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Journal of International Crisis and Risk Communication Research

Novel all-optical switching mechanisms in media with quadratic nonlinearity

Vladislav A. Dubikovskiy, Andrey E. Kobyakov, David J. Hagan

Published May 7, 2000• 0 citations
OpenAlex

Abstract

A study is carried out to demonstrate that even a weak nonlinear coupling into additional waves can substantially change the system's behavior. A generic analytical approach toward multiple wave mixing in quadratic media is developed and novel mechanisms of all-optical modulation are identified.

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The emergence of standing-wave states and modulational instability in a system of coupled nonlocal nonlinear Hartree equations is considered. Such equations naturally arise in the mean-field description of two-component Bose-Einstein condensates and in nonlinear optical media with long-range interactions. By analytical stability analysis, applying a Lens-type transformation, we determine the modulational instability gain spectrum and identify the conditions under which uniform (steady) states become unstable. We consider a quadratic external potential of the form Vj(x) = λjx2, where the parameter λj may take positive, negative, or zero values, allowing us to explore trapping, expulsive, and homogeneous configurations for all types of atomic interactions. Numerical simulations reveal rich dynamical behavior characterized by the onset of phase segregation and overlapping patterns in the unstable regime. The interplay between strong nonlinearity and nonlocal coupling drives spontaneous structure formation and collective excitation modes in coupled nonlocal systems.
In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.
Abstract Precise light manipulation in optical media has been important for developing new communication protocols, particle tracking and control, environmental sensing and quantum computing, to cite a few applications. Here, we explore the nonlinear light-matter interactions of Hermite-Gaussian (HG) beams with a rubidium vapor. We analytically and numerically predict the possibility of generating a nearly pure optical HG mode as a result of the four-wave mixing of two different HG modes. In contrast, four-wave mixing of other linear solutions of the paraxial wave equation in a third-order nonlinear medium results in the up-converted beam consisting of a superposition of multiple modes. In addition, we identify a large family of solutions of the paraxial wave equation, including cylindrical and elliptical modes, that can be generated in the process of the four-wave mixing by precisely adjusting the weights of the input HG beams. This study may find applications in the development of new classical and quantum optical sources, with more spatial versatility.