We theoretically model two-dimensional waveguides with different surface perturbations and examine the effects of these perturbations on the transmission of light with wavelengths in visible and IR parts of the spectrum. Surface perturbations are modelled as sine, square and triangular waves with different amplitudes and periods, and as volumetric fractal-voronoi noise with different amplitudes and at different length scales. We use refractive indices which are characteristic for soft matter and solid-state photonics, in order to examine the effects of surface perturbations in different well-known systems. The effects of surface perturbations greatly depend on the wavelength and polarization of the incident light.
We demonstrate the emergence of slow-light in dual-periodic dielectric one-dimensional photonic crystals with self-similar features at different length scales. Specifically, using numerical modelling, we explore self-similar photonic crystals which are formed as effective combinations of dual periodic stacks of dielectric layers and show that the emergent photonic band diagram can be widely designed by different structural parameters. The width and the position of bandgaps can be designed to work over a wide range of bands and frequencies. The proposed design also leads to the emergence of flat bands and major slow-light regimes, with possible group refractive index of light as large as 103 and in a range of bands.
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