Surface effects and band measurements in photonic crystals

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Abstract
An analytic study of Bloch waves near photonic crystal surfaces has been carried out. This is a generalization of Heine’s theory of metal/semiconductor interfaces. The main concern of this study is how the surfaces of a finite system affect band determination–which usually involves transmission measurements on small photonic crystals. An analytic expression for transmission is obtained. The results show that the usual band measurements could lead to considerable errors, especially when they involve narrow band gaps. A possible method to improve band measurements has been suggested. The analytic surface analysis has been demonstrated to be fairly accurate, even for a small system. The theory is expected to be applicable to other surface-related problems of photonic systems.