Theory of periodic states for feedback-controlled photorefractive nonlinear systems

Certain feedback loops can be used in photorefractive optical schemes to implement periodic states and create spatial gratings characterized by extremely high or low diffraction efficiencies. This highly nonlinear phenomenon is studied both experimentally and numerically. An analytical method is developed for analyzing periodic states with the use of symmetries of time-dependent diffraction equations and fast feedback response. The method is applied to describe the properties of periodic states, including their spatial structure, diffraction-efficiency oscillation period and amplitude, and characteristics of feedback-controlled strong phase modulation.     

Critical slowing down of space-charge field relaxation in photorefractive sillenites

We propose a theoretical model for the recently reported anomalously long decay of a space-charge field that was resonantly excited in a photorefractive sillenite crystal [Phys. Rev. Lett. 79, 67 (1997)]. The model is based on the conventional concept of charge transfer and does not require excessively large values of the quality factor for space-charge waves. The effect in question is qualified as a critical slowing of the relaxation process as the threshold of optical oscillation is approached.     

Numerical reconstruction stability of fiber Bragg gratings

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.     

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has T?plitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.     

Nonlinear resonances free of field and doppler broadenings

For the case where the Rabi frequencies of the guiding fields are much larger than the relaxation constants but much smaller than the Doppler broadening, it is shown that resonances which are neither field nor Doppler broadened can appear in the absorption (or gain) spectrum of the probe field. A classification of four-level systems according to the number of resonances is made for cases where two strong fields interact either with opposite or adjoining transitions. The conditions under which the number of resonances reaches eight, while for stationary atoms the maximum number is four, are found. A method is proposed for calculating the number of resonances in a multilevel system with several strong fields using analysis of the extremum points of the frequency branches in the velocity-frequency plane.     

Deceleration and shape-transformation of light pulses during?phase conjugation in photorefractive media

We have theoretically investigated the main features of pulse deceleration and pulse-shape transformations during phase conjugation in photorefractive nonlinear media. The main attention in article is paid to the critical features which occur near the threshold of mirrorless oscillation. It is shown that the effects of critical enhancement when approaching the threshold do not lead to superior light slowing down characteristics as compared to the case of two-beam coupling. At the same time, essentially new features of pulse-shape transformation occur above the threshold.     

Erratum to: Several Articles in JETP Letters Published Online First

JETP Letters - An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022330013     

Adiabatic Growing,Multistability, and Control of Soliton-Comb States in χ(2) Microresonators for Pumping into Second-Harmonic Modes

JETP Letters - Realization of soliton-combs regimes in $${{\chi }^{{(2)}}}$$ microresonators is an important and timely problem. No regular techniques for its solution is known so far. We propose...     

Photorefractive deceleration of light pulses

We theoretically study the effect of light deceleration in photorefractive nonlinear media. This includes consideration of different types of the photorefractive nonlinear response, different wave interaction schemes, and an analysis of the influence of the input parameters, such as the input temporal pulse width and the coupling strength, on the output pulse characteristics: the time delay, the propagation velocity, the amplification factor, and the output width. We show that photorefractive light deceleration has numerous advantages over other known techniques. It works already at low intensities, at room temperature, and within wide spectral ranges and offers a vast variety of handles for manipulating light pulses. An analogy with the light deceleration method based on the quantum effect of electromagnetically induced transparency in ultracold resonant gases is also considered. The text was submitted by the authors in English.