To quantify the CCW light enhancement, we use an optical circulator to monitor the feedback light intensity and compare the intensities with and without auxiliary-prism enhancement [Fig. 2(b)]. Furthermore, we set up a WGMR SIL laser to verify the improvement in performance with the feedback-enhancement approach [Fig. 5(a)].

The results show that the performance of the WGMR SIL laser improves after applying the enhanced feedback approach. In terms of instantaneous frequency noise [Fig. 4(b)], the free-running case is approximately 3.5×10⁵ Hz²/Hz (instantaneous line width is about1.1MHz), the Rayleigh backscattering SIL case is approximately 40 Hz²/Hz (instantaneous line width is about 125 Hz), and the enhanced feedback SIL case is 2.5 Hz²/Hz (instantaneous line width is about7 Hz), obtaining linewidth suppression gains of almost 50 dB and 10 dB. In terms of the SIL range [Fig. 5(a)], the Rayleigh backscattering SIL case is approximately 0.8 GHz, and the enhanced feedback SIL case expands the range up to 8 GHz, substantially enhancing the injection locking robustness. In terms of the RIN [Fig. 5(b)], the free-running case is approximately -142 dBc/Hz at 10 MHz, the Rayleigh backscattering SIL case is approximately -147 dBc/Hz at 10 MHz, and the enhanced-feedback SIL suppresses the RIN to -152 dBc/Hz at 10 MHz.

Narrow linewidth lasers based on whispering-gallery-mode resonator (WGMR) self-injection locking (SIL) have the potential for use in fields such as coherent optical communication, optical atomic clocks, high-resolution spectroscopy, and precision frequency measurement. The intensity of SIL optical feedback is a crucial parameter that determines the performance of locked lasers, including instantaneous linewidth, locking range, and relative intensity noise (RIN). At present, the SIL technique commonly uses WGMR Rayleigh backscattering to create optical feedback. However, the optical feedback intensity is uncontrollable. Investigations have been successfully conducted on the feedback control of on-chip WGMRs such as Si₃N₄, and AlN using micro-cavity refectors. However, there are few studies on how to control the feedback intensity for high-Q fluoride crystalline WGMRs. Liang et al. proposed a feedback-intensity enhancement scheme for crystalline WGMRs using a set of optical components, including a coupling prism, collimation lenses, and a mirror reflector. However, the additional components increased the complexity and instability of the system. In this study, we propose a compact and easy-to-operate feedback-enhancement approach for crystalline WGMRs that replaces the set of feedback-enhanced components with a designed auxiliary prism, which can be integrated with the WGMR. It provides a compact solution for controlling feedback intensity in WGMR SIL technology.

We design an auxiliary prism to enhance the counterclockwise (CCW) light amplitude inside the WGMR (Fig. 1). The auxiliary prism first extracts the clockwise (CW) light from the WGMR with a specific angle Φ that is determined by the coupling phase-matching condition. The coupled output beam travels over an optical length d in the prism and is then vertically reflected by highly reflective film coated on the prism. Finally, it is coupled back into the WGMR along the original trace to enhance the CCW light amplitude with any additional optical components. The bottom angle of the auxiliary prism is crucial and designed to equal the angle Φ for high back-coupling efficiency. In the experiment, we use a homemade high-Q value (1.97×10⁹) MgF₂ WGMR [Fig. 2(a)] as the platform and an auxiliary prism to enhance the amplitude of CCW light with the transverse electric (TE) mode. The bottom angle of the prism is designed as 52.3° (for the TE mode at 1.55 μm). The output coupling point is also important and should ensure that d is approximately equal to the Rayleigh length of the light to prevent beam divergence. Therefore, the coupling point between WGMR and auxiliary prism is chosen as approximately 500 μm from the bottom corner of the prism.

Compared to the WGMR Rayleigh backscattering technique, the auxiliary prism improves the intensity of CCW light with the TE mode in the WGMR by two orders of magnitude [Fig. 3(a)] and does not enhance the intensity of the feedback light with the transverse magnetic (TM) mode [Fig. 3(b)]. If the bottom angle of the prism can be further optimized, the feedback intensity can be further increased.

We propose a crystalline WGMR feedback-enhancement approach with an auxiliary prism and successfully improve the CCW light intensity in the WGMR by almost two orders of magnitude. With the auxiliary-prism enhancement, the WGMR SIL laser performance, including the instantaneous linewidth, locking range, and RIN, is significantly improved compared to those in the free-running and Rayleigh backscattering SIL cases. The proposed approach provides a compact solution for controlling feedback intensity in WGMRs and is especially suitable for long-wavelength SIL lasers in which the resonator Rayleigh backscattering amplitude is low.