A Cavity-Enhanced Spectroscopist's Lens on Molecular Polaritons

Abstract

Polariton chemistry has been hailed as a potential new route to direct molecular processes with electromagnetic fields. To make further strides, it is essential for the community to clarify which unusual polaritonic phenomena are true hallmarks of cavity quantum electrodynamics and which can be rationalized with classical optical physics. Here, we provide a tutorial perspective on the formation, spectroscopy, and behavior of molecular polaritons using classical optics. Where possible, we draw connections to cavity-enhanced spectroscopy and recast open questions in terms that may be more familiar to the broader community of physical chemists.

Figures (11)

• Figure 1: A bright optical transition of an ensemble of molecules can resonantly couple to a confined photonic mode of an optical cavity. The emergence of the strong coupling regime coincides with the resolution of two distinct peaks in the cavity transmission spectrum. This regime can be described using the language of either classical optical physics or cavity quantum electrodynamics.
• Figure 2: An incident electromagnetic wave of amplitude $E_0$ and wavenumber $\tilde{\nu}$ impinges on a Fabry-Pérot cavity of length $L$. The cavity is constructed from two mirrors with reflection and transmission amplitude coefficients $r_1$, $r_2$, $t_1$, and $t_2$, and is filled with a dielectric medium with complex refractive index $\tilde{n}(\tilde{\nu})$. We calculate the transmitted [$E_T(\tilde{\nu})$], reflected [$E_R(\tilde{\nu})$], and circulating [$E_C(\tilde{\nu},z)$] field amplitudes by considering the interference of partial waves transmitted and reflected by each cavity mirror.
• Figure 3: (a) The transmission and reflection spectra of an empty Fabry-Pérot cavity composed of two identical mirrors, taking $R = 0.95$, $T=0.05$, $\ell = 0$, $L=50\,\upmu$m, $\alpha(\tilde{\nu})=0$, and $n(\tilde{\nu})=1$. (b) The intensity of light circulating in the same cavity, spatially averaged along the cavity's longitudinal $z$ axis. (c) Maxima in the transmitted and circulating spectra occur when the round-trip phase accrued by light traveling in the cavity, $\delta(\tilde{\nu})= 4 \pi L n(\tilde{\nu}) \tilde{\nu}$, takes on a value equal to an integer multiple of $2\pi$, as marked with blue dots.
• Figure 4: Optical cavity spectra change drastically in the presence of a strongly-absorbing intracavity medium. (a) The imaginary [$\kappa(\tilde{\nu})$, blue] and real [$n(\tilde{\nu})$, orange] components of the refractive index for a representative molecular absorber. The absorber has a Voigt lineshape centered at $\tilde{\nu}_0=$ 2000cm^-1 with Lorentzian broadening of $\gamma_L=2cm^{-1}$ fwhm and Gaussian broadening of $\gamma_G=4cm^{-1}$ fwhm. The peak absorption coefficient is $\alpha(\tilde{\nu}_0) = 800cm^{-1}$. The background refractive index is taken to be $n_0=1$. (b, c) The intensity spectra of light transmitted, reflected, absorbed, and circulating in an $L=50\, \upmu$m FP cavity composed of two identical mirrors, with $R = 0.95$ and $T = 0.05$. The cavity is filled with the material whose complex refractive index is shown in panel (a). Spectra are calculated using the relevant expressions from Table \ref{['tab:table1']}. The circulating field is spatially averaged along the cavity longitudinal $z$ axis. (d) Maxima in the transmitted and circulating spectra occur when the round-trip phase accrued by light traveling in the cavity, $\delta(\tilde{\nu})= 4 \pi L n(\tilde{\nu}) \tilde{\nu}$, coincides with an integer multiple of $2\pi$, as marked with blue dots.
• Figure 5: (a) Cavity transmission spectra simulated as a function of cavity length, $L$. The cavity and intracavity medium are the same as those simulated in Fig. \ref{['fig:coupledcavity']}, albeit with $L$ scanned from 49.25µ m to 50.75µ m. The polaritonic cavity modes exhibit an avoided crossing as they pass through resonance with the $\tilde{\nu}_0 = 2000cm^{-1}$ band center. (b) The round-trip phase accrued by light traveling in the cavity, $\delta(\tilde{\nu})= 4 \pi L n(\tilde{\nu}) \tilde{\nu}$, calculated for $L= 49.6$, $50.0$, and and 50.4µ m, corresponding to the color-coded lines in panel (a). Resonant frequencies that yield constructive cavity interference are marked with colored dots. As $L$ increases, $\delta(\tilde{\nu})$ is offset vertically and the resonant frequencies redshift.