20 November 2012 Simplified modal method for subwavelength gratings
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A modal method is concerned with the modes excited, propagating, and coupled out into diffraction orders of a grating. Compared with the well-known rigorous-coupled-wave algorithm (RCWA), the modal method is less recognized. While the RCWA is a pure-numerical method, the modal method reveals a clear physical picture of the modes inside the grating. When a grating has a large period, it usually has too-many modes that are excited and propagating, and its analysis would be too complex. When a grating has a subwavelength period or a close-to-wavelength period, a few modes will be excited and propagating. When a few modes are concerned in the analysis, we have a simplified modal method. We have developed a simplified modal method to explain diffraction due to a deep-etched fused silica grating. Here the “deep-etched” means that the grating has a high ratio of deep-etched depth to the groove width. When a deep-etched fused silica grating has a subwavelength period, there are a few (one to two) lower modes that are propagating modes, and higher-order modes are evanescent. We have developed an average effective-index concept to describe a triangular deep-etched grating, and obtained simple analytical equations to describe a three-port beam-splitting grating. These analytical equations are impossible to obtain with the pure-numerical RCWA. This simplified modal method should be a useful tool for designing a variety of subwavelength deep-etched fused silica gratings for practical applications.
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Changhe Zhou, Changhe Zhou, } "Simplified modal method for subwavelength gratings", Proc. SPIE 8564, Nanophotonics and Micro/Nano Optics, 856412 (20 November 2012); doi: 10.1117/12.2002702; https://doi.org/10.1117/12.2002702

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