15 September 2004 Two-dimensional discrete photonic crystals of finite size
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Abstract
As any lattice-like structure supporting forbidden bands, a discrete periodic network can be considered as a special class of artificial Photonic Crystals (PC). In contrast to usual continuous PC, such a structure can be described exactly in the frame of linear algebra. We investigate theoretically and experimentally Two-Dimensional Discrete Photonic Crystals (2D-DPC) of finite size, made of ideal transmission lines interconnected by reciprocal, lossless and passive four-port networks. The intrinsic spectral responses between any two ports of a DPC (scattering parameters) are defined as its transmission coefficients when all external ports are perfectly matched (antireflection coating). The structure symmetries enable us to accelerate the calculation. In a DPC with arbitrary termination at each port, the spectral responses, including forbidden bands, are quite simply expressed as linear combinations of its intrinsic responses. Extremely sensitive to boundary conditions, they are thus reconfigurable. Since we use normalized units, our results are universally valid at any frequency. We illustrate the concept experimentally in the low microwave band [f < 10 GHz] where, thanks to easier technological control, it is possible to achieve the wanted performance at a given target frequency.
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Laurence Le Floc'h, Veronique Quintard, Jean-Francois Favennec, Yann G. Boucher, "Two-dimensional discrete photonic crystals of finite size", Proc. SPIE 5450, Photonic Crystal Materials and Nanostructures, (15 September 2004); doi: 10.1117/12.544791; https://doi.org/10.1117/12.544791
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