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Optics of Floquet-Bloch waves in dielectric gratings

Abstract

The behavior of light in dielectric gratings is discussed in terms of the optical Floquet-Bloch waves (or modes). The emphasis is on the development of a good physical understanding of the nature of these waves, using the wavevector diagram to summarize their spatial dispersion and spectra. It is shown that Floquet-Bloch theory offers some advantages conceptually over the commonly used coupled-wave theory, because the rays of the Floquet-Bloch waves (given by their group velocities) play the same role in a periodic medium as do those of plane waves in isotropic or graded-index media. The effect on power conservation of truncating the Floquet expansions for the Floquet-Bloch waves is considered in detail. Using the greater intuitive power of Floquet-Bloch theory, it is shown (in contrast to recent claims to the contrary) how rigorous coupled-wave theory can be applied to symmetrical reflection gratings, and secondly how the light in these gratings can be viewed in terms of the multiple-beam interference of Floquet-Bloch waves, leading to behavior reminiscent of a low-finesse Fabry-Perot cavity.

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Russell, P.S.J. Optics of Floquet-Bloch waves in dielectric gratings. Appl. Phys. B 39, 231–246 (1986). https://doi.org/10.1007/BF00697490

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  • DOI: https://doi.org/10.1007/BF00697490

PACS

  • 42.10
  • 42.80