Fourier Synthesis Dispersion Engineering of Photonic Crystal Microrings for Broadband Frequency Combs

Phase-stabilised self-injection-locked microcomb

Microresonator frequency combs (microcombs) hold great potential for precision metrology within a compact form factor, impacting a wide range of applications such as point-of-care diagnostics, environmental monitoring, time-keeping, navigation and astronomy. Through the principle of self-injection locking, electrically-driven chip-based microcombs with minimal complexity are now feasible. However, phase-stabilisation of such self-injection-locked microcombs-a prerequisite for metrological frequency combs-has not yet been attained. Here, we address this critical need by demonstrating full phase-stabilisation of a self-injection-locked microcomb. The microresonator is implemented in a silicon nitride photonic chip, and by controlling a pump laser diode and a microheater with low voltage signals (less than 1.57 V), we achieve independent control of the comb's offset and repetition rate frequencies. Both actuators reach a bandwidth of over 100 kHz, enabling phase-locking of the microcomb to external frequency references. These results establish photonic chip-based, self-injection-locked microcombs as low-complexity yet versatile sources for coherent precision metrology in emerging applications.

Band flipping and bandgap closing in a photonic crystal ring and its applications

The size of the bandgap in a photonic crystal ring is typically intuitively considered to monotonically grow as the modulation amplitude of the grating increases, causing increasingly large frequency splittings between the "dielectric" and "air" bands. In contrast, here we report that as the modulation amplitude in a photonic crystal ring increases, the bandgap does not simply increase monotonically. Instead, after the initial increase, the bandgap closes and then reopens again with the two bands flipped in energy. The air and dielectric band edges are degenerate at the bandgap closing point. We demonstrate this behavior experimentally in silicon nitride photonic crystal microrings, where we show that the bandgap is closed to within the linewidth of the optical cavity mode, whose intrinsic quality factor remains unperturbed with a value ≈ 1×106. Moreover, through finite-element simulations, we show that such bandgap closing and band flipping phenomena exist in a variety of photonic crystal rings with varying unit cell geometries and cladding layers. At the bandgap closing point, the two standing wave modes with a degenerate frequency are particularly promising for single-frequency lasing applications. Along this line, we propose a compact self-injection locking scheme that integrates many core functionalities in one photonic crystal ring. Additionally, the single-frequency lasing might be applicable to distributed-feedback (DFB) lasers to increase their manufacturing yield.

Spectral Engineering of Optical Microresonators in Anisotropic Lithium Niobate Crystal

On-chip optical microresonators are essential building blocks in integrated optics. The ability to arbitrarily engineer their resonant frequencies is crucial for exploring novel physics in synthetic frequency dimensions and practical applications like nonlinear optical parametric processes and dispersion-engineered frequency comb generation. Photonic crystal ring (PhCR) resonators are a versatile tool for such arbitrary frequency engineering, by controllably creating mode splitting at selected resonances. To date, these PhCRs have mostly been demonstrated in isotropic photonic materials, while such engineering can be significantly more complicated in anisotropic platforms that often offer more fruitful optical properties. Here, the spectral engineering of chip-scale optical microresonators is realized in the anisotropic lithium niobate (LN) crystal by a gradient design that precisely compensates for variations in both refractive index and perturbation strength. Controllable frequency splitting is experimentally demonstrated at single and multiple selected resonances in LN PhCR resonators with different sizes, while maintaining high quality-factors up to 1 × 106. Moreover, a sharp boundary is experimentally constructed in the synthetic frequency dimension based on an actively modulated x-cut LN gradient-PhCR, opening up new paths toward the arbitrary control of electro-optic comb spectral shapes and exploration of novel physics in the frequency degree of freedom.

Multi-mode microcavity frequency engineering through a shifted grating in a photonic crystal ring

Frequency engineering of whispering-gallery resonances is essential in microcavity nonlinear optics. The key is to control the frequencies of the cavity modes involved in the underlying nonlinear optical process to satisfy its energy conservation criterion. Compared to the conventional method that tailors dispersion by cross-sectional geometry, thereby impacting all cavity mode frequencies, grating-assisted microring cavities, often termed as photonic crystal microrings, provide more enabling capabilities through mode-selective frequency control. For example, a simple single period grating added to a microring has been used for single frequency engineering in Kerr optical parametric oscillation (OPO) and frequency combs. Recently, this approach has been extended to multi-frequency engineering by using multi-period grating functions, but at the cost of increasingly complex grating profiles that require challenging fabrication. Here, we demonstrate a simple approach, which we term as shifted grating multiple mode splitting (SGMMS), where spatial displacement of a single period grating imprinted on the inner boundary of the microring creates a rotational asymmetry that frequency splits multiple adjacent cavity modes. This approach is easy to implement and presents no additional fabrication challenges compared to an unshifted grating, and yet is very powerful in providing multi-frequency engineering functionality for nonlinear optics. We showcase an example where SGMMS enables OPO across a wide range of pump wavelengths in a normal-dispersion device that otherwise would not support OPO.