Abstract
A guided-mode resonance (GMR) filter consists of a sub-wavelength waveguide grating on a transparent substrate to give a narrowband reflection with polarization selectivity for an incident wave from the air to a waveguide surface. The GMR is a kind of Fano resonance and its reflection spectrum shows a sharp peak. A spectral line width is determined by the coupling strength of the grating. A resonance wavelength is determined by a grating period and a guided mode index. Reflection behaviour of a GMR filter of a grating in two stacked waveguides of a symmetric structure was theoretically discussed with multiple guided modes. It was found that there were two regimes of reflection behaviour. One is a separate-waveguides regime where guided mode indices are degenerated and two GMR filters emerge to construct a vertical cavity resonator. The other is a combined-waveguide regime where the mode-index degeneration is resolved to give different resonance wavelengths. Flat-top spectra preferable in many practical applications were also discussed.
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