The application of the Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) series expansions in the paraxial simulation
of optical pulses is described and presented through examples of pulse modulation by diffractive Fresnel lenses and
Using the FDTD technique we exhibit the physical propagation of a Hermite-Gaussian mode outside of the paraxial
regime, with a width parameter of the same order of magnitude as the wavelength. In higher order modes this causes
evanescence at the source of such modes, and we describe the loss of energy caused by this phenomenon. Using recently
derived expressions for the non-paraxial propagation of Hermite-Gaussian modes, we discuss the use of modal
techniques outside of the usual paraxial restriction, which allows for an efficient modal synthesis of Rayleigh-Sommerfeld diffraction effects in the far-field.