Chiral Light-Matter Interaction in Optical Resonators

The Purcell effect explains the modification of the spontaneous decay rate of quantum emitters in a resonant cavity. For quantum emitters such as chiral molecules, however, the cavity modification of the spontaneous decay rate has been little known. Here we extend Purcell’s work to the chiral light-matter interaction in optical resonators and find the differential spontaneous decay rate of chiral molecules coupled to left and right circularly polarized resonator modes. We determine the chiral Purcell factor, which characterizes the ability of optical resonators to enhance chiroptical signals, by the quality factor and the chiral mode volume of a resonator, representing, respectively, the temporal confinement of light and the spatial confinement of the helicity of light. We show that the chiral Purcell effect can be applied to chiroptical spectroscopy. Specifically, we propose a realistic scheme to achieve resonator enhanced chiroptical spectroscopy that uses the double fishnet structure as a nanoscale cuvette supporting the chiral Purcell effect.

Figure 1

Enhanced (FD)CD $\mathrm{\Delta }\mathrm{\Gamma }/\mathrm{\Delta }{\mathrm{\Gamma }}_0$ of a polarization-preserving cavity with mirror reflectivity $R=90.0\%$ (black line) and 99.8% (red line) and a chiral molecule sample with refractive index 1.5. Inset shows the polarization inside the two cavities.

Figure 2

Proposed experiment for the chiral Purcell effect using the double fishnet structure. The double fishnet structure comprises metal-dielectric-metal (MDM) multilayers with square-shaped metamaterial cavities of sides $h$ and lattice constant $a$. Inset shows a vertical cross section of the metamaterial cavity containing flavin mononucleotide, a biomolecule which exhibits chiroptical signals in the visible spectral range.

Figure 3

(a) Spatial dependence of the local (FD)CD enhancement $\mathrm{\Delta }\mathrm{\Gamma }(\mathbf{r})/\mathrm{\Delta }{\mathrm{\Gamma }}_0$ inside the metamaterial cavity at ${\lambda }_{0,2}=677$ and ${\lambda }_{0,1}=897\mathrm{nm}$. (b) The (FD)CD spectrum of molecules at the center (black), left (red), and upper left (blue) positions inside the cavity. Inset shows a horizontal cross section of the double fishnet structure and molecular positions (black, red, and blue diamonds).

Figure 4

Volume-averaged (FD)CD enhancement $⟨\mathrm{\Delta }\mathrm{\Gamma }/\mathrm{\Delta }{\mathrm{\Gamma }}_0⟩$ of the double fishnet structure. Inset displays a vertical cross section of the metamaterial cavity region suggested for the nanoscale container of chiral molecules.