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Exceptional points enhance sensing in an optical microcavity

Abstract

Sensors play an important part in many aspects of daily life such as infrared sensors in home security systems, particle sensors for environmental monitoring and motion sensors in mobile phones. High-quality optical microcavities are prime candidates for sensing applications because of their ability to enhance light–matter interactions in a very confined volume. Examples of such devices include mechanical transducers1, magnetometers2, single-particle absorption spectrometers3, and microcavity sensors for sizing single particles4 and detecting nanometre-scale objects such as single nanoparticles and atomic ions5,6,7. Traditionally, a very small perturbation near an optical microcavity introduces either a change in the linewidth or a frequency shift or splitting of a resonance that is proportional to the strength of the perturbation. Here we demonstrate an alternative sensing scheme, by which the sensitivity of microcavities can be enhanced when operated at non-Hermitian spectral degeneracies known as exceptional points8,9,10,11,12,13,14,15,16. In our experiments, we use two nanoscale scatterers to tune a whispering-gallery-mode micro-toroid cavity, in which light propagates along a concave surface by continuous total internal reflection, in a precise and controlled manner to exceptional points12,13. A target nanoscale object that subsequently enters the evanescent field of the cavity perturbs the system from its exceptional point, leading to frequency splitting. Owing to the complex-square-root topology near an exceptional point, this frequency splitting scales as the square root of the perturbation strength and is therefore larger (for sufficiently small perturbations) than the splitting observed in traditional non-exceptional-point sensing schemes. Our demonstration of exceptional-point-enhanced sensitivity paves the way for sensors with unprecedented sensitivity.

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Figure 1: A comparison of sensors operating at an exceptional point and a diabolic point.
Figure 2: Dependence of the complex frequency splitting Δω on the perturbation strength for diabolic- and exceptional-point sensors.
Figure 3: Sensitivity enhancement at exceptional points.
Figure 4: Optical-gain-assisted sensing with an exceptional-point sensor.

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Acknowledgements

This work was supported by the National Science Foundation (grant number EFMA1641109) and the Army Research Office (grant number s W911NF1210026, W911NF1710189 and W911NF1610339). J.W. acknowledges funding from the DFG (project number WI1986/6-1). We thank S. Rotter and X. F. Jiang for discussions.

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Authors and Affiliations

Authors

Contributions

J.W., Ş.K.Ö. and L.Y. conceived the idea. W.C., Ş.K.Ö. and L.Y. designed the experiments. W.C. and G.Z. fabricated the devices. W.C. performed the measurement with help from G.Z. Numerical simulations and theoretical framework were provided by W.C. and J.W. All authors discussed the results and contributed to the manuscript. L.Y. supervised the research.

Corresponding author

Correspondence to Lan Yang.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks K. Bliokh, M. Rechtsman and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Figure 1 Experimental set-up for the study of exceptional-point sensors.

a, The probe light is coupled into a micro-toroid cavity through a fibre-taper waveguide with light in either the clockwise or anticlockwise injection direction, controlled by an optical switch (OS). Fibre-based polarization controllers (PCs) are used to optimize the coupling conditions. The transmission and reflection signals at the output ports of the fibre-taper waveguide are received by the photodetectors (PDs), which are monitored by an oscilloscope (OSC). The positions of the micro-toroid cavity and the silica nano-tips are controlled by nano-positioning stages. TLD, tunable laser diode; C, optical circulator; WGM cavity, whispering-gallery-mode cavity. b, An optical image of a micro-toroid cavity together with a fibre-taper waveguide and three silica nano-tips. c, SEM image of a micro-toroid cavity. The major and minor diameters are about 80 μm and 10 μm, respectively.

Extended Data Figure 2 Effects of the first two scatterers on the complex frequency splitting and backscattering of light.

a, A whispering-gallery-mode (WGM) cavity with three scatterers (s1, s2 and s3) at angular position βj. The angular position of the first scatterer β1 is set to be zero. The two large scatterers are exploited to obtain an exceptional point, and the small scatterer is used to investigate the sensing applications. b, Dependence of the complex frequency splitting on the angular position of the second scatterer. The size and position of the first scatterer are fixed. The blue squares and red circles denote the frequency splitting and difference in linewidth, respectively. These quantities vary periodically when the angular positions of the second scatterer are tuned, and an exceptional point (EP) is obtained when both frequency splitting and difference in linewidth vanish. c, When the system is at an exceptional point, the reflection spectrum exhibits a strong resonance peak for light injection in the anticlockwise (ACW) direction, whereas it vanishes for light injection in the clockwise (CW) direction. d, When the system is far away from exceptional points, similar reflection spectra are obtained for light injections in the clockwise and anticlockwise directions. In c and d, the red (blue) curves show the reflection spectrum when the light is injected in the anticlockwise (clockwise) direction.

Extended Data Figure 3 Numerical simulations of the dependence of the complex frequency splitting on the perturbation strength for diabolic- and exceptional point sensors.

a, Variations of the complex frequency splitting when a target scatterer is moved towards the sensor with a diabolic point (red circles) and an exceptional point (blue squares). The insets illustrate the corresponding models of the sensors used in the numerical simulations. b, Dependence of the enhancement in the complex frequency splitting |ΔωEPωDP| on the perturbation strength ϵ of the target scatterer. Theoretical prediction (black curve) is given by equation (1), with A(2)ei2mβ = 2.836 + 2.649i. The inset shows the relationship between |ΔωEP| and ϵ on a logarithmic scale, which confirms the experimental results and theoretical predictions.

Extended Data Figure 4 Dependence of the complex frequency splitting on the angular position of a target scatterer with sufficiently large perturbation strength.

a, b, Experimentally obtained (a) and numerically simulated (b) variations in frequency splitting (blue squares) and difference in linewidth (red circles) when the angular position β of the target scatterer is varied. Owing to the interference of light scattered by the target scatterer and the intrinsic scattered light, the angular position (in the azimuthal direction) of the target scatterer can affect the complex frequency splitting. The frequency splitting and difference in linewidth vary periodically when the angular position of the target scatterer is changed. In certain ranges, the trends of the variations in the frequency splitting and difference in linewidth are opposite. In contrast, at particular angular positions, the frequency splitting and difference in linewidth both tend to vanish, owing to the destructive interference between the backscattering induced by the target scatterer and the intrinsic backscattering when the target scatterer is not sufficiently small (leading to |A(2)| ≈ |ϵ|). These observations agree with the predictions from equation (1).

Extended Data Figure 5 Numerical simulation of the dependence of the complex frequency splitting on the angular position of a target scatterer with sufficiently small perturbation strength.

Here, the target scatterer is sufficiently small, leading to . The frequency splitting (difference in linewidth) changes periodically from minimum (maximum) to maximum (minimum), and the absolute value of the complex frequency splitting is close to constant, agreeing well with the predictions from equation (2). Black crosses, blue squares and red circles denote the absolute value of the complex frequency splitting, and the absolute values of its real and imaginary parts, respectively.

Extended Data Figure 6 Detection of a single polystyrene nanoparticle with a radius of 200 nm using an exceptional-point sensor.

a, A polystyrene nanoparticle is transferred from a nano-tip to the surface of a micro-toroid (top to bottom). A blue-light laser is aimed into the fibre taper to enable monitoring of the process. Frequency splitting in the transmission spectrum of the cavity was observed, confirming that the particle was placed within the mode volume. b, c, Optical image of an exceptional-point (b) and diabolic-point (c) sensor with a nanoparticle. d, e, The transmission spectra of the exceptional-point (d) and diabolic-point (e) sensor before (i) and after (ii) adsorption of a nanoparticle on the surface of the micro-toroid. The inset in d shows fully asymmetric backscattering with clockwise and anticlockwise injection directions.

Extended Data Figure 7 Effect of optical gain in a cavity coupled with a fibre-taper waveguide.

a, Complex frequency splitting of an active exceptional-point sensor subject to a perturbation. As the gain increases, the frequency splitting and difference in linewidth remain stable (left panel). Note that the optical gain can improve the resolvability of splitting modes, whereas it does not enhance the sensitivity (that is, the complex frequency splitting). The optical gain compensates the losses and thus drives the cavity from an under-coupling regime closer to a critical point (right panels). This is equivalent to the case in which the coupling strength between a fibre-taper waveguide and a cavity is increased, whereas the intrinsic loss of the resonance is fixed. b, Complex frequency splitting of a diabolic-point sensor subject to a perturbation (different from a; left panel). As the coupling strength between the fibre-taper waveguide and the cavity increases, the frequency splitting and difference in linewidth remains unchanged (right panels).

Extended Data Figure 8 Dependence of the complex frequency splitting on the position of a nano-tip.

The nano-tip is moved continuously towards and away from a cavity for three cycles. Blue squares and red circles denote frequency splitting and difference in linewidth, respectively. The insets illustrate a target scatterer being moved towards or away from the cavity.

Extended Data Figure 9 Finite-element simulations of the field distribution of modes.

a, The electric-field distribution in an exceptional-point sensor coupled with a waveguide. b, c, The electric-field distribution in the exceptional-point sensor when subject to two different perturbations. The distance between the target scatterer and the cavity is 0.5 μm (b) or 0 μm (c). At the exceptional point, the cavity supports only one travelling mode (for example, the clockwise-travelling mode in a), which can be observed directly from the output of the waveguide. Also, there is no interference pattern in the electric-field distribution within the cavity (a). When the system is perturbed by a target scatterer (b, c), it shifts away from the exceptional point, resulting in bidirectional transmission in the waveguide and an interference pattern with clear nodes and antinodes in the electric-field distribution in the cavity.

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Chen, W., Kaya Özdemir, Ş., Zhao, G. et al. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017). https://doi.org/10.1038/nature23281

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