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A multi-reflection model of grating diffraction based on the simplified modal method is proposed. Simulation results for a guided mode resonance Brewster grating using our method and rigorous coupled wave analysis are presented to verify our model. The solution of our method is in good agreement with that of rigorous coupled wave analysis. Benefiting from its clear physical view, this model helps us to better understand the diffraction process inside subwavelength gratings. On the basis of the multi-reflection model, we developed a matrix Fabry-Perot (FP) resonance condition and a single-mode resonance condition to evaluate the resonance wavelength. These resonance conditions may be helpful for simplifying design of guided mode resonance (GMR) gratings., Comment: 12 pages, 7 figures, preparing submitting to Optics Express

Perfect optical vortices (POVs) provide an enabling solution to address the predicament induced by the strong dependence of classical optical vortices on theirs carried topological charges. Here, a type of generalized POVs with controllable impulse ring profile was proposed and demonstrated. Especially, a type of "absolute" dark POVs surrounded by two bright ringlobes in each side was presented, which provides a perfect annular potential well along those dark impulse rings for trapping steadily low-index particles, cells, or quantum gas, etc. In further, several POVs with different impulse ring profiles, including conventional POVs with bright rings, dark POVs mentioned above, and also POVs with controllable impulse ring profile, were demonstrated. This work opens up new possibilities to reshape arbitrarily the impulse ring profile for perfect vortices, and this type of novel POVs will enrich functions of optical vortices and it should be of high interest for its potential applications in optical manipulation, both quantum and classical optical communications, enhanced optical imaging, and also novel structured pumping lasers, etc.., Comment: There was a serious error in figure S1 and it has been corrected in the second version. Also, figure 4 was improved. I am the first time to use arXiv to upload the preprint version and I thought the replacement would 'replace' completely the first version. Afer replacement, I found the incorrect first version was still avaible for public. I am sorry for this trouble. Thanks

The Simplified Modal Method (SMM) provides a quick and intuitive way to analyze the performance of gratings of rectangular shapes. For non-rectangular shapes, a version of SMM has been developed, but it applies only to the Littrow-mounting incidence case and it neglects reflection. Here, we use the theory of mode-coupling in a tapered waveguide to improve SMM so that it applies to non-rectangular gratings at arbitrary angles of incidence. Moreover, this new 'Tapered Simplified Modal Method' (TSMM) allows us to properly account for reflected light. We present here the analytical development of the theory and numerical simulations, demonstrating the validity of the method., Comment: 13 pages, 8 figures