Beam Propagation In Nonlinear Media Research Articles

Wide-spectrum optical soliton solutions to the time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law

The time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law and its soliton solutions have significant implications to examine the dynamics of optical solitons, self-phase modulation, optical beam propagation in nonlinear media, pulse propagation in optical fibers, nonlinear waveguides, and signal transmission systems. This study focuses on the investigation of different soliton solutions related to various aspects of optical solitons, including their formation, propagation traits, and stability analysis of the mentioned equation. Soliton solutions are able to carry out long-distance transmission without frequent amplification and regeneration. We exploit an advanced mathematical technique, the (G′/G,1/G)-expansion method to descend and analyze the soliton solutions. As a result, a significant number of definitive and efficient solitons, such as compacton, bell-shaped, anti-peakon, breather, periodic, and singular solitons have resulted. The uniqueness of the obtained solutions is established by comparing them with previous results. Also, we discuss in detail the implications of fractional derivative and the application of the obtained solutions to optical fiber communication and other relevant fields. The findings of the present study provide valuable insights into the fundamental nature of optical solitons. These insights will contribute to the design and optimization of future optical networks, enabling the development of faster, more reliable, and higher-capacity communication systems.

Electromagnetic beam propagation in nonlinear media

We deduce a complete wave propagation equation that includes inhomogeneity of the dielectric constant and present this propagation equation in compact vector form. Although similar equations are known in narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.

Iterative nonlinear beam propagation using Hamiltonian ray tracing and Wigner distribution function

We present an iterative method for simulating beam propagation in nonlinear media using Hamiltonian ray tracing. The Wigner distribution function of the input beam is computed at the entrance plane and is used as the initial condition for solving the Hamiltonian equations. Examples are given for the study of periodic self-focusing, spatial solitons, and Gaussian-Schell model in Kerr-effect media. Simulation results show good agreement with the split-step beam propagation method. The main advantage of ray tracing, even in the nonlinear case, is that ray diagrams are intuitive and easy to interpret in terms of traditional optical engineering terms, such as aberrations, ray-intercept plots, etc.

Nonlinear Optics of Photons and Atoms

In this presentation we intend to focus on the exchange of experience between nonlinear optics (optical pulse and beam propagation in nonlinear media) and atom optics (dynamics of coherent waves generated from Bose-Einstein condensates). A common ground here is the nonlinear Schrodinger equation, which with the proper substitution of variables describes both types of phenomena. In nonlinear optics it is a light propagation equation that relates the signal at the end of the nonlinear crystal to the signal at the input face of the medium. In Bose-Einstein condensate dynamics it is the called the Gross-Pitaevskii equation. We will discuss various types of phenomena which have realisations both in the nonlinear optics and atom optics. We will concentrate our consideration on soliton formation, which is a challenge to fundamental and applied research in these two domains of physics.

Numerical studies of beam and pulse propagation in lasers and nonlinear media: Transverse pattern dynamics and nonparaxial effects

A review of recent work in numerical modelling of transverse pattern formation and dynamics in lasers and nonparaxial beam propagation is presented. The algorithms developed involve the field decomposition in terms of the Gaussian-Laguerre modes. Three models are discussed in detail. In the first one, the transverse pattern evolution of a short pulse in a ring unidirectional laser with a homogeneously broadened optically thin active medium is considered under the approximation of transversely synchronous pulse. The pulse-train envelope and transverse pattern dynamics are studied numerically using more than 200 empty cavity modes. In the second model the limitation of thin active medium is removed, and the propagation of self-acting beam through the active medium of arbitrary thickness is taken into account solving the conventional paraxial wave equation. Stationary regimes with deformed modes, quasi-periodic oscillations, and mode-locking regimes are observed. Phase singularities (optical vortices) in the transverse field pattern are demonstrated. In the third model, the Gauss-Laguerre decomposition is used to solve the Helmholtz equation describing wide-angle (nonparaxial) beam propagation in nonlinear media. The role of backward waves in wide-angle Kerr self-focusing is discussed.

Vector effects in self-focusing.

Using a Hertz vector formulation, it is possible to simplify the equations for beam propagation in nonlinear media without resorting to the scalar approximation. A numerical method to take advantage of the formulation is developed and applied to the problem of self-focusing. It is found that filament-like solutions can result for some values of the nonlinear index of refraction when the scalar approximation is not made even though the paraxial approximation is still used. \textcopyright{} 1996 The American Physical Society.

Rotating elliptical gaussian beams in nonlinear media

An analytical treatment of rotating elliptical gaussian beam propagation in nonlinear media is presented. It is shown that the self-focusing threshold depends on the parameter specifying the beam rotation and is higher than for the beam without rotation. It is established by the following rule: the greater the difference between the light beam and the axially symmetric one, the higher the threshold power needed for its self-focusing.

On the Theory of Light Beam Propagation in Non-linear Media

Abstract The propagation of two (laser and Stokes) light beams in a medium which is non-linear due to the dependence of the refractive index on the light intensity and simultaneously Raman active is considered. Numerical solutions of the problem describing different types of multifoci structure in the beams (an independent multifoci structure in a laser beam accompanied by a secondary subsequence of ‘weak’ foci in a Stokes beam; a ‘mixed’ multifoci structure of the beams; an independent multifoci structure in a Stokes beam) are obtained. A low stability of the propagation pattern of the beams with respect to external perturbations is discovered in the finite range of the parameters of the problem and a qualitative explanation of this phenomenon is proposed.