Metasurface-Based Hybrid Optical Cavities for Chiral Sensing

Quantum metasurfaces, i.e., two-dimensional subwavelength arrays of quantum emitters, can be employed as mirrors towards the design of hybrid cavities, where the optical response is given by the interplay of a cavity-confined field and the surface modes supported by the arrays. We show that stacked layers of quantum metasurfaces with orthogonal dipole orientation can serve as helicity-preserving cavities. These structures exhibit ultranarrow resonances and can enhance the intensity of the incoming field by orders of magnitude, while simultaneously preserving the handedness of the field circulating inside the resonator, as opposed to conventional cavities. The rapid phase shift in the cavity transmission around the resonance can be exploited for the sensitive detection of chiral scatterers passing through the cavity. We discuss possible applications of these resonators as sensors for the discrimination of chiral molecules. Our approach describes a new way of chiral sensing via the measurement of particle-induced phase shifts.

Figure 1

Helicity-preserving metasurface cavity. (a) A HP metasurface cavity can be constructed with composite mirrors of orthogonal dipole orientation (e.g., along $x$ and $y$), with an appropriate relative phase separation of ${\varphi }_m=k_l{\ell }_m=\pi /2+2\pi n_m$. (b),(c) Absolute value squared of RS vectors ${\mathcal{G}}_{\pm }(\mathbf{R})$ for a cavity length $\ell =12.505\lambda$, ${\ell }_m=5\lambda /4$, for square lattices with lattice spacing $a=0.8\lambda$ illuminated by RCP light with input polarization vector ${\mathbf{E}}_{\mathrm{in}}^{(+)}=(1,\mathrm{i},0{)}^{\top }/\sqrt{2}$ close to the cavity resonance. The plots are normalized to the input intensity $I_{\mathrm{in}}=|{\mathbf{E}}_{\mathrm{in}}^{(+)}{|}^2$. The metasurfaces are defined with a finite curvature radius, leading to Gaussian confinement of the mode (beam waist $w_0=8\lambda$). (d) Cavity transmission $|t_c{|}^2$ as a function of the laser detuning $\mathrm{\Delta }$ for different cavity lengths $\ell$. (e) Chiral sensing with HP metasurface cavities: Ideal chiral scatterers passing through a cavity with the same handedness yield a phase shift in the cavity transmission output which can be measured by homodyne detection [local oscillator (LO)] and leads to a phase detection sequence as schematically illustrated in the diagram.

Figure 2

Chiral sensing.—(a) Cavity phase ${\phi }_c=\arg (t_c)$ versus small perturbations of the cavity length $\delta {\ell }_s$ for different cavity lengths $\ell$ (square lattice, $a=0.8\lambda$). For each $\ell$, the resonance condition described by Eq. (7) is fulfilled. (b) Illustration of phase uncertainty in phase space for a coherent state. (c) Homodyne detection signal $⟨m_{-}(t)⟩$ for (ideal) right- and left-handed chiral scatterers passing through a RCP cavity with corresponding shot noise shown as shaded area. The dashed black line indicates the entry of a particle into the cavity and the dotted red line indicates its exit. In addition, a rotational average was performed as detailed in the Supplemental Material [55]. We have used ${\mathrm{\Delta }}_s=10{\mathrm{\Gamma }}_0$, ${\gamma }_s={\mathrm{\Gamma }}_0$, with an average of one photon within the time interval ${\mathrm{\Gamma }}_0^{-1}$, i.e., $F={\mathrm{\Gamma }}_0$, an integration time of $T{\mathrm{\Gamma }}_0=2000$ and a detuning of $\mathrm{\Delta }={\mathrm{\Gamma }}_0/100$.