Anomalous refractive properties of a two-dimensional photonic band-gap prism

An analysis of the optical response of a triangular-shaped photonic band-gap prism is presented. Numerical simulations have been performed in the framework of multiple-scattering theory, which is applied considering spot illumination to avoid diffraction effects. First of all, refractive properties in the frequency range below the first TM band gap are analyzed and compared with the available experimental data. It validates the approach employed and supports the predictions obtained in the frequency range above the gap. At these high frequencies we found an unusual superprism effect characterized by an angle sensitivity and a frequency sensitivity of the intensity of outgoing beams. We report several representative examples that could be used in device applications. The results are interpreted in terms of the corresponding semi-infinite photonic crystal, through the analysis of the coupling between external radiation and bulk eigenmodes, using the two-dimensional-layerKorringa-Kohn-Rostoker method. The procedure presented here constitutes a simple but functional alternative to the methods used until now with the same purpose. I. INTRODUCTION Since the seminal works of Yablonovitch 1 and John, 2 photonic crystals ~PC’s ! have generated a great interest, both in fundamental and applied physics. These materials could have an important role in the development of the photonic information technology. This is especially true in the case of twodimensional ~2D! PC’s due to their easy fabrication by standard lithographic techniques. On the other hand, recent advances in growing techniques are also allowing the fabrication of planar devices based on three-dimensional ~3D! systems. 3 The study of optical properties of PC using numerical tools 4‐7 is an essential procedure in order to further increase the understanding of physical properties of PC’s. The potential applications of PC’s has motivated the development of efficient theoretical methods that allow us to obtain realistic comparisons between theory and experiments. One of the most versatile methods is the multiple-scattering method ~MSM!. Its formalism is based on the expansion of the 2D ~3D! radiation field in cylindrical ~spherical! harmonics centered at each scattering object, and it has been successfully applied in the analysis of interaction of radiation with dielectric and metallic finite 2D and 3D structures. 8‐1 7 Several authors have analyzed the optical response of structures based on 2D PC’s. 18 ‐22 Recently, 2D PC’s with