CALCULATION OF PHOTONIC BAND STRUCTURES OF PERIODIC MULTILAYER GRATING SYSTEMS BY USE OF A CURVILINEAR COORDINATE TRANSFORMATION

We present a theoretical study of photonic band structures of multilay er grating systems, in which the periodicity in one plane is provided by a grating and the periodicity perpendicular to the plane is obtaine d by multilayering repeat units. Our method is based on the Chandezon transformation technique together with a scattering matrix approach. I t is numerically stable and computationally efficient. Calculations ha ve been performed for several multilayer systems involving a monograti ng generating a solid with two-dimensional periodicity. Results are pr esented that show the effect of the amplitudes and the relative phase of the gratings on the subsequent optical band structure. It is found that when all interfaces have the same profile, there are no appreciab le bandgaps in the direction of the grating. In contrast, if adjacent interfaces are out of phase, there are large bandgaps in all the direc tions in the two-dimensional plane containing the grating vector and t he layer periodicity vector. (C) 1998 Optical Society of America.