On Computation of Scattering Matrices and on Surface Waves for Diffraction Gratings

Summary.  A method for the numerical computation of the so-called augmented scattering matrices (ASM) is suggested for diffraction gratings. To construct such (unitary) matrices one has to take into account not only the oscillating modes but also those which exponentially grow (attenuate) in amplitude away from the grating. The method uses an optimization procedure to identify the coefficients in the asymptotics of such modes. A justification of the approach is given and its numerical implementation is discussed. Reliable numerical results allow us to study the occurrences of surface waves by means of a general existence criterion based on the properties of ASM. To illustrate the method we give some examples of surface waves in gratings. Received October 25, 2001 / Revised version received May 23, 2002 / Published online October 29, 2002 Mathematics Subject Classification (1991): 78M10, 78M50, 78A45