A two-dimensional optical field paraxial propagation scheme, in Cartesian and cylindrical coordinate systems, is proposed. This is achieved by extending the method originally proposed by Ladouceurâ€¦ (More)

Molecular clock analyses estimate that crown-group animals began diversifying hundreds of millions of years before the start of the Cambrian period. However, the fossil record has not yieldedâ€¦ (More)

The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves theâ€¦ (More)

We obtain a Fourier transform scaling relation to find analytically, numerically, or experimentally the spectrum of an arbitrary scaled two-dimensional Dirac delta curve from the spectrum of theâ€¦ (More)

We introduce the paraxial group, the group of symmetries of the paraxial-wave equation and its action on paraxial beams. The transformations, elements of the group, are used to obtain closed-formâ€¦ (More)

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of theâ€¦ (More)

The propagation of Helmholtz-Gauss beams in media exhibiting loss or gain is studied. The general expressions for the field propagation, the time-averaged power on propagation, the trajectory of theâ€¦ (More)