Related papers: Optical Darboux Transformer
The Lax representation for the nonstationary Schr\"odinger equation with rather arbitrary potential is proposed. Some examples of the construction of exact solutions are given by means of Darboux Transformation method.
Control of light through a microscope objective with a high numerical aperture is a common requirement in applications such as optogenetics, adaptive optics, or laser processing. Light propagation, including polarization effects, can be…
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…
Nonlinear metasurfaces are multifunctional photonic elements that generate and control light, enabling multiple proof-of-principle applications, such as in nonlinear holography, beam shaping, and nanoscale sources of entangled photon pairs.…
The Darboux transformation between ordinary differential equations is a 19th century technique that has seen wide use in quantum theory for producing exactly solvable potentials for the Schr\"odinger equation with specific spectral…
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…
An image-based technique for measuring the complex field in the pupil of an imaging system is presented. Two point source images, one with a small modification introduced in the pupil, are combined using a simple and non-iterative…
Controlling the spectral and angular response of infrared (IR) radiation is a challenging task of paramount importance to various emerging photonic applications. Here, we overcome these problems by proposing and analyzing a new design of a…
For the nonlocal Davey-Stewartson I equation, the Darboux transformation is considered and explicit expressions of the solutions are obtained. Like the nonlocal equations in 1+1 dimensions, many solutions may have singularities. However, by…
A home-built compact system that functions as both a transfer stage for deterministic transfer processes and a mask aligner for contact photolithography, is constructed. The precision translation sample stage and optical microscope are…
In this article, the Darboux transformation for the non-isospectral AKNS hierarchy is constructed. We show that the Darboux transformation for the non-isospectral AKNS hierarchy is not an auto-B\"acklund transformation, because the integral…
We consider the Moutard transformation which is a two-dimensional version of the well-known Darboux transformation. We give an algebraic interpretation of the Moutard transformation as a conjugation in an appropriate ring and the…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case. We discuss different approaches to the…
The purpose of this paper is to study Toda-Darboux transforms, i.e., Darboux transforms for operators L(t) flowing according to the Toda lattice. Each element of the null-space $L(t)-z$ specifies a factorization for all t and thus a…
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary…
We define two isomorphic algebras of differential operators: the first algebra consists of ordinary differential operators and contains the hypergeometric differential operator, while the second one consists of partial differential…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
A new strategy, using Darboux transformations, of finding self-switching solutions of $i\dot{\rho} = [H, f({\rho})]$ is introduced. Unlike the previous ones, working for any f but for Hamiltonians whose spectrum contains at least three…
Nonlinear optical processing of ambient natural light is highly desired in computational imaging and sensing applications. A strong optical nonlinear response that can work under weak broadband incoherent light is essential for this…