Abstract
One of the most important properties of photonic band-gap (PBG) materials is the confinement of light whose frequency lies in the bandgap [1]. Many of the envisioned applications of PBG materials rely on the degree to which this confinement characteristic is realized. It follows, therefore, that while it is important to examine the special properties of PBG materials in its perfect form, it may also be important to study the wave behavior in imperfect PBG materials, so as to gain the knowledge about PBG material requirements in practical applications. In particular, it is of interest to see what happens to waves when there is a density of imperfections, or impurities, in PBG materials.
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The fact that the tunneling need not be symmetric can easily be seen from the fact that tij ≠t jt , in general. This can be demonstrated in the case of two intermediate scatterings by impurity potentials denoted as vn and vm: \( {\int {{\phi_j}(z'){v_n}(z'){G_{{nm}}}(z',z){v_m}(z)\phi }_i}(z)dz'dz \ne {\int {{\phi_i}(z'){v_n}(z'){G_{{nm}}}(z',z){v_m}(z)\phi }_j}(z)dz'dz \) where fi is the wave function of the ith channel and G denotes the Green’s function. Only in the case of single scattering does t ij ≠t ji .
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© 1996 Kluwer Academic Publishers
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Zhang, ZQ., Sheng, P. (1996). Wave Confinement and Localization: Dimensional Crossover Effect. In: Soukoulis, C.M. (eds) Photonic Band Gap Materials. NATO ASI Series, vol 315. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1665-4_41
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DOI: https://doi.org/10.1007/978-94-009-1665-4_41
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