Related papers: Forward-backward equations for nonlinear propagati…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse…
We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified (2+1)-dimensional dissipative nonlinear parabolic differential equation, given field moduli over three…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 1+1D generalized nonlinear Schr\"odinger equation with a periodic nonlinear…
Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for…
Here we outline a description of paraxial light propagation from a modal perspective. By decomposing the initial transverse field into a spatial basis whose elements have known and analytical propagation characteristics, we are able to…
The importance of ultrasound is well established in the imaging of human tissue. In order to enhance image quality by exploiting nonlinear effects, recently techniques such as harmonic imaging and nonlinearity parameter tomography have been…
I present an overview of pulse propagation methods used in nonlinear optics, covering both full-field and envelope-and-carrier methods. Both wideband and narrowband cases are discussed. Three basic forms are considered -- those based on (a)…
Characterizing electromagnetic wave propagation in nonlinear and inhomogeneous media is of great interest from both theoretical and practical perspectives, even though it is extremely complicated. In fact, it is still an unresolved issue to…
In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…
A non-linear backward equation with diffusive terms is postulated for the probability density that depends on the Bohmian quantum potential. An associated nonlinear Schr\"{o}dinger equation is also introduced and extension of the analysis…
The distinctive features of passing the two-component extremely short pulses through the nonlinear media are discussed. The equations considered describe the propagation in the two-level anisotropic medium of the electromagnetic pulses…
We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration…
We have developed a computational method to describe the nonlinear light propagation of an intense and ultrashort pulse at oblique incidence on a flat surface. In the method, coupled equations of macroscopic light propagation and…
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…
A concept of a family of unique backward-wave photonic devices, such as frequency up and down converting nonlinear-optical mirrors, sensors, modulators, filters and amplifiers is proposed. Novel materials are considered, which support…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
We present a systematic study on linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media and vacuum. The applied method of amplitude envelopes gives the opportunity to estimate the limits of slowly…