Engineering Fano resonances in discrete arrays

Abstract

We study transmission properties of discrete arrays composed of a linear waveguide coupled to a system of N side defect states. This simple system can be used to model discrete networks of coupled defect modes in photonic crystals, complex waveguide arrays in two-dimensional nonlinear lattices, and ring-resonator structures. We demonstrate the basic principles of the resonant scattering management through engineering Fano resonances and find exact results for the wave transmission coefficient. We reveal conditions for perfect reflections and transmissions due to either destructive or constructive interferences, and associate them with Fano resonances, also demonstrating how these resonances can be tuned by nonlinear defects.

Controlled electron transport in coupled Aharonov–Bohm rings

“…Atomic clusters dangling from a linear chain provide such an example [28,29], and the present case is no exception. However, in this case interesting changes in the Fano lineshapes in the transmission spectrum take place as the flux through the secondary ring is varied keeping the primary flux fixed.…”

Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices

“…First, the Fano-Anderson effect [41,42] caused by the insertion of a bound state into a continuum is an exciting field, and has been investigated recently in nanoscale systems [43]. In this context, our study provides examples where one can observe at least one effect of inserting multiple bound states, in fact, an infinity of them in a singular continuum, or a pure point spectrum.…”

All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures

“…Then, in Sec. III.A we derive a system of effective discrete equations [25,26] and utilize a recently developed approach for its analysis [22,23]. Specifically, in Sec.…”

“…To address these issues, we employ a recently developed approach [22][23][24] and describe the photonic-crystal devices via effective discrete equations that are derived by means of a Green's function formalism [25][26][27][28][29]. This approach allows us to study the effect of the discrete nature of the device on its transmission properties.…”