Role of magnetic and diamagnetic interactions in molecular optics and scattering

This paper aims to explicitly clarify the role and interpretation of diamagnetic interactions between molecules and light in quantum electrodynamics. In contrast to their electric and magnetic counterparts, the diamagnetic couplings between light and matter have received relatively little interest in the field of molecular optics. This intriguing disregard of an interaction term is puzzling. The diamagnetic couplings possess unique physical properties that warrant their inclusion in any multiphoton process, and the lack of gauge invariance for paramagnetic and diamagnetic susceptibilities necessitates their inclusion. Their role and importance within nonrelativistic molecular quantum electrodynamics in the Coulomb gauge is illuminated, and it is highlighted how for any multiphoton process their inclusion should be implicit. As an indicative example of the theory presented, the diamagnetic contributions to both forward and nonforward Rayleigh scattering are derived and put into context alongside the electric and magnetic molecular responses. The work represents clarification of diamagnetic couplings in molecular quantum electrodynamics, which subsequently should proffer the study of diamagnetic interactions in molecular optics due to their unique physical attributes and necessary inclusion in multiphoton processes.

Figure 1

Two topologically distinct time-ordered Feynman graphs representing the scattering of an incident photon into an output photon of the same mode $\left(\mathit{k},\eta \right)$. For nonforward scattering the output mode $\left({\mathit{k}}^{\prime },{\eta }^{\prime }\right)$ is not equal to that of the input $\left(\mathit{k},\eta \right)$.

Figure 2

Time-ordered Feynman graph representing the lowest-order diamagnetic scattering of an incident photon into an output photon of the same mode $\left(\mathit{k},\eta \right)$. For nonforward scattering the output mode $\left({\mathit{k}}^{\prime },{\eta }^{\prime }\right)$ is not equal to that of the input $\left(\mathit{k},\eta \right)$.