Exact analytical results expressed in terms of Bessel functions for the bandgaps, reflectance and transmittance of one-dimensional photonic crystals with a sawtooth refractive index profile on the period are derived, to our knowledge for the first time. This extends the set of exactly solvable models with periodic refractive indices. Asymptotic approximations to the above exact results have been also obtained.
Morozov, G. V., Sprung, D. W. L., & Martorell, J. (2013). One-dimensional photonic crystals with a sawtooth refractive index: another exactly solvable potential. New Journal of Physics, 15, . https://doi.org/10.1088/1367-2630/15/10/103009