2 May 2014 A Bloch modal approach for engineering waveguide and cavity modes in two-dimensional photonic crystals
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In open nanophotonic structures, the natural modes are so-called quasi-normal modes satisfying an outgoing wave boundary condition. We present a new scheme based on a modal expansion technique, a scattering matrix approach and Bloch modes of periodic structures for determining these quasi-normal modes. As opposed to spatial discretization methods like the finite-difference time-domain method and the finite element method, the present approach satisfies automatically the outgoing wave boundary condition in the propagation direction which represents a significant advantage of our new method. The scheme uses no external excitation and determines the quasi-normal modes as unity eigenvalues of the cavity roundtrip matrix. We demonstrate the method and the quasi-normal modes for two types of two-dimensional photonic crystal structures, and discuss the quasi-normal mode field distributions and Q-factors in relation to the transmission spectra of these structures.
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Jakob Rosenkrantz de Lasson, Jakob Rosenkrantz de Lasson, Philip Trøst Kristensen, Philip Trøst Kristensen, Jesper Mørk, Jesper Mørk, Niels Gregersen, Niels Gregersen, "A Bloch modal approach for engineering waveguide and cavity modes in two-dimensional photonic crystals", Proc. SPIE 9127, Photonic Crystal Materials and Devices XI, 91270F (2 May 2014); doi: 10.1117/12.2051885; https://doi.org/10.1117/12.2051885


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