Effects of spatial modes in harmonic generation in isotropic media

The dependence of the direct harmonic generation processes on the spatial mode of the fundamental laser is investigated. The following assumptions have been made: isotropic nonlinear medium, no absorption, no pump depletion, no saturation effects; the laser is assumed to be in a pure rectangular Hermite-Gaussian rectangular mode TEM
_pq
. An analytical expression of the harmonic electric field is derived, showing that the
N
th harmonic of TEM
_pq
mode is, in the general case, a mixture of modes whose highest order is TEM
_NP,Nq
.