[Paper Review] Continuum model of strong light-matter coupling for molecular polaritons

Suman Gunasekaran, Ryan F. Pinard+1 more|arXiv (Cornell University)|Aug 17, 2023

Strong Light-Matter Interactions4 citations

TL;DR

This paper introduces a continuum formalism for molecular polaritons that unifies light-matter coupling with linear dispersion by expressing polariton modes through light and matter local densities of states (LDOS). It derives exact LDOS expressions for a planar cavity using only the linear response of mirrors (reflectance) and dielectric (susceptibility), showing that coupled mode theory provides an accurate approximation in the strong coupling regime, thus offering a rigorous, empirically grounded framework for polariton analysis.

ABSTRACT

Strong coupling between light and matter generates hybrid polariton modes. We present a continuum formalism that expresses the polariton modes in terms of light and matter densities of states (DOS). We derive exact expressions for the light and matter DOS for a planar cavity containing a strongly dispersive dielectric. We show that these DOS depend exclusively on the linear response of the cavity components, i.e., the reflectance of the mirrors and the susceptibility of the dielectric. We further show that, within the strong coupling regime, the light and matter DOS are well-approximated by coupled mode theory. Altogether, our continuum formalism offers a unified treatment of polaritons that connects the framework of light-matter coupling with that of linear dispersion.

Motivation & Objective

• To address the lack of theoretical rigor in conventional light-matter coupling models for polaritons, which often rely on heuristic coupled oscillator approaches.
• To unify the light-matter coupling framework with the dispersion-based approach by formulating polaritons in terms of continuous densities of states (DOS).
• To derive exact expressions for light and matter local densities of states (LDOS) in a planar cavity using only the linear response functions of cavity components.
• To demonstrate that coupled mode theory (CMT) provides a valid approximation of the exact LDOS in the strong coupling regime.
• To establish a practical, empirically grounded formalism that connects Maxwell’s equations with polariton mode structure through physically interpretable parameters like filling fraction.

Proposed method

• Formulates polaritons using a continuum approach based on light and matter local densities of states (LDOS), derived from the linear response of cavity components.
• Derives exact LDOS expressions for transverse-electric (TE) modes in a planar cavity using the wave equation and Lorentz oscillator model for the dielectric.
• Models the dielectric as N uniformly distributed oscillators with resonance frequency ωj, damping γj, and oscillator strength fj, governed by the Lorentz equation.
• Uses the Dyson equation and Green’s function formalism to relate the filled cavity’s response to the bare cavity’s quasinormal modes.
• Connects the continuum LDOS formalism to coupled mode theory (CMT) by deriving the filling fraction as a bridge between Maxwell’s equations and CMT matrix elements.
• Demonstrates that the filling fraction, defined via mode overlap and normalization, physically links the photonic mode structure to the perturbation from the dielectric.

Experimental results

Research questions

• RQ1 Can a rigorous, continuous formalism for polaritons be developed that avoids reliance on discrete quasi-normal modes or heuristic coupled oscillator models?
• RQ2 How do the light and matter local densities of states (LDOS) in a planar cavity depend solely on the linear response functions—mirror reflectance and dielectric susceptibility—without invoking discrete modes?
• RQ3 To what extent does coupled mode theory (CMT) accurately approximate the exact LDOS derived from Maxwell’s equations in the strong coupling regime?
• RQ4 What is the physical meaning of the filling fraction in CMT, and how is it connected to the full electromagnetic solution via Green’s functions and quasinormal modes?
• RQ5 Can the continuum LDOS formalism be used to quantitatively predict polariton dispersion and mode structure using only experimentally measurable linear response functions?

Key findings

• The light and matter local densities of states (LDOS) in a planar cavity are exactly expressible in terms of the mirror reflectance and dielectric susceptibility, with no dependence on discrete mode assumptions.
• The exact LDOS expressions are derived from Maxwell’s equations and the Lorentz oscillator model, providing a first-principles foundation for polariton modes.
• In the strong coupling regime, the exact LDOS are well-approximated by coupled mode theory (CMT), validating CMT’s use in this regime.
• The filling fraction, a key parameter in CMT, is rigorously defined as a complex overlap integral between the photonic mode and dielectric region, linking CMT to the full electromagnetic solution.
• The formalism establishes a direct connection between the Green’s function of the cavity and the matrix elements of the Hamiltonian in CMT, providing a physical interpretation for the coupling strength.
• The approach offers a unified, empirically grounded framework that replaces heuristic fitting with measurable linear response functions, significantly enhancing predictive power and theoretical consistency.