Modeling of aperiodic fractal waveguide structures for multifrequency light transport

In this paper we present the design of a novel waveguide structure capable of multifrequency transmission bands with strongly enhanced electric field states. The concept of the structure is based on aperiodic and quasiperiodic fractal ordering of scattering subunits combined within a traditional channel-waveguide scheme. The resulting three dimensional fractal waveguides are characterized by complex transmission spectra and sustain quasi-localized field modes with strong enhancement effects due to the lack of translational symmetry. In the paper we will describe how it is possible to accurately model these complex waveguide structures within a simple one dimensional model. We will explore the formation of photonic band gaps and the character of the quasi-localized states in fractal waveguide structures generated according to different deterministic rules, such as Fibonacci, Thue-Morse, and Rudin-Shapiro sequences. Furthermore, we will qualitatively compare the characteristics of the optical gaps and field states in periodic, fractal, and aperiodic waveguides. The results of our comparative study will show that the fractal waveguides based on the Thue-Morse sequence exhibit the richest transmission spectra with the strongest field enhancement effects occurring at multiple frequencies. The proposed fractal waveguide design can provide an attractive route towards the fabrication of optically active devices for multi-wavelength operation.