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Self-injection locking is a dynamic phenomenon representing stabilization ofthe emission frequency of an oscillator with a passive cavity enablingfrequency 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 (WGM) microresonator can result in multipleorders of magnitude reduction of the laser linewidth. The phenomenon wasbroadly studied in experiments, but its detailed theoretical model allowingimproving the stabilization performance does not exist. In this paper wedevelop such a theory. We introduce five parameters identifying efficiency ofthe self-injection locking in an experiment, comprising back-scatteringefficiency, phase delay between the laser and the high-Q cavities, frequencydetuning between the laser and the high-Q cavities, the pump couplingefficiency, the optical path length between the laser and the microresonator.Our calculations show that the laser linewidth can be improved by two orders ofmagnitude compared with the case of not optimal self-injection locking. Wepresent recommendations on the experimental realization of the optimalself-injection locking regime. The theoretical model provides deeperunderstanding of the self-injection locking and benefits multiple practicalapplications of self-injection locked oscillators.

Optimization of laser stabilization via self-injection locking to WGM microresonator