Hermite–sinusoidal-Gaussian beams in complex optical systems

Abstract

Sinusoidal-Gaussian beams have recently been obtained as exact solutions of the paraxial wave equation for propagation in complex optical systems. Another useful set of beam solutions for Cartesian coordinate systems is based on Hermite-Gaussian functions. A generalization of these solution sets is developed here. The new solutions are referred to as Hermite-sinusoidal-Gaussian beams, because they are in the form of a product of Hermite-polynomial functions of either complex or real argument, sinusoidal functions of complex argument, and Gaussian functions of complex argument. These beams are valid for propagation through systems that can be represented in terms of complex beam matrices, and the previous beam solution sets are special cases of these more general results. Propagation characteristics and applications of these beams are discussed, including their use as a basis set for propagation of arbitrary electromagnetic beams.

Evolution of Cos-Gaussian Beams in a Strongly Nonlocal Nonlinear Medium

“…Recently, there has been growing interest in the study of Hermitesinusoidal-Gaussian (HSG) beams as a result of the works of Casperson and Tovar [14] and Chen et al [15]. Propagation of HSG laser beams in free space, in complex optical systems, in turbulence and in Kerr media have been studied extensively [14][15][16][17][18][19][20].…”

“…Propagation of HSG laser beams in free space, in complex optical systems, in turbulence and in Kerr media have been studied extensively [14][15][16][17][18][19][20]. These studies indicate that the shape of HSG laser beams changes during propagation.…”

“…As a special case of the HSG beams, the cos-Gaussian beams have many interesting applications such as optimizing the efficiency of laser amplifiers. This is because of its unique profile as a Gaussian beam that modulates with a cos function [14][15][16][17].…”

Focusing of hyperbolic-cosine-Gaussian beam with a non-spiral vortex

“…Casperson and co-workers introduced general solution of the Helmholtz equation, namely, HermiteSinusoidal-Gaussian beams in 1990s [15,16]. ChG beams are regarded as the special case of Hermite-sinusoidalGaussian beams, and are of practical interest because their profiles can be altered by choosing suitable beam parameters in cosh parts [17].…”

Physical conditions for sources radiating a cosh-Gaussian model beam

“…On the other hand, experimental methods for generating some special distributed beams have been reported and have been applied in some works, for example, optical measurements, free space optical communications, etc. Based on the Helmholtz equations, Casperson et al [1,2] derived one particular solution of Hermitesine-Gaussian model beams, by disposing and solving the wave equations. In the same report, they further pointed out that this class of beam could be produced in the experimental aspect, by performing the optical systems involving a sineGaussian aperture and a laser cavity [3] .…”