Leaky modes of waveguides as a classical optics analogy of quantum resonances

TL;DR

This paper proposes a classical optics waveguide model to simulate quantum resonances, establishing a complete analogy between leaky modes in optics and quantum scattering states, with practical calculations for dielectric slabs.

Contribution

It introduces a novel analogy between waveguide leaky modes and quantum resonances, providing a new classical optics framework for quantum phenomena analysis.

Findings

Leaky modes correspond to quantum resonances with finite lifetime.

The model accurately predicts attenuation of resonances in dielectric slabs.

Complete analogy established between guided/leaky modes and bound/scattering states.

Abstract

A classical optics waveguide structure is proposed to simulate resonances of short range one-dimensional potentials in quantum mechanics. The analogy is based on the well known resemblance between the guided and radiation modes of a waveguide with the bound and scattering states of a quantum well. As resonances are scattering states that spend some time in the zone of influence of the scatterer, we associate them with the leaky modes of a waveguide, the latter characterized by suffering attenuation in the direction of propagation but increasing exponentially in the transverse directions. The resemblance is complete since resonances (leaky modes) can be interpreted as bound states (guided modes) with definite lifetime (longitudinal shift). As an immediate application we calculate the leaky modes (resonances) associated with a dielectric homogeneous slab (square well potential) and show that these modes are attenuated as they propagate.