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Register a new userSelf-Injection Locking and Phase-Locked States in Microresonator-Based Optical Frequency Combs
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Microresonator-based optical frequency combs have been a topic of extensive research during the last few years. Several theoretical models for the comb generation have been proposed; however, they do not comprehensively address experimental results that show a variety of independent comb generation mechanisms. Here, we present frequency-domain experiments that illuminate the transition of microcombs into phase-locked states, which show characteristics of injection locking between ensembles of comb modes. In addition, we demonstrate the existence of equidistant optical frequency combs that are phase stable but with non-deterministic phase relationships between individual comb modes.
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Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The requirement on external driving lasers has been significantly relaxed with the demonstration of soliton formation via self-injection locking of the pump laser to the microresonator. Yet to date, the dynamics of this process has not been fully understood. Prior models of self-injection locking were not able to explain sufficiently large detunings, crucial for soliton formation. Here we develop a theoretical model of self-injection locking to a nonlinear microresonator (nonlinear self-injection locking) for the first time and show that self- and cross-phase modulation of the clockwise and counter-clockwise light enables soliton formation. Using an integrated soliton microcomb of directly detectable 30 GHz repetition rate, consisting of a DFB laser self-injection-locked to a Si3N4 microresonator chip, we study the soliton formation dynamics via self-injection locking, as well as the repetition rate evolution, experimentally. We reveal that Kerr nonlinearity in microresonator significantly modifies locking dynamics, making laser emission frequency red detuned. We propose and implement a novel technique for measurements of the nonlinear frequency tuning curve and concurrent observation of microcomb states switching in real time.
Experiments and theoretical modeling yielded significant progress towards understanding of Kerr-effect induced optical frequency comb generation in microresonators. However, the simultaneous interaction of hundreds or thousands of optical comb frequencies with the same number of resonator modes leads to complicated nonlinear dynamics that are far from fully understood. An important prerequisite for modeling the comb formation process is the knowledge of phase and amplitude of the comb modes as well as the detuning from their respective microresonator modes. Here, we present comprehensive measurements that fully characterize optical microcomb states. We introduce a way of measuring resonator dispersion and detuning of comb modes in a hot resonator while generating an optical frequency comb. The presented phase measurements show unpredicted comb states with discrete {pi} and {pi}/2 steps in the comb phases that are not observed in conventional optical frequency combs.
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 (WGM) microresonator can result in multiple orders of magnitude reduction of the laser linewidth. The phenomenon was broadly studied in experiments, but its detailed theoretical model allowing improving the stabilization performance does not exist. In this paper we develop such a theory. We introduce five parameters identifying efficiency of the self-injection locking in an experiment, comprising back-scattering 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, the optical path length between the laser and the microresonator. Our calculations show that the laser linewidth can be improved by two orders of magnitude compared with the case of not optimal self-injection locking. We present recommendations on the experimental realization of the optimal self-injection locking regime. The theoretical model provides deeper understanding of the self-injection locking and benefits multiple practical applications of self-injection locked oscillators.
We present homogeneous quantum cascade lasers (QCLs) emitting around 3 THz which display bandwidths up to 950 GHz with a single stable beatnote. Devices are spontaneously operating in a harmonic comb state, and when in a dense mode regime they can be injection locked at the cavity roundtrip frequency with very small RF powers down to -55 dBm. When operated in the electrically unstable region of negative differential resistance, the device displays ultra-broadband operation exceeding 1.83 THz ($Delta f/f=50%$) with high phase noise, exhibiting self-sustained, periodic voltage oscillations. The low CW threshold (115 A$cdot$ cm$^{-2}$) and broadband comb operation ($Delta f/f=25%$) make these sources extremely appealing for on-chip frequency comb applications.
Taking advantage of an extended Lugiato--Lefever equation with third-order dispersion, we numerically show that dark cavity solitons formed in normal dispersion of microresonators are capable of emitting dispersive waves in both normal and anomalous dispersion regions, resembling the behavior of the commonly encountered bright cavity solitons. The generated dispersive waves can be accurately predicted by the dissipative radiation theory. In addition, we demonstrate the stability enhancement of Kerr frequency combs in normal dispersion regime in case the dispersive wave is emitted by dark solitons in presence of third-order dispersion.
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