Abstract
Based on Bragg law, Airy's formulae, and second-order Taylor series expansion, the relationships between wavelength selectivity and angular selectivity of the ordinary and phase-shifted Rugate coatings are investigated, respectively. And their expressions of the wavelength selectivity bandwidth and the angular selectivity bandwidth of these two types of Rugate gratings are put forward. The results show that when the incidence angle is far away from 0 rad, the bandwidth of the wavelength selectivity is proportional to that of the angular selectivity. And when the incidence angle approaches or even equals 0 rad (frequently-used cases), the bandwidth of the wavelength selectivity is squarely proportional to that of the angular selectivity. The results are instructive for the design and application of Rugate coatings.
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