Interfering resonances and bound states in the continuum

Abstract

We study transport properties of an arbitrary two terminal Hermitian system within a tight-binding approximation and derive the expression for the transparency in the form, which enables one to determine exact energies of perfect (unity) transmittance, zero transmittance (Fano resonance) and bound state in the continuum (BIC). These energies correspond to the real roots of two energy-dependent functions that are obtained from two non-Hermitian Hamiltonians: the Feshbach's effective Hamiltonian and the auxiliary Hamiltonian, which can be easily deduced from the effective one. BICs and scattering states are deeply connected to each other. We show that transformation of a scattering state into a BIC can be formally described as a "phase transition" with divergent generalized response function. Design rules for quantum conductors and waveguides are presented, which determine structures exhibiting coalescence of both resonances and antiresonances resulting in the formation of almost rectangular transparency and reflection windows. The results can find applications in construction of molecular conductors, broad band filters, quantum heat engines and waveguides with controllable BIC formation.

Observation of trapped light within the radiation continuum

“…4b). These evidences quantitatively verify that we have observed the predicted bound state of light.We have observed an optical state that remains perfectly confined even though there exist symmetry-compatible radiation modes in its close vicinity; this realizes the long sought-after idea 7 of trapping waves within the radiation continuum, without symmetry incompatibility [5][6][7][8][10][11][12][13][14][15][16] . The state has a high quality factor (implying low loss and large field enhancement), large area, and strong confinement near the surface, making it potentially useful for chemical/biological sensing, organic light emitting devices, and large-area laser applications.…”

“…6 and 14 are most closely related to what is demonstrated here. While no general explanation exists, some cases have been interpreted as two interfering resonances that leaves one resonance with zero width 6,11,12 . Among these many proposals, most cannot be readily realized due to their inherent fragility.…”

“…Here we predict and experimentally demonstrate that light can be perfectly confined in a patterned dielectric slab, even though outgoing waves are allowed in the surrounding medium. Technically, this is an observation of an "embedded eigenvalue" 9 -namely a bound state in a continuum of radiation modes-that is not due to symmetry incompatibility [5][6][7][8][10][11][12][13][14][15][16] . Such a bound 1 state can exist stably in a general class of geometries where all of its radiation amplitudes vanish simultaneously due to destructive interference.…”

“…This method to trap electromagnetic waves is also applicable to electronic 12 and mechanical waves 14,15 .…”

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

“…This effect, which is exclusively associated with the positions of DA and DN and not with any other parameter like the coupling, is the plasmonic equivalent of a quantum mechanical effect known in literature as bound state in the continuum (BIC). 56,57 This system is in fact equivalent to two states that are in interaction with radiation. The tunability of plasmonic systems enables positioning the diabatic states very close to each other while maintaining appreciable coupling.…”