Emergence and highly directed output of long-lived resonances in photonic step ladder structure

Abstract

A bound state eigenfunction is defined here to be strictly localized within a subspace of a system and has no decreasing behavior. Its eigenvalue can be within state continua. Bound states in the continuum (BICs) and long-lived resonances have become a unique way to produce the extreme localization of light waves. In this communication, we present a theoretical and numerical demonstration of infinite bound states in the continuum (IBIC) and long-lived resonances in photonic ladder-like structures with four semi-infinite leads, together with their existence conditions. IBIC states are localized in an infinite subspace domain. Some of these states are inactive in the scattering and induce output zeros. Other are scattering active and induce output ones in the middle of long-lived resonances. Several continua of IBIC states remain hidden. They are bound in one of two infinite guides and some of them also in the closed loop. These discoveries are reported here for the first time to our knowledge. The ladder reference structure is composed of connected open loops of lengths L1 and L2 and four semi-infinite leads. The obtained results take due account of the state number conservation between the final system and the reference one. This conservation rule enables to find all the states of the final system and among them the bound in the continuum ones. In addition, we show the existence of long-lived resonances in each of two parallel output lines and long-lived anti-resonances in each of the two other output lines, when one uses two identical parallel simultaneous inputs. The analytical results are obtained by means of the Green’s function technique. The structures and the long-lived resonances presented in this work may have potential applications, in particular in sensing, filtering and communications.