Hermite-Sinusoidal-Gaussian Beams in Complex Optical systems 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 times sinusoidal functions
of complex argument times 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..