Modal Processes in Two-Dimensional Resonant Reflectors and Their Correlation With Spectra of One-Dimensional Equivalents

We explain modal processes in 2-D guided-mode resonance reflectors with subwavelength periods in terms of the mode structure of quasi-equivalent 1-D grating-based reflectors. The 1-D gratings are designed via a second-order effective-medium theory. The principal features in the reflection spectra of the 2-D devices show good quantitative agreement with the corresponding 1-D grating spectra for small modulation strength. Thereby, clear connections are established with the TE and TM modal states of a reflector. For reflectors made with silicon that has a high index of refraction, there is qualitative agreement between the 2-D spectra and the concomitant 1-D modal signatures. Two-dimensional reflectors with periodic rods and holes are treated. In both cases, it is found that the spectra are dominated by contributions from a single polarization state in the 1-D grating equivalent. The results and methods provided herein enable improved understanding of the physical properties of 2-D resonant reflectors and the related 2-D modulated devices, including photonic crystal slabs. Hence, this methodology facilitates the design of 2-D reflectors in general as is straightforwardly applied to device architectures, materials, and spectral regions beyond those treated here.