A dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media

TL;DR

This paper introduces a dual-Lagrangian formalism for quantum optics in dielectric media, providing an alternative approach that aligns with traditional methods and offers new insights into electromagnetic duality and polariton behavior.

Contribution

The paper develops a dual-Lagrangian description for quantum optics in dielectric media, connecting it to existing equations and exploring electromagnetic duality in quantization.

Findings

Derives the dual formalism equivalent to standard quantum optics in dielectrics.

Shows the dual formalism reproduces the Huttner-Barnett equations.

Discusses the role of electromagnetic duality in optical quantization.

Abstract

We develop a dual description of quantum optics adapted to dielectric systems without magnetic property. Our formalism, which is shown to be equivalent to the standard one within some dipolar approximations discussed in the article, is applied to the description of polaritons in dielectric media. We show that the dual formalism leads to the Huttner-Barnett equations [B. Huttner, S. M. Barnett, Phys. Rev. A \textbf{46}, 4306 (1992)] for QED in dielectric systems. More generally, we discuss the role of electromagnetic duality in the quantization procedure for optical systems and derive the structure of the dynamical laws in the various representations.