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.