Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator

The poles and zeros of the scattering operator of a corrugated waveguide and of a bare grating are studied mathematically and numerically. An initial tutorial section recalls how their use can explain grating anomalies and other curious phenomena in linear optics. This approach is then used in nonlinear optics to understand and predict curious efficiency-curve shapes observed in the study of second-harmonic generation and optical bistability enhanced by a corrugated surface.