Sinusoidal-Gaussian beams in complex optical systems

Abstract

Sinusoidal-Gaussian beam solutions are derived for the propagation of electromagnetic waves in free space and in media having at most quadratic transverse variations of the index of refraction and the gain or loss. The resulting expressions are also valid for propagation through other real and complex lens elements and systems that can be represented in terms of complex beam matrices. The solutions are in the form of sinusoidal functions of complex argument times a conventional Gaussian beam factor. In the limit of large Gaussian beam size, the sine and cosine factors of the beams are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar fundamental Gaussian form. Alternate hyperbolic-sinusoidal-Gaussian beam solutions are also found.

Transformation and spatial shaping of partially coherent cosh-Gaussian beams through an astigmatic lens

“…In Refs. [9,12] it was pointed out that ChG beams cannot retain their shapes unchanged upon propagation and different beam profiles can be obtained at a certain place by varying the decentered parameter g. Our study has shown that, by an appropriate choice of the spatial coherence parameter b and/or astigmatic coefficient C 6 , the spatial shaping of partially coherent ChG beams is achievable …”

Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

“…Two concrete examples of seed functions of the modified kind are provided by the cosh-Gaussian beams [17] and the modified Bessel beams [18,19].…”

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].…”