Classical harmonic oscillator with Dirac-like parameters and possible applications

Abstract

"We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the “supersymmetric” one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schr¨odinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of thesemodes. Generalizations to severalK parameters are also possible and lead to analytical results. If the problem is passed to the physical optics (and/or acoustics) context by switching from the oscillator equation to the corresponding Helmholtz equation, one may hope to detect the K-modes as waveguide modes of specially designed waveguides and/or cavities."