Exceptional-surface-enhanced rotation sensing with robustness in a whispering-gallery-mode microresonator

Traditional optical gyroscopes rely on the Sagnac effect that the resonant frequency shift is linear with the rotation rate. Recently, optical gyroscopes operating near an exceptional point (EP) have been extensively investigated to improve the response to rotation. However, the high-performance implementation of this kind of gyroscope requires strict conditions, which restrict the practical application of these devices. In this paper, a non-Hermitian photonic configuration based on a single resonator is proposed to establish an exceptional surface (EP surface) constructed of numerous EPs. It is demonstrated theoretically that rotation-induced frequency splitting in our configuration is four orders of magnitude higher than that in the traditional gyroscope. We also investigate the shot-noise-limited minimum detectable rotation rate compared to the conventional gyroscope with the same radius and intrinsic loss, when the system is tuned around the EP. This proposed approach attempts to combine robustness with high sensitivity detection of the rotation.

Figure 1

(a) Schematic of a non-Hermitian photonic structure. A WGM microresonator is coupled to a fiber taper with a reflector on one side and a phase-shifted FBG on the other side. The blue (dashed line) box shows a schematic of a phase-shift FBG. At the phase-shifted FBG, the left-incident signal is $S_{\text{in}}$ and the right-incident signal is the CCW mode. (b) Schematic diagram of an EP surface [31]. The EP surface exhibits the characteristic that the operating point of the system will shift along the surface when it experiences undesired perturbations. (c) Optical mode-coupling situations in the absence or presence of the rotation. The CW and CCW optical modes in the WGM microresonator are represented by red solid and dotted circles, respectively.

Figure 2

(a) Reflection spectra and transmission spectra of a $\pi$-shifted FBG at $\mathrm{\Delta }{\omega }_s=0$ with an effective index $n_{\text{eff}}=1.44$, a uniform index modulation $\mathrm{\Delta }{n}_{\mathrm{ac}}=5\times {10}^{-4}$, a nominal period $\mathrm{\Lambda }=538.19$ nm, a Bragg wavelength ${\lambda }_B=1550\text{nm}$, length $l=2$ mm, and $\mathrm{\Omega }=0$. (b) Reflection and transmission spectra of the $\pi$-shifted FBG as functions of the rotation rate with the system operating at an EP surface, with length $l=8$ mm and $\mathrm{\Delta }{\omega }_B=0$.

Figure 3

Numerical simulations of the complex eigenfrequency splitting dependent on the phases ${\varphi }_1$ and ${\varphi }_2$ with rotation rate $\mathrm{\Omega }=5$ rad/s: (a) the real part $\text{Re}\left(\mathrm{\Delta }{\omega }_{\text{sp}}\right)$ of the eigenfrequency splitting and (b) the imaginary part $\text{Im}\left(\mathrm{\Delta }{\omega }_{\text{sp}}\right)$ of the eigenfrequency splitting. The parameters are $\kappa =2.25\times {10}^8\mathrm{Hz}$, $R=171.31\mu \text{m}$, and $r_m=0.8$.

Figure 4

Series of normalized transmission spectra of the cases of the EP sensor and conventional gyroscope as a function of rotation rate $\mathrm{\Omega }$. Note that the normalized transmission spectra of the conventional gyroscope are depicted with rotation rate $\mathrm{\Omega }\times 100$.

Figure 5

Trajectory of the transmission peaks as a function of the rotation rate $\mathrm{\Omega }$. The red solid line and white dashed line highlight the eigenfrequencies with the variation of rotation rate $\mathrm{\Omega }$. Here $\mathrm{\Delta }{\omega }_{\pm }={\omega }_{\pm }-{\omega }_0$ are the eigenfrequency detunings.

Figure 6

Comparison of the Sagnac scale factor $S_{\text{ES}}$ [given in Eq. (16)] of the EP surface system and the Sagnac scale factor of the conventional gyroscope. The inset shows the Sagnac scale factor of the conventional gyroscope.

Figure 7

Shot-noise-limited ${\mathrm{\Omega }}_{\text{min}}$ of the EP gyroscope plotted versus rotation rate. The black dashed line is the optimized shot-noise-limited ${\mathrm{\Omega }}_{\text{min}}$ of the conventional gyroscope.