Fig. 1. Illustration of past techniques using grating-assisted microrings for frequency engineering and the current approach of shifted grating multiple mode splitting (SGMMS). (a) In the single frequency engineering case, a simple sinusoidal modulation of the inner boundary of the ring causes one mode, whose number of modulation periods is twice the m number, to have its resonance frequency split into two. Other modes that are not matched can remain in their clockwise (CW) and counterclockwise (CCW) traveling-wave propagation, and have no splitting in general. This process is termed selective mode splitting [18], as illustrated in the right panel of (a). Fourier analysis of the grating spatial frequency produces a delta function at the selected mode, and the microring cavity transmission displays that only the targeted mode is split. (b) Selective mode splitting can be extended to multi-frequency engineering by a simple sum of different spatial frequencies, termed as multiple selective mode splitting (MSMS) [23], with the corresponding Fourier components and device transmission shown on the right. (c) An apodized or chirped grating, with more detailed Fourier analysis [24] or inverse design [26], can yield a continuous modulation of grating spatial frequencies, with the splitting amplitudes typically varying in a continuous function versus mode frequencies. The shape of the grating profiles can be nontrivial to design and fabricate. We propose to circumvent these issues by using a simple single frequency sinusoidal grating with an offset shifted from the ring center. The SGMMS technique can introduce controlled mode splitting in multiple modes by an intuitive design. We note that the displayed triangular function for the spectral profile of the mode splitting is for illustration purpose only, and generally speaking, one can have various line shapes depending on the specific grating parameters in use.

Fig. 2. Experimental demonstration of SGMMS. (a) Illustration of the SGMMS device with upward-shifted grating. The red and black circles indicate the centers of the inside boundary (i.e., the shifted grating) and the outside boundary of the microring, respectively. (b) Scanning electron microscope (SEM) image of an SGMMS microring, false colored in red, with coupling waveguides on the left and right sides. In this paper, only the right waveguide is used in experiments. The grating has a nominal shift S=256  nm. The nominal average ring width is RW=1.5  μm. Zoom-in images of three parts of the microrings, highlighted by the dashed boxes, are shown in (c) and (d). (c) An SEM image of the microring shows a sinusoidal modulation with a nominal amplitude of A=12  nm. (d) The narrowest and widest RWs are measured to be (1.1±0.1)μm and (1.6±0.1)μm, respectively, where the quoted uncertainty is the one standard deviation from multiple estimates from the SEM image. (e) Normalized transmission spectra for the SMS device (top panel) with A=8  nm and S=0  nm and the SGMMS device (bottom panel) with the same A but S=256  nm. Labels (m,S) represent the azimuthal mode number and the shift in nanometers, respectively. (f) Scaled transmission spectra from (e) with annotations of the fitted Q values. In the top panel, the SMS device shows a mode splitting of approximately 100 pm only at m=165 and negligible mode splittings at nearby modes. In the bottom panel, the SGMMS modulation introduces mode splittings across multiple modes. The mode splittings for m=168, 165, and 162 are approximately 52, 32, and 16 pm, respectively. All these modes show high optical quality, with intrinsic Q around 106. (g) Summary of the measured mode splittings (2β) across all modes in (e). (h) Evolution of mode splittings from S=0  nm to S=256  nm, with a fixed A=12  nm. Above S=50  nm, adjacent modes increasingly start to show appreciable mode splittings. The uncertainties in mode splitting values in (g) and (h) are smaller than the data point size.

Fig. 3. Application of SGMMS for pump-mode-selectable optical parametric oscillation. (a) Transmission spectrum of a fabricated SGMMS device with A=12  nm and S=256  nm. The resonance dips for the fundamental TE modes are circled in red. The target SMS mode is near 1552 nm with m=165. (b) Summary of the measured mode splitting values for the device in (a) from m=175 to m=153. With a shift S=256  nm, there are 10 modes (from m=171 to m=162) with mode splitting values larger than 10 pm. (c) Optical spectra from a series of OPO experiments, where the pump mode is varied between any of the six split modes at m={165,163,162,161,160,159}. On the y axis, 0 dB is referenced to 1 mW, i.e., dBm. (d) Frequency mismatch diagrams when pumping at m={165,162,159}. The gray curves are from finite-element-method simulations, and the circles are from experimental measurements. The uncertainties are smaller than the symbol size. The mode splittings for relevant mode numbers are illustrated in colored circles, while their central (un-split) frequencies are in solid black circles. Modes that are unrelated to the OPO process only have their central frequencies shown, in empty black circles. The frequency matching condition for OPO is achieved at the red dashed lines. The colored columns highlighting involved modes in both (c) and (d) are for guidance of viewing.