Microcavity Sensor Enhanced by Spontaneous Chiral Symmetry Breaking

An optical microcavity provides a prominent platform for single-nanoparticle detection with ultrahigh sensitivity. Recently, microcavity sensors working at the exceptional point have caught great attention due to their ability to enhance sensitivity, but suffer from simultaneously amplified noise. Here, we propose employing a nonlinear microcavity to enhance the sensitivity of single-nanoparticle detection based on spontaneous chiral symmetry breaking. It is found that sensors operating at the symmetry-breaking threshold experience a gigantic enhancement in sensitivity, which is caused by the square-root response to perturbation in a lossless microcavity. Through the analysis for a realistic microcavity, a 30-fold sensitivity enhancement is demonstrated by working at the threshold, and the enhancement is also confirmed by numerical simulation. Furthermore, the noise performance is analyzed to be superior in thermorefractive noise and quantum noise performance in comparison to a conventional microcavity-sensing scheme. Merging the spontaneous chiral symmetry-breaking effect with practical sensing applications, the results pave a universal way for high-performance microcavity sensing with enhanced sensitivity and reduced noise.

Figure 1

(a) Schematic of the microcavity sensor enhanced by spontaneous chiral symmetry breaking. Left: visualization of the chiral optical field in a disk microcavity with ${\chi }^{(3)}$ Kerr nonlinearity, where red and blue dashed curves represent the unperturbed CCW and CW traveling waves with an effective coupling strength of $g_{\mathrm{eff}}$. $\epsilon e^{i\varphi }$ is the perturbation induced by an attached nanoparticle, which changes the traveling waves into the chiral optical fields marked by solid curves. Right: coupling mechanism between CW and CCW waves. (b) The dashed (solid) curves show the dependence of the chirality $C$ on the intracavity intensity $A^2$ before (after) perturbation. (i)–(iii) The intensity of CCW and CW waves at different intracavity intensities.

Figure 2

Sensing analysis in a lossless microcavity. (a) The response of the signal $\mathrm{\Delta }D$ to the perturbation strength $\epsilon /g_0$ and the intracavity intensity $A^2$. The gray zone represents $\mathrm{\Delta }D=0$. (b) A logarithmic plot of the relationship between $\mathrm{\Delta }D$ and $\epsilon /g_0$ at intracavity intensities $A^2=1.5$, 2, 2.5. The gray dashed lines are linear fitting functions for perturbations $\epsilon /g_0<0.01$. (c) The response of the sensitivity $\mathrm{\Delta }D/\epsilon$ to the perturbation strength $\epsilon /g_0$ at $A^2=1.5$, 2, 2.5. The intensities are normalized by $g_0/M$.

Figure 3

(a) Top: a lossy microcavity sensor with an add-drop coupling structure. The red (blue) curve represents the CCW (CW) wave. A nanoparticle attached to the cavity induces an extra coupling strength $\epsilon$. Bottom: typical drop-port spectra with input power $P_{\mathrm{in}}$ of $50$ and $200\mu \mathrm{W}$ from each port of the the bus waveguide. (b) Dependence of the output signal $\mathrm{\Delta }D$ on the input power $P_{\mathrm{in}}$ and the linear coupling strength $g_0$, under a perturbation strength of $\epsilon /2\pi =0.05$ MHz. (c) The output signal $\mathrm{\Delta }D$ versus the input power at the intrinsic coupling strength of $g_0/2\pi =4.5$ MHz, corresponding to the dashed line in (b). (d) Dependence of the output signal $\mathrm{\Delta }D$ and the sensitivity $\mathrm{\Delta }D/\epsilon$ on the perturbation strength $\epsilon$ at the chiral symmetry-breaking threshold. The blue dots are the signal from calculation and the red line is a fitting curve with a power function, and the blue line is the calculated sensitivity. The experimental adaptable parameters used in this calculation are ${\kappa }_{1,0}/2\pi ={\kappa }_{2,0}/2\pi =2.8$ MHz, ${\kappa }_{\mathrm{in}}={\kappa }_{\mathrm{out}}=0.2{\kappa }_{1,0}$, $M=1.33\times {10}^{13}$ MHz/J.

Figure 4

Sensitivity analysis with two-dimensional numerical simulation results. (a) Output spectra obtained during the frequency scanning before (top) and after (bottom) perturbation. The dots and lines are simulation results and theoretical fitting, respectively. (b) The dependence of the intensity difference between CW and CCW outputs before ($D$, dark blue) and after perturbation ($D^{\mathrm{\prime }}$, light blue) on the input power $P_{\mathrm{in}}$ under a perturbation strength of $\epsilon /g_0=0.05$. The sensing signal $\mathrm{\Delta }D$ is denoted in the orange dots. (c) Plots of the signal $\mathrm{\Delta }D$ versus the perturbation strength $\epsilon$ at the SCSB threshold in linear coordinate and logarithm coordinate (inset). Output intensity results are normalized by the input intensity and the perturbation $\epsilon$ is normalized by $g_0$.

Figure 5

Relative noise level compared to the signal. (a) Thermorefractive noise. (b) Quantum shot noise. (c) Relative laser-intensity noise. (d) Relative laser-phase noise. The black lines represent the proposed sensing method in this work, and the red lines represent the sensing method based on directly detecting backscattering intensities. The gradient gray curve in (d) covers the calculation from $P_{\mathrm{in}}=335$ to $355\mu \mathrm{W}$, where the top curve represents $P_{\mathrm{in}}=335\mu \mathrm{W}$.