Classical harmonic oscillator with Dirac-like parameters and possible applications

TL;DR

This paper introduces a new class of damped oscillation modes called K-modes, derived via a supersymmetric matrix approach, with potential applications in waveguide design and wave physics.

Contribution

It develops a novel parametric framework for classical oscillators using supersymmetric techniques, linking them to Dirac-like equations and exploring physical optics applications.

Findings

Defined K-modes with damping and absorption properties.

Established analytical results for multi-parameter generalizations.

Suggested potential detection of K-modes in waveguide systems.

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 Schroedinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of these modes. Generalizations to several K 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