Книга: Vortex Laser Beams

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