A novel view of plane wave expansion method in photonic crystals

We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions, propagating or evanescent, of the translation operators $\{{\bf T_R} \}$, at a fixed frequency. With these eigenfunctions and their eigenvalues, the transmitted and reflected waves can be determined. Two kinds of applications are presented for 2D photonic crystals. The first is a selection rule for determine the normal direction of the vacuum-photonic crystal interface to achieve the highest attenuation effect at a gap frequency. The second is to calculate the transmittance and reflectance for a light incident from vacuum to an semi-infinite photonic crystal. As an example we recalculate a system studied previously by K. Sakoda et al. and get results in agreement with theirs

Magnetoconductance oscillations in semiconductor-superconductor junctions with a laterally isolating barrier layer inside semiconductor region

The oscillatory characteristics of magnetoconductance for a junction composed of a superconductor and a semiconductor, in which two parallel quantum wave guides are coupled with each other through a potential barrier layer, are studied systematically. To model the imperfectness of the interface, we introduce a $\delta-$ function scattering potential barrier lying close to the interface of the junction. The magnetoconductance oscillations (MCO) in this system stem from two sources: one is the interference of wave functions of quasi-particles due to multiple Andreev reflections at the interface; the other is attributed to the variation of the number of the propagation modes when introducing the isolating barrier layer. The introduction of the isolating layer in the quantum wave-guides strongly modifies MCO. We also present a physical picture for the MCO based on a phenomenological argument. The theoretically fitted results are in good agreement with numerical ones. Copyright Springer-Verlag Berlin/Heidelberg 2003