Resonance Anomalies in the Lamellar Grating

The problem of diffraction by a perfectly conducting lamellar grating is examined numerically and analytically by use of a modal expansion technique. At various complex wavelengths, with a positive imaginary part, individual mode amplitudes have poles which give rise to resonance effects in the orders at nearby real wavelengths. These are the well-known resonance anomalies. We determine the trajectories of these poles as functions of groove depth, finding that as this parameter increases they move in the complex wavelength plane to a mode threshold, or cut-off wavelength—from a Rayleigh wavelength in the case of S -polarization and from zero wavelength in the case of P -polarization. It is emphasized that the modal expansion technique is particularly valuable in gaining an understanding of the dynamics of diffraction gratings, and that the resonance poles are perhaps the basic dynamical objects determining their behaviour.