Fig. 1. Self-modulation resonator sensing mechanism. (a) Schematic diagram of the self-modulation LiNbO3 resonator, (b) displacement sensing response reading principle, (c) evanescent field attenuation rate as a function of coupling distance as well as resonator diameter for transverse magnetic (TM) mode, and (d) evanescent field attenuation rate as a function of coupling distance as well as resonator diameter for transverse electric (TE) mode.

Fig. 2. Resonator test results. (a)–(d) Losses of the LiNbO3 resonator as a function of coupling distance for R=1.5,2.5,4,5  mm; (e) and (f) variation of evanescent field attenuation rate for different radius resonators for TM and TE modes, respectively.

Fig. 3. Displacement sensing platform. (a) Prism coupling displacement sensing system based on self-modulation of the LiNbO3 resonator, which includes the polarization controller (PC), photoelectric detector (PD), bandpass filter (BPF), oscilloscope (OSC), and function generator (FG). (b) LiNbO3 resonator with gold electrodes sputtered on the top and bottom surfaces and its Q-value. (c) Response amplitude as a function of the loaded modulation voltage and frequency. (d) Maximum filtered signal normalized response amplitude corresponding to different Q-values.

Fig. 4. Displacement sensing test results. (a) Transmission as a function of coupling gap d at various ratios of scattering loss to coupling loss (κe/κex), (b) power spectral density of the displacement sensing system, (c) experimental results on the variation of response amplitude with displacement, and (d) displacement sensing scale factor.

Fig. 5. Stability of the displacement sensing system. (a) Output signal of the displacement sensing system at rest; (b) Allan deviation.

Fig. 6. Comparison of detection limits for resonator displacement sensing.

Fig. 7. Resonator mode simulation result.

Fig. 8. Normalized field strength distributions for different sizes of resonators.

Fig. 9. Evanescent field attenuation rate as a function of the resonator radius and sidewall curvature radius.

Fig. 10. Transmission spectrum derivation. (a) Transmission spectrum; (b) transmission spectrum versus coupling distance derivation.

Fig. 11. Coupling sensing model response signal.