We present the analysis of the self-injection locking of a single-frequency laser diode to a high-Q whispering gallery mode (WGM) microresonator with Rayleigh backscattering. Simple analytical formulas for the width of the locking band and resulting laser linewidth are derived.

Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.

Using the parity and time reversal symmetries of a two-dimensional spin-orbit coupled Bose-Einstein condensate in a lattice created by the Zeeman field, we identify and find numerically various families of localized solutions, including multipole and half-vortex solitons. The obtained solutions may exist at any direction of the gauge field with respect to the lattice and can be found either in finite gaps (for repulsive interatomic interactions) or in a semi-infinite gap (for attractive interactions). The existence of half-vortices requires higher symmetry (the reflection with respect to the field direction). Stability of these modes makes them feasible for experimental observation.

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons is injection locked by the external drive at long timescales, but exhibits an unexpected suppression of the fast timing jitter. Counterintuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long timescale stability of the Kerr frequency comb’s repetition rate is improved by more than 4 orders of magnitude, the purified microwave signal shows a reduction of the phase noise by 30 dB at offset frequencies above 10 kHz.

Optical whispering gallery mode (WGM) resonators allow combination of small mode volume with high $Q$-factor. Silicon is a major material for modern microelectronics and photonics. However, relatively low $Q$-factors of optical Si microresonators demonstrated so far have limited some promising applications. We report what we believe is first time measurement of a $Q$-factor of $1.2\times {10}^9$ in millimeter scale crystalline silicon optical resonators at 1550 nm wavelength. A novel silicon hemispherical coupler allowed us to reach up to 35% of coupling efficiency.