Local normal-mode analysis of second harmonic generation in a periodic waveguide

A new theoretical analysis method based on the local normal-mode expansion is proposed for analysis of optical second harmonic generation (SHG) under quasi-phase-matching in a waveguide with a periodic structure. Nonlinear coupled mode equations, SHG efficiency, and effective SHG coefficient are derived. In addition, SHG devices quasi-phase-matched with corrugation and with periodic domain inversion are studied analytically and numerically. The results are compared to those obtained by the conventional ideal normal-mode expansion. It is shown that in a corrugated waveguide the local normal-mode expansion method presents a different result from the ideal normal-mode expansion since the periodic variation of the modal field profile is dominant in the quasi-phase-matching process. On the other hand, in the periodically domain-inverted ferroelectric waveguide, it is shown that the variation of the modal field profile is sufficiently small and both expansion methods coincide with each other.