ABSTRACT
A conventional starting point for introducing the basic types of deterministic optical beam-like fields is solving the Helmholtz equation within the paraxial approximation. Virtually all monographs on laser optics include such treatment. Often the solutions may be found by their direct substitution into the governing differential equation. The Hermite-Gaussian modes are generalizations of the fundamental Gaussian mode possessing rectangular symmetry. Their free-space spatial evolution under paraxial conditions belongs to Refs. Another powerful approach for synthesis of the novel deterministic beams is based on the spatial superposition of basic fields, such as Gaussian beams, for example. Optical fields, which possess uniform amplitude or intensity profiles in some part of the transverse cross-section, are required in material thermal processing, inertial confinement fusion and are beneficial for other applications, such as laser communications. For convenient analytical calculations it is preferable to smooth the edge of the profile in order to avoid fringing.
