Abstract

One of the attractive features of grating couplers for second harmonic generation is that these couplers enable electromagnetic resonances at the pump and/or the second harmonic frequency. It is usually believed that the resonant excitation of guided waves (waveguide modes or surface plasmons) leads to an increase of the second harmonic efficiency. This may not be always the case, as reported by M. Kull et al. [1]. This effect has received no explanation till now. We show here that the dips observed in ref. [1] are due to the existence of nonlinear zeros. In the following the undepleted pump approximation is assumed. It simplifies the problem of second harmonic generation at grating couplers so that there exists a scattering matrix [2] at the second harmonic frequency 2ω which linearly links the vector B_2ω of scattered amplitudes (at 2ω) to a source vector A_2ω, which comes from the square of the field amplitudes at ω: Thus A_2ω has a double complex pole, denoted by β_1p when the scattered amplitudes at w have a single pole β_1p. Given another resonance at 2ω, the scattering matrix S will present another single pole, denoted by β_2p.

© 1995 Optical Society of America