Transmission through Cantor filters revisited

Omnidirectional bandgap in Cantor dielectric multilayers

“…The transmission coefficient of the multilayer can be computed using the method of the characteristic matrixes along with the Snell's law at each interface [11]. Some papers [5][6][7][8][9][10] dealt with the analysis of transmission properties of Cantor multilayers for normal incidence. In this case the transmissivity of the multilayer exhibits several transparency/opacity windows.…”

“…On the other hand, dielectric Cantor fractal multilayers have been extensively analyzed in the literature [5][6][7][8], but it has not been showed whether such systems can exhibit omnidirectional bandgap.…”

Electromagnetic waves in fractal nanostructures

“…Initially, fractal nanostructures were only studied comparatively along with QP structures [16], although in some papers a rigorous analytical treatment appears for some cases [22][23][24]. Other than that, fractal structures have mainly been studied phenomenologically from the point of view of designing some optical devices [25][26][27][28][29], about which certain controversies also existed [30].…”

Optical resonances in multilayer structures

“…For higher generation Cantor structures, in the all-positive (PIM-PIM) case a considerable attenuation is caused by a high number of layers, thus they become practically useless for filtering applications [139]. However, due to the effect of phase compensation, in the case of NIM-PIM structures one can use a much larger number of layers (higher generations) in Cantor-type filters and still have a significant transmission and significant absorptance/emittance tailoring effects.…”

“…Theoretically, for a full fractal set the division should continue infinitely long, but in reality a truncated set is retained (a pre-fractal set). One of the reasons is that a Cantor structure with a very large number of layers would have a strongly decreased transmissivity and thus would become useless from the practical point of view [139]. A non-periodic multilayer can be in-bound (with the total thickness of the structure given at the beginning, while one performs its subdivision to develop higher generations) or out-bound (single layer thickness is given, one stacks such strata according to a sequence rule to develop higher generations) [15].…”