
A ring-shaped optical cavity has degenerate resonant modes, because clockwise and anticlockwise waves resonate at the same frequencies. The degeneracy can be lifted, and the frequencies split, by a perturbation such as a physical rotation or the presence of a molecule or nanoparticle. Typically, the frequency splitting is proportional to the perturbation’s magnitude, as illustrated in the top panel of the figure for a hypothetical complex-valued perturbation ε (that is, one that can affect both the light’s frequency and its phase). Because the plot’s shape resembles a yo-yo-like toy called a diabolo, the degeneracy has been dubbed a diabolic point. The mode splitting around a diabolic point is the basis for optical gyroscopes, and it’s been explored for other sensing applications.
There’s another type of degeneracy, called an exceptional point, where not only do resonant frequencies coincide but their resonant modes do too. In the case of the ring resonator, inserting reflectors to scatter light from the anticlockwise mode into the clockwise mode (but not vice versa) creates an exceptional point with a single resonant mode, the clockwise-traveling wave. Perturbing the system splits that mode into two resonances, each with a small admixture of the anticlockwise wave, and the frequency splitting scales with the square root of the perturbation magnitude, as shown in the bottom panel.
Exceptional points have long been studied as mathematical curiosities, but in 2014, Jan Wiersig of the University of Magdeburg in Germany proposed that the square-root scaling could be put to good use for ultrasensitive measurements of small perturbations. Now Lan Yang and her colleagues at Washington University in St. Louis have created a proof-of-principle exceptional-point sensor that can detect a polystyrene nanoparticle twice as effectively as a diabolic-point sensor can. One challenge in practical sensor design is that although the frequency splitting is greater around an exceptional point, the split resonances themselves are also broader and thus harder to resolve. Yang and company showed that they could partially mitigate the broadening by doping the resonator with erbium ions that produce optical gain.
Meanwhile, Mercedeh Khajavikhan and her colleagues at the University of Central Florida in Orlando have used a trio of coupled ring resonators to create a third-order exceptional point—the coalescence of three modes rather than two. They found, as expected, that the frequency splitting around the degeneracy scales with the cube root of the perturbation. Their experiment was the first demonstration of such a higher-order exceptional point in an optical system and may open the door to even better detection sensitivity. (W. Chen et al., Nature 548, 192, 2017; H. Hodaei et al., Nature 548, 187, 2017.)