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The optical transmittance of one-dimensional photonic structures generated from lossless dielectric slabs with linear, or piecewise linear, profiles of their electric permittivity for linearly polarized, normally incident electromagnetic radiation is studied both analytically and numerically. Resorting to an analysis of the respective photonic modes, the dependence on frequency of the optical property addressed is first established for the singly graded slab and the doubly graded slab, i.e. for the proper dielectric constituents, and subsequently for the photonic structures derived from them. Considering the singly graded periodic structure, the transmittance reveals a series of photonic bands and gaps, exhibiting maxima less than unity, as for the singly graded slab, and tending to saturate in a periodic sequence of centro-symmetric columnar peaks, separated by gaps of identical widths, at large frequencies; an asset that recommends this type of photonic structure as ideal. Looking at the doubly graded periodic structure, the transmittance reveals two series of photonic bands and gaps, exhibiting maxima of full transparency, as for the doubly graded slab, or maxima of reduced transparency and tending to saturate in essentially constant values with zero gaps at large frequencies; a trait known for all frequencies from an optically homogeneous, non-dispersive medium of semi-infinite extent. The properties revealed for both the singly graded periodic structure and the doubly graded periodic structure offer unique possibilities regarding practical applications of such novel photonic composites, optical filters exploiting their transmittance or optical mirrors utilizing their reflectance only being the most obvious.

This paper is dedicated to Professor A M Stoneham FRS on the occasion of his 70th birthday.