Optimization of Laser Stabilization via Self-Injection Locking to a Whispering-Gallery-Mode Microresonator
Ramzil R. Galiev, Nikita M. Kondratiev, Valery E. Lobanov, Andrey B. Matsko, Igor A. Bilenko
Abstract
Self-injection locking is a dynamic phenomenon representing stabilization of the emission frequency of an oscillator with a passive cavity enabling frequency-filtered coherent feedback to the oscillator cavity. For instance, self-injection locking of a semiconductor laser to a high-quality-factor (high-$Q$) whispering-gallery-mode microresonator can result in reduction of the laser linewidth by multiple orders of magnitude. The phenomenon was broadly studied in experiments, but there was no detailed theoretical model allowing improvement of the stabilization performance. In this paper we develop such a theory. We introduce five parameters identifying the efficiency of the self-injection locking in an experiment, comprising backscattering efficiency, phase delay between the laser and the high-$Q$ cavities, frequency detuning between the laser and the high-$Q$ cavities, the pump coupling efficiency, and the optical path length between the laser and the microresonator. Our calculations show that the laser linewidth can be reduced by 2 orders of magnitude compared with the case of nonoptimal self-injection locking. We present recommendations for experimental realization of the optimal self-injection-locking regime. The theoretical model provides deeper understanding of self-injection locking and benefits multiple practical applications of self-injection-locked oscillators.