beam forms scattered breathing solitons when the fractional diffraction effect equilibrates with nonlinear effect. Under the power function modulation, the soliton maintains an equidistant linear transmission along the z-axis, and the number of solitons is equal to the mode. In the cosine modulation, the soliton distorts and its energy rapidly decreases after a certain distance of transmission. The time of the distortion varies with the Lévy index, photorefractive coefficient, modulation frequency and order. The freak spots exhibit a “flower” shape pattern. If a parabolic potential is introduced, the HG beam forms crawling soliton pairs or merges into a single bounded breathing soliton by adjusting the correlation among the Lévy index, nonlinear and parabolic coefficients. By increasing the nonlinear coefficient in the negative QPM regime, the defocusing HG beam emits several “filiform” breathing solitons during its propagation, which move in a parallel straight line to each other. The HG beam is transformed into a single fine breathing soliton after being focused under a positive QPM. The time of the formation and breathing rate varies with the Lévy index, QPM and nonlinear coefficients. Moreover, the number of solitons changes irregularly with modes. These results are significant for applications in optical communication, optical device design, and optical signal processing.

Creation of periodic structures in a thick photopolymerizing layer

AbstractThe possibility of optical creation of polymer structures with a periodic distribution of the refractive index in a layer of a photopolymerizing composition, the thickness of which significantly exceeds the depth of field of the used projection system, is considered. Nonlinear wave processes in such an irreversible photorefractive medium for grating‐forming radiation are considered. Using computer simulation, modes of stable self‐channeling of closely propagating light beams have been found, as a result of which regular extended waveguide tracks can be obtained. The results of experiments on the creation of thick polymer gratings using a conventional incoherent projection system are demonstrated. In a composition based on industrial monomer OCM‐2, gratings with a period of 10 μm and a thickness of more than 1 mm were obtained.

Why phenomenological theory cannot be used to analyze the dynamics of dark photorefractive solitons

The currently used theory of both bright and dark spatial photorefractive (PR) solitons is a phenomenological theory. In the work we consider the dynamics of dark beams using a microscopic model based on the PR transport equations. It is generally believed that such a theory is more accurate. It has been found that these two approaches can give completely different predictions regarding the formation time of dark beams. The discrepancies can reach up to two orders of magnitude. An approximate analytical solution was presented and a new time constant was introduced taking into account crystals from three classes of PR materials: ferroelectrics, sillenites and semiconductors. Full Text: PDF References A. Katti, R.A. Yadav, Optical Spatial Solitons in Photorefractive Materials (Singapore, Springer, 2021) CrossRef E. DelRe, M. Segev, Ch. 23 in Self-focusing: Past and Present, ed. by R.W. Boyd, S.G. Lukishova, Y.R. Shen (New York, Springer, 2009). CrossRef M. Wichtowski, "On conformity of solutions for one-dimensional photorefractive screening solitons with the Kukhtarev–Vinetskii model", Appl. Phys. B 120, 527 (2015). CrossRef M. Segev, B. Crosignani, P. Di Porto et al., in Photorefractive Spatial Solitons, (Kluwer Academic Publisher, New York, 2002). DirectLink K. Zhan, Ch. Hou, S. Pu, "Temporal behavior of spatial solitons in centrosymmetric photorefractive crystals", Opt. Laser Technol. 43, 1274 (2011). CrossRef J. Maufoy, N. Fressengeas, D.Wolfersberger, G. Kugel, "Simulation of the temporal behavior of soliton propagation in photorefractive media", Phys. Rev. E 59, 6116 (1999). CrossRef A. Katti, M.S. Pande, "Formation characteristics of dark solitons in photorefractive crystals having both linear and quadratic electro-optic effect simultaneously", Opt. Quantum Electron. 55, 1132 (2023). CrossRef

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.

Temporal behavior of bright and dark spatial solitons in photorefractive crystals having both the linear and quadratic electro-optic effects based on low amplitude approximations

We investigate the formation or time evolution characteristics of bright and dark optical spatial solitons in novel photorefractive media with linear and quadratic electro-optic effects. This study was carried out at low amplitude. By the application of low amplitude approximation to the time-dependent wave (soliton) propagation equation, bright soliton solution (BSS) and dark soliton solution (DSS) were each obtained analytically, and both are exact solutions. The change in soliton width or the intensity full width at half maximum (FWHM) of two soliton types can also be calculated directly from the BSS and the DSS, providing a suitable description of the bright and dark solitons time evolution in novel photorefractive media. Only steady state solitons are formed in low amplitude, and the quasi-steady state soliton does not exist as reported at high saturation values. We compare analytical BSS with numerical calculation results of previous studies and find good agreement between analytics and numerics on the amplitude limit. In contrast to bright solitons, which can arise in the dominant linear or quadratic electro-optic effect, dark solitons in novel photorefractive media always exist under the dominant quadratic electro-optic effects only. We found that the time evolution of dark solitons from the DSS corresponds with time-independent optical spatial solitons studies in a similar media. Lastly, BSS and DSS found at low amplitude limits are fundamental soliton solutions or initial state soliton (at low peak intensity ratio regime) that can play an important role in further investigations of optical spatial solitons formation in novel photorefractive media.

Reservoir computing with nonlinear optical media

Reservoir computing is a versatile approach for implementing physically Recurrent Neural networks which take advantage of a reservoir, consisting of a set of interconnected neurons with temporal dynamics, whose weights and biases are fixed and do not need to be optimized. Instead, the training takes place only at the output layer towards a specific task. One important requirement for these systems to work is nonlinearity, which in optical setups is usually obtained via the saturation of the detection device. In this work, we explore a distinct approach using a photorefractive crystal as the source of the nonlinearity in the reservoir. Furthermore, by leveraging on the time response of the photorefractive media, one can also have the temporal interaction required for such architecture. If we space out in time the propagation of different states, the temporal interaction is lost, and the system can work as an extreme learning machine. This corresponds to a physical implementation of a Feed-Forward Neural Network with a single hidden layer and fixed random weights and biases. Some preliminary results are presented and discussed.

The generation and manipulation of spatiotemporal vortex in nonlocal self-temporal photorefractive media

The generation and manipulation of spatiotemporal vortex in nonlocal self-temporal photorefractive media

Numerical methods for generation and characterization of disordered aperiodic photonic lattices.

We introduce numerical modeling of two different methods for the deterministic randomization of two-dimensional aperiodic photonic lattices based on Mathieu beams, optically induced in a photorefractive media. For both methods we compare light transport and localization in such lattices along the propagation, for various disorder strengths. A disorder-enhanced light transport is observed for all disorder strengths. With increasing disorder strength light transport becomes diffusive-like and with further increase of disorder strength the Anderson localization is observed. This trend is more noticeable for longer propagation distances. The influence of input lattice intensity on the localization effects is studied. The difference in light transport between two randomization methods is attributed to various levels of input lattice intensity. We observe more pronounced localization for one of the methods. Localization lengths differ along different directions, due to the crystal and lattice anisotropy. We analyze localization effects comparing uniform and on-site probe beam excitation positions and different probe beam widths.

Controllable propagation of Pearcey–Gaussian beamsin photorefractive media with fractional Schrödinger equation

Taking the fractional Schrödinger equation as the theoretical model, the evolution behavior of the Pearcey–Gaussian beam in the photorefractive medium is studied. The results show that breathing solitons are generated when the nonlinear effect and the diffraction effect are balanced with each other. Nonlinear coefficients, Lévy index and beams amplitude affect breathing period of the soliton and maximum peak intensity. Within a certain range, the breathing period of the soliton decreases with the increase of the nonlinear coefficient and the Lévy index. However when the beams amplitude increases, the breathing period and the maximum peak intensity of the soliton increase. Under the photorefractive effect, due to the bidirectional self-acceleration property of the Pearcey beam, the solitons formed will propagate vertically. These properties can be used to manipulate the beam and have potential applications in optical switching, plasma channeling, particle manipulation, etc.

Multiple input/output waveguides light-induced by a single Bessel beam for all-optical interconnects.

We numerically study photo-induced waveguides using a single Bessel beam in a photorefractive (PR) medium. Under self-focusing nonlinearity, we demonstrate the possibility for creating complex waveguiding structures with multiple input/output channels. The truncation of the incoming Bessel beam, the nonlinearity of the PR medium, the light intensity, and the order and the size of the Bessel beam are the key parameters for achieving different configurations with high guiding efficiencies. As such, not only classical X or Y couplers but also more complex structures can be generated with up to 7 identified inputs/outputs. These results provide large opportunities for all-optical interconnects.

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.

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity* *Project supported by the National Natural Science Foundation of China (Grant No. 11704339), the Applied Basic Research Program of Shanxi Province, China (Grant No. 201901D211466), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2019JM-307), and the Scientific and Technological Innovation Programs of Higher Education

We investigate the properties of fundamental, multi-peak, and multi-peaked twisted solitons in three types of finitewaveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Two opposite soliton self-bending signals are considered for different families of solitons. Power thresholdless fundamental and multi-peaked solitons are stable in the low power region. The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals. When solitons tend to self-bend toward the waveguide lattice, stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region. Three-peaked twisted solitons are stable in the lower (upper) cutoff region for a shallow (deep) lattice depth. Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.

Gap solitons supported by an optical lattice in biased photorefractive crystals having both the linear and quadratic electro-optic effect

Abstract We investigate the existence and stability of gap solitons supported by an optical lattice in biased photorefractive (PR) crystals having both the linear and quadratic electro-optic effect. Such PR crystals have an interesting interplay between the linear and quadratic nonlinearities. Gap solitons are predicted for the first time in such novel PR media. Taking a relevant example (PMN-0.33PT), we find that the gap solitons in the first finite bandgap are single humped, positive and symmetric solitons while those in the second finite band gap are antisymmetric and double humped. The power of the gap soliton depends upon the value of the axial propagation constant. We delineate three power regimes and study the gap soliton profiles in each region. The gap solitons in the first finite band gap are not linearly stable while those in the second finite band gap are found to be stable against small perturbations. We study their stability properties in detail throughout the finite band gaps. The interplay between the linear and quadratic electro-optic effect is studied by investigating the spatial profiles and stability of the gap solitons for different ratios of the linear and quadratic nonlinear coefficients.

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.

Positive vector solutions for a Schrödinger system with external source terms

This paper is concerned with the existence of many synchronized vector solutions for the following Schrodinger system with external source terms $$\begin{aligned} \left\{ \begin{array}{ll} - \Delta u + u=a(x) u^3+\beta u v^2+f(x), &{}\quad x\in {\mathbb {R}}^3,\\ - \Delta v + v=b(x) v^3+\beta u^2 v+g(x), &{}\quad x\in {\mathbb {R}}^3,\\ u,v >0, &{}\quad x\in {\mathbb {R}}^3, \end{array} \right. \end{aligned}$$where $$\beta \in {\mathbb {R}}$$ is a coupling constant, $$a, b\in C({\mathbb {R}}^3)$$ and $$f,\ g\in L^2({\mathbb {R}}^3)\cap L^\infty ({\mathbb {R}}^3)$$. This type of system arises in Bose–Einstein condensates and Kerr-like photo refractive media. This paper tries to reveal the influence of the external source terms f and g on the number of the solutions. It is shown that the level set of the corresponding functional has a quite rich topology and the system admits k spikes synchronized vector solutions for any $$k\in \mathbb {Z}^+$$ when f and g are small and a(x), b(x) satisfy some additional assumptions at infinity. The proof is based on the Lyapunov–Schmidt reduction scheme and the main ingredient is to improve the estimate on the remainder term obtained in the reduction process.

Gaussian soliton pairs in an unbiased photorefractive crystal due to the pyroelectric effect

The characteristics of the dynamical evolution of incoherently coupled Gaussian soliton pairs in unbiased photorefractive media forming solely due to the pyroelectric effect are studied for the first time. A parameter space spawning a large set of bright Gaussian soliton pairs in unbiased photorefractive crystals having a large pyroelectric coefficient has been found. These soliton pairs can exist if the light beams have similar polarization, equal wavelength and are mutually incoherent. A change in the temperature of the photorefractive crystal induces a temporary pyroelectric field resulting in the formation of a space-charge field. The existence curve for these soliton pairs is studied for different values of the temperature change. It is also established that both individual components of the soliton pair should have equal spatial widths for stable propagation. The whole parameter space in which these soliton pairs exist as a changeless entity has been investigated in terms of the spatial width of the soliton pair, their peak power, and the magnitude of temperature change of the crystal. The magnitude of the temperature change profoundly affects the evolution characteristics of these Gaussian soliton pairs. The stability of such soliton pairs has been demonstrated using the paraxial theory. Bistable states have been shown to exist in the system irrespective of the magnitude of the temperature change for the case when both components of the soliton pair have equal power. A lithium niobate (LN) crystal has been considered to illustrate the relevant results.

Topological control of extreme waves

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, transitions between extreme waves are allowed. However, these have never been experimentally observed because control strategies are still missing. We introduce the new concept of topological control based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the nonlinear Schrödinger equation solutions through Riemann theta functions. We demonstrate the concept experimentally by reporting observations of supervised transitions between waves with different genera. Considering the box problem in a focusing photorefractive medium, we tailor the time-dependent nonlinearity and dispersion to explore each region in the state diagram of the nonlinear wave propagation. Our result is the first realization of topological control of nonlinear waves. This new technique casts light on shock and rogue waves generation and can be extended to other nonlinear phenomena.

Necklacelike solitons formed by manipulating vortex beams in a synthetic structure

We embed a helical lattice into a portion of a bulk photorefractive medium to form a synthetic structure and numerically investigate the nonlinear transmission of a probe vortex beam in the structure. Numerical demonstrations confirm that the structure can stabilize multisoliton states in the form of nonrotating and nonexpanding necklacelike solitons. Lattice structure and the amplitude, width, and topological charge of the probe vortex beam can influence the structure of necklacelike solitons. Interestingly, an increase in beam intensity may lead to multiplication of the number of bright “spots.”