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 quasi-periodic fractal ordering of scattering subunits combined within a traditional channel-waveguide scheme. The resulting 3-D 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 this paper, we will describe how it is possible to accurately model these complex waveguide structures within a simple 1-D 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 fractal waveguides based on aperiodic order exhibit the richest transmission spectra with field-enhancement effects occurring at multiple frequencies. The proposed fractal waveguide design can provide an attractive route toward the fabrication of optically active devices for multiwavelength operation.
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