By the transfer matrix approach we numerically study the electromagnetic properties (narrow peak positions) of the transmission spectra for microspheres coated by a multilayered stack with the generalized Cantor structure (fractal). As opposed to the standard Cantor system with removed γ/3 [γ=1] section we consider here the solid stack with Si/SiO2 layers at general γ value. In such a solid composition the SiO2 layers replace the empty Cantor sections and the parameter γ acquires meaning of a specific control parameter. At successive generations the central layers (in blocks of the spherical stack) acquire a progressive decreased width that leads to generation of the radially inhomogeneous defects. We show that the wave phase interference in such a fractal pattern leads to formation of very narrow electromagnetic transmittance resonances that can be used in modern optoelectronics.
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