Cavity with an embedded polarized film: an adapted spectral approach

TL;DR

This paper develops a spectral approach to analyze the modes of a cavity with an embedded polarized dielectric film, deriving orthogonal modes and demonstrating mode switching with minimal energy, applicable to various nano-physics systems.

Contribution

It introduces a novel spectral method to derive and analyze the normal modes of a cavity with an embedded polarized film, including mode orthogonality and switching capabilities.

Findings

Derived orthogonal normal modes for the system.

Demonstrated mode switching with minimal energy input.

Validated amplitude equations for complex system behavior.

Abstract

We consider the modes of the electric field of a cavity where there is an embedded polarized dielectric film. The model consists in the Maxwell equations coupled to a Duffing oscillator for the film which we assume infinitely thin. We derive the normal modes of the system and show that they are orthogonal with a special scalar product which we introduce. These modes are well suited to describe the system even for a film of finite thickness. By acting on the film we demonstrate switching from one cavity mode to another. Since the system is linear, little energy is needed for this conversion. Moreover the amplitude equations describe very well this complex system under different perturbations (damping, forcing and nonlinearity) with very few modes. These results are very general and can be applied to different situations like for an atom in a cavity or a Josephson junction in a capacitor and this could be very useful for many nano-physics applications.