SCI Библиотека

Derivation of analytical solutions of Maxwell’s equations, as well as other mathematical tools widely employed in optics-such as a Helmholtz equation or paraxial Schrodinger-type equations-has always been in the focus of interest of optical researchers. The said solutions describe in detail properties of coherent electromagnetic light !elds and laser beams, which have found numerous practical applications. In particular, widely known light !elds that can be described analytically include plane or spherical waves and Gaussian and Bessel beams [1], to name just a few. Recently, new promising light beams that can be described by exact analytical relations have been proposed. These include Hermite-Gaussian and Laguerre-Gaussian modal beams [2], Hermite-Laguerre-Gauss beams [3], elliptic Mathieu and Ince beams [4,5], hypergeometric beams [6], accelerating Airy beams [7], and self-focusing Pearcey beams [8]. Further research of elegant Laguerre-Gaussian and Hermite-Gaussian beams is currently underway [9,10], with their behavior being described using polynomials with complex argument. The elliptic Laguerre-Gaussian beams have been studied using a number of approaches [11,12]. Recent years have seen an increase of interest in deriving exact solutions of paraxial Schrodingertype equations in cylindrical coordinates. More recently, hypergeometric Gaussian beams [13] and circular beams [14] have been proposed. A number of well-studied light beams, such as conventional and elegant Laguerre-Gaussian modes, quadratic Bessel-Gaussian beams [15], and Gaussian optical vortices [16], have been shown to be a particular case of the circular beams [14]. Light !elds can be grouped into two classes: those that carry orbital angular momentum (OAM) [17] and those devoid of OAM. Beams that carry OAM are termed as vortex or singular beams. The vortex laser beams are characterized by a helical or spiral phase, wavefront dislocations, and isolated intensity s. Currently, vortex laser beams have been put to many practical uses, including tur

The exact solutions of Maxwell’s equations or other equations of optics – the Helmholtz equation, he paraxial propagation equation of the Schrödinger type – have always attracted the attention of researchers. These solutions describe electromagnetic coherent light fields and laser beams, which are widely used in practice and whose properties can be described in detail analytically. Such well-known light fields that have an exact analytical description include: plane wave, spherical wave, aussian, and Bessel beams [1]. Some time ago, new light beams that had an accurate analytical description were discovered: Hermite–Gauss and–Laguerre Gauss mode beams [2], Hermite–Laguerre–Gauss beams [3], Mathieu [4]beams, [6], accelerated Airy beams [7], Pearcey self-focussing beams [8], and others. Light fields can be divided into two classes having orbital angular momentum (OAM) [9] and not having it. Beams with OAM are called vortex or singular. The vortex laser beams [10] have such distinctive features: a helical or spiral phase, wavefront dislocations, isolated points of zero intensity. The vortex laser beams have recently become widespread, they are used in sounding the atmosphere in the presence of turbulence [11], in wireless communication systems [12], to condense information transmission channels through fibers [13], in astronomy [14], quantum computer science [15] and micromanipulations [16]. The authors have previously written about vortex laser beams [10], but over the past several years, new vortex beams have appeared: asymmetric Bessel and Laguerre–Gauss beams, Hermite–Gauss vortex beams, Lommel modes, Pearcey half-beams, vector vortex Hankel beams and others. This book is devoted to their consideration.