Optical transmittance of photonic structures with logarithmically similar dielectricconstituents**This paper is dedicated to the memory of Dr E H Brandt, great scientist and dearfriend.

Abstract

The optical transmittance of one-dimensional, logarithmically similar, layered stacks ofpairs of lossless dielectric plates for linearly polarized, normally incident electromagneticradiation is studied both analytically and numerically. Resorting to an analysis of therespective photonic modes, the dependence on frequency of the optical property addressedis established for a singly logarithmic stack as well as for two of its symmetric derivatives,an outbound doubly logarithmic stack and an inbound doubly logarithmic stack. Givenspecified constraints on the structural and dielectric parameters that delineate these stacks,the following key results come to the fore: the transmittance of the singly logarithmicstack shows single oscillatory maxima of almost full height at low frequencies andtotal quench at larger frequencies; the transmittance of the outbound doublylogarithmic stack shows twinned oscillatory maxima of full height at low frequencies,supplemented with a sharp, full resonance at a higher frequency against a background ofsuppressed transparency; the transmittance of the inbound doubly logarithmic stackshows twinned oscillatory maxima of full height at low frequencies, supplementedwith a series of pairs of sharp spikes of full transparency for higher frequenciesagainst a background of suppressed transparency. Thus, one-dimensional photonicstructures generated by logarithmically similar dielectric constituents are capable ofunfolding desirable and useful optical properties: transparency at low frequencies,but opacity, or selectivity, at higher frequencies, in one single photonic device.