Calculation of photonic band structures of periodic multilayer grating systems by use of a curvilinear coordinate transformation

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Abstract
We present a theoretical study of photonic band structures of multilayer grating systems, in which the periodicity in one plane is provided by a grating and the periodicity perpendicular to the plane is obtained by multilayering repeat units. Our method is based on the Chandezon transformation technique together with a scattering matrix approach. It is numerically stable and computationally efficient. Calculations have been performed for several multilayer systems involving a monograting generating a solid with two-dimensional periodicity. Results are presented 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 appreciable bandgaps in the direction of the grating. In contrast, if adjacent interfaces are out of phase, there are large bandgaps in all the directions in the two-dimensional plane containing the grating vector and the layer periodicity vector.