One-dimensional PhC mirrors are constructed in a single-mode silica slab waveguide with a row of elliptical holes. The
photonic band gap (PBG) of the PhC structure is attained by fast eigen-mode calculations. Being aware that component radiated waves of the PhC mirror are generated at interfaces between different waveguide sections, when propagating guided waves impinge on these interfaces, we point out that the total radiation loss of the PhC mirror is consequence of interferometric interplays of component radiated waves. We visualize this radiation generation process with intuitive pictures. We also estimate total radiation losses of PhC mirrors by using an analytical model. For uniform PhC mirrors, our model explains the oscillations of the total radiation loss with the increase of the period number. The calculated results agree well with the numerical simulations in terms of the oscillation period, the damping speed, the initial phase, and the relative intensity. For non-uniform PhC mirrors, our model finds that the progressively tapered transition from the feeding waveguide to the PhC mirror does not yield the lowest radiation loss. This finding is against to the well known “impedance-matching” picture. The matching of our model with the simulated results certifies the interferometric nature of the radiation generation process in a PhC mirror especially when a low-index waveguide is considered.
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Wei Ding ; Rong-juan Liu and Zhi-yuan Li
Reducing radiation losses of one-dimensional photonic-crystal mirrors in a silica waveguide
", Proc. SPIE 8564, Nanophotonics and Micro/Nano Optics, 85640L (November 20, 2012); doi:10.1117/12.2000615; http://dx.doi.org/10.1117/12.2000615