The paper is aimed at constructing exact solutions of Maxwell's equations for homogeneous media, convenient for modeling ultrashort pulses of various shapes. An analytical description of a family of simple closed-form few-cycle electromagnetic pulses that are free of backward propagating components and have finite energy is presented. The mathematical framework rests on using, as a component of Hertz's potential, a certain axisymmetric exact solution of the linear wave equation, which is studied here in detail. Depending on the choice of free parameters in this solution and on polarization of the potential, the resulting electromagnetic pulses can be pancake-like, ball-like, needle-like, and doughnut-like. Expressions for spectra of the electric field components of the pulses are obtained. Based on the derived formulas, typical examples of pulses with different types of localization and their spectra are calculated and plotted. (c) 2024 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.
We obtain a family of simple closed-form exact solutions of the three-dimensional wave equation that are free of backward components. The solutions have no singularities and possess finite energy. They describe single-cycle and subcycle pulses. Depending on two parameters, the family yields pulses with different types of localization, in particular, focused pancakes, balls, and needles.
We introduce a simple exact solution of the wave equation in free space. It describes unidirectional finite-energy single-cycle and sub-cycle pulses. Depending on the ratio of its free parameters, the solution can yield, in particular, pancake, ball, and needle pulses.
We introduce a simple exact solution of the wave equation in free space. It describes unidirectional finite-energy single-cycle and sub-cycle pulses. Depending on the ratio of its free parameters, the solution can yield, in particular, pancake, ball and needle pulses.
We address propagation of paraxial Gaussian-type beam modes in longitudinally inhomogeneous axisymmetric lens-like media, with a specific case of a transition of waveguide into antiwaveguide. Higher-order modes are described in a unified manner using a so-called secondary parabolic equation. Analyzing a linear transition from waveguide to antiwaveguide where beams are described in terms of Airy functions, we conclude that the width of a localized Gaussian-type beam in inhomogeneous media can dramatically grow. This fact should be taken into account in numerical procedures employing summation of Gaussian beams. Copyright (C) EPLA, 2019
We consider higher mode solutions of the paraxial parabolic equation. They have a form of a product of a fundamental simple astigmatic mode and a factor called the amplitude. We are concerned with construction of amplitudes which are not polynomial with respect to transverse coordinates. A class of such solutions is presented, and several examples are considered.
A new method for the measurement of color differences is described. By means of the method, it becomes possible to find the shortest (i.e., in terms of color discrimination thresholds) path between two color points which in a standard non-equicontrast CIE 1931 color space is not a straight line. The method is based on local transformations of infinitely small regions of a given color space with the use of data on color discrimination thresholds obtained by interpolation or approximation of experimental data.
