Ms. Laurence Le Floc'h Profile

Laurence Le Floc'h

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Proceedings Article | 15 September 2004 Paper

Two-dimensional discrete photonic crystals of finite size

Laurence Le Floc'h, Veronique Quintard, Jean-Francois Favennec, Yann Boucher

Proceedings Volume 5450, (2004) https://doi.org/10.1117/12.544791

KEYWORDS: Crystals, Photonic crystals, Scattering, Solids, Microwave radiation, Dispersion, Linear algebra, Dielectrics, Wave propagation, Network security

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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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