Propagation of Laguerre-Bessel-Gaussian beams New exact solutions to the paraxial wave equation are obtained in the
form of a product of Laguerre polynomials, Bessel functions, and Gaussian
functions. In the limit of large Laguerre-Gaussian beam size, the Bessel
factor dominates and the solution sets reduce to the modes of closed resonators,
hollow metal waveguides, and dielectric waveguides. In the opposite
limit the solutions reduce to Laguerre-Gaussian modes of open resonators
and graded-index waveguides. While these solutions are valid for electromagnetic
waves traveling through free space, they are also valid for propagation
through circularly symmetric optical systems representable by ABCD matrices
An interesting feature of the new solution set is the existence of
three mode indices, where only two are required for an orthogonal expansion.
As an example, Laguerre-Gaussian beam propagation through an optical system
that contains a Bessel-like amplitude filter is discussed..