Numerical study of solitonic pulse generation in the self-injection locking regime at normal and anomalous group velocity dispersion.

We developed an original model describing the process of the frequency comb generation in the self-injection locking regime and performed numerical simulation of this process. Generation of the dissipative Kerr solitons in the self-injection locking regime at anomalous group velocity dispersion was studied numerically. Different regimes of the soliton excitation depending on the locking phase, backscattering parameter and pump power were identified. It was also proposed and confirmed numerically that self-injection locking may provide an easy way for the generation of the frequency combs at normal group velocity dispersion. Generation of platicons was demonstrated and studied in detail. The parameter range providing platicon excitation was found.

Dynamics of soliton self-injection locking in optical microresonators.

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 demonstration of soliton formation via self-injection locking of the pump laser to the microresonator has significantly relaxed the requirement on the external driving lasers. Yet to date, the nonlinear dynamics of this process has not been fully understood. Here, we develop an original theoretical model of the laser self-injection locking to a nonlinear microresonator, i.e., nonlinear self-injection locking, and construct state-of-the-art hybrid integrated soliton microcombs with electronically detectable repetition rate of 30 GHz and 35 GHz, consisting of a DFB laser butt-coupled to a silicon nitride microresonator chip. We reveal that the microresonator's Kerr nonlinearity significantly modifies the laser diode behavior and the locking dynamics, forcing laser emission frequency to be red-detuned. A novel technique to study the soliton formation dynamics as well as the repetition rate evolution in real-time uncover non-trivial features of the soliton self-injection locking, including soliton generation at both directions of the diode current sweep. Our findings provide the guidelines to build electrically driven integrated microcomb devices that employ full control of the rich dynamics of laser self-injection locking, key for future deployment of microcombs for system applications.

Author Correction: Electrically pumped photonic integrated soliton microcomb.

The original version of this Article contained an error in the first sentence of the Acknowledgements, which incorrectly read 'This publication was supported by Contract HR0011-15-C-0055 (DODOS) from the Defense Advanced Research Projects Agency (DARPA), Defense Sciences Office (DSO).' The correct version states 'Microsystems Technology Office (MTO)' in place of 'Defense Sciences Office (DSO)'. This has been corrected in both the PDF and HTML versions of the Article.

Electrically pumped photonic integrated soliton microcomb.

Microcombs provide a path to broad-bandwidth integrated frequency combs with low power consumption, which are compatible with wafer-scale fabrication. Yet, electrically-driven, photonic chip-based microcombs are inhibited by the required high threshold power and the frequency agility of the laser for soliton initiation. Here we demonstrate an electrically-driven soliton microcomb by coupling a III-V-material-based (indium phosphide) multiple-longitudinal-mode laser diode chip to a high-Q silicon nitride microresonator fabricated using the photonic Damascene process. The laser diode is self-injection locked to the microresonator, which is accompanied by the narrowing of the laser linewidth, and the simultaneous formation of dissipative Kerr solitons. By tuning the laser diode current, we observe transitions from modulation instability, breather solitons, to single-soliton states. The system operating at an electronically-detectable sub-100-GHz mode spacing requires less than 1 Watt of electrical power, can fit in a volume of ca. 1 cm3, and does not require on-chip filters and heaters, thus simplifying the integrated microcomb.

Influence of acoustic energy walk-off on acousto-optic diffraction characteristics.

Influence of acoustic beam energy walk-off on characteristics of Bragg diffraction of light is studied theoretically and experimentally by the example of a paratellurite single crystal. Two cases of isotropic and anisotropic light scattering are examined. Angular and frequency characteristics of acousto-optic interaction are calculated in wide ranges of Bragg angles and ultrasound frequencies by means of modified Raman-Nath equations. It is shown that the walk-off can substantially change the width of angular and frequency ranges, resulting in their narrowing or broadening subject to position of the operating point in the Bragg angle frequency characteristic. Coefficients of broadening are introduced for characterization of this effect. It is established that frequency dependences of the broadening coefficients are similar to the Bragg angle frequency characteristics. Experimental verification of the calculations is carried out with a paratellurite cell of 10.5° crystal cut.