Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides

TL;DR

This paper investigates spectral singularities in complex potentials and demonstrates their application in designing waveguides that exhibit resonance phenomena across a wide range of wavelengths, including visible light.

Contribution

It introduces the concept of spectral singularities in complex barrier potentials and applies this to develop waveguides functioning as resonators with tunable resonance at various wavelengths.

Findings

Spectral singularities can be realized at nearly any wavelength within the visible spectrum.

Waveguides designed with gain regions can exhibit resonance phenomena linked to spectral singularities.

The study provides a practical approach to harnessing spectral singularities for optical device applications.

Abstract

A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission coefficients. This property reveals an interesting resonance effect with possible applications in waveguide physics. We study the spectral singularities of a complex barrier potential and explore their application in designing a waveguide that functions as a resonator. We show that for the easily accessible sizes of the waveguide and its gain region, we can realize the spectral singularity-related resonance phenomenon at almost every wavelength within the visible spectrum or outside it.