ON THE LIMITS OF VALIDITY OF THE 2-WAVE APPROXIMATION IN THE DYNAMICAL THEORY OF ELECTROMAGNETIC SCATTERING BY PERIODIC DIELECTRIC MEDIA

We investigate the accuracy and limits of validity of the two-wave app roximation in the dynamical theory of electromagnetic scattering by pe riodic dielectric media. The errors ensuing from the approximation are estimated by applying the dynamical theory to a scattering problem fo r which an alternative exact electromagnetic solution is available and comparing results. The conditions for applying the approximate theory and its accuracy are discussed in terms of concepts peculiar to the c lassical dynamical theory of the scattering of X-rays in crystals, suc h as the Ewald sphere in the reciprocal space and the resonance error. After introducing the basic equations of the dynamical theory of elec tromagnetic scattering by three dimensional periodic dielectric media, the theory is applied to the scattering by one-dimensional periodic l ayered structures where a rigorous analytical solution is available. T he analysis of the errors involved in the two-wave approximation indic ates that, in the general case, the quality of the approximation canno t be quantified in terms of just the resonance error but it is also st rongly affected by the dielectric contrast. Simple formulae are report ed yielding a reliable error estimate in many practical cases. An exte nsion of the results to the two and three dimensional case is also pro vided. Finally, it is suggested that a modification of the boundary co nditions which are usually enforced in the dynamical theory when solvi ng the propagation equation could improve its accuracy and extend the limits of validity of the two-wave approximation.