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One-dimensional photonic crystals with a sawtooth refractive index: another exactly solvable potential

This paper will be of significant interest to physicists working in the area of photonic crystals and thin films, as linearly graded refractive index layers are within present technological capabilities. Moreover, since the basic results are obtained in the exact analytical form, the paper should be of considerable general interest to theorists. The difficulty of obtaining meaningful analytical solutions is well understood within this field, with few exact solutions for 1D photonic crystals (periodic thin films) after several decades of study. The paper will thus serve as a key reference in the characterisation and understanding of graded index optical films.