EFFECTS OF SPATIAL MODES ON 3RD-HARMONIC GENERATION

The theory of third-harmonic generation is extended to the treatment of a generating electric field having a cylindrical spatial-mode structure. In the tight-focusing approximation it is proved that third-harmonic generation is only possible in negatively dispersive media (Δk<0). For a laser beam which consists of a pure TEMpl mode, the generated field is a superposition of modes with a fixed angular mode number 3l and a radial mode number in the range from 0 to 3p with the exception of 3p-1, which is always 0. The generated power has a functional dependence on b Δk which is single peaked for p=0 and multipeaked for p0. For a phase-matched situation, the conversion efficiency decreases as either p or l increases. However, for a system where the number density of the negatively dispersive medium is proportional to the mismatch wave vector Δk, the TEM00 mode will not give the maximum conversion efficiency. It is noted that reliable determinations of refractive indices from phase-matching curves and third-order susceptibilities from absolute efficiencies of third-harmonic generation depend critically upon knowledge of the spatial structure of the generating field. © 1979 The American Physical Society.