Second-harmonic generation by a nonlinear line source in a step index fiber

Using Hertz potentials it is possible to analyze the problem where a dominant HE
11
fundamental excites a nonlinear line of material on the axis of a fiber. For a nonlinear line with a specified crystal symmetry of
\bar{4}3
m, it is shown that a second-harmonic field may be generated, but only in a TM
om
mode; this then indicates that harmonic generation and mode conversion act as simultaneous processes. Phase matching constraints are discussed and it is shown that the field buildup properties are analogous to those found in rectangular geometries.