Electromagnetic Continuum Induced Nonlinearity

TL;DR

This paper reveals that standard Hamiltonian models are insufficient for capturing higher-order nonlinear effects in opto-mechanical systems, highlighting a dissipative nonlinearity induced by electromagnetic continuum interactions.

Contribution

It introduces a new perspective on opto-mechanical nonlinearity, emphasizing the role of electromagnetic continuum effects beyond traditional Hamiltonian approaches.

Findings

Standard Hamiltonian models are inadequate for higher-order nonlinear effects.

Electromagnetic continuum induces a large mechanical nonlinearity.

Dissipative nonlinearity cannot be captured by conventional Hamiltonian formalism.

Abstract

A nonrelativistic Hamiltonian describing interaction between a mechanical degree of freedom and radiation pressure is commonly used as an ultimate tool for studying system behavior in opto-mechanics. This Hamiltonian is derived from the equation of motion of a mechanical degree of freedom and the optical wave equation with time-varying boundary conditions. We show that this approach is deficient for studying higher order nonlinear effects in an open resonant opto-mechanical system. Opto-mechanical interaction induces a large mechanical nonlinearity resulting from a strong dependence of the power of the light confined in the optical cavity on the mechanical degrees of freedom of the cavity due to coupling with electromagnetic continuum. This dissipative nonlinearity cannot be inferred from the standard Hamiltonian formalism.