Total resonant transmission and reflection by periodic structures (Q2884624)

The interaction in a periodic slab between guided modes and incident plane waves originating from sources exterior of the waveguide results in resonant fields in the waveguide and causes an anomalous energy transmission across it. The fields produced by sources inside the guide lose energy by radiation into the ambient space and the guide acts as an obstacle for fields originating in the ambient space.NEWLINENEWLINEThe analysis of this paper is based on the treatment of the scattering problem about the frequency and wavenumber for two-dimensional lossless structures in earlier works [\textit{S. P. Shipman} and \textit{S. Venakides}, ``Resonant transmission near non-robust periodic slab modes'', Phys. Rev. E 71, 026611 (2005); \textit{N. Ptitsyna, S. P. Shipman}, and \textit{S. Venakides}, ``Fano resonances of waves in periodic slabs'', in: Proceedings of the 12th International Conference on Electromagnetic Theory (MMET 2008), Piscataway, NJ, IEEE Press, 73--78 (2008); \textit{S. P. Shipman}, ``Resonant scattering by open periodic waveguides'', in: M. Ehrhardt, Wave propagation in periodic media. Analysis, numerical techniques and practical applications, Oak Park, IL, Bentham Science Publishers, E-Book Series Progress in Computational Physics (PiCP), vol. 1, 7--50 (2010)] including an asymptotic formula for the transmission line anomalies in the case of perturbation of the incidence angle.NEWLINENEWLINENow the authors extend their results establishing conditions under which the transmittance attains maximal and minimal values at each of the anomalies near the guided mode frequencies, that means, the slab transitions can be completely transparent or opaque, respectively, between two closely spaced frequencies. The total transmission and total reflection are achieved for a structurally symmetrical slab that admits a guided mode at an isolated wavenumber-frequency pair. The result is formulated as a theorem which is proved for the case of a single sharp peak and dip. The proof is based on a variational formulation of the scattering problem.NEWLINENEWLINEAdditionally, degenerated and multiple anomalies which can be emanated from a single guided mode frequency are treated.