Transformation optics enabled ultra-sharp bending for multimode micro-ring resonators

Achieving ultra-low propagation loss in optical waveguides is crucial for boosting the quality factor of micro-resonators and large-scale photonic integration. Much effort has been paid to design and fabricate multimode waveguides to reduce the scattering loss at waveguide surfaces. Although various adiabatic curves, including Euler bends, hyperbolic tangent functions, and Bezier curves have been proposed to ensure fundamental mode transmission and reduce bending radius, the footprint is still large because of large waveguide dimensions. In this study, transformation optics (TO) is proposed to obtain exceptionally sharp bending for multimode waveguide micro-ring resonators (MRRs) based on silicon. Results show that an intrinsic quality factor (Q) of 13 ± 1.5 million for the silicon-based MRR is obtained, which indicates that the propagation loss of fabricated silicon waveguide is only 3.8 ± 0.33 dB/m. Notably, only TE0 mode is excited and inter-mode crosstalk is effectively suppressed through adiabatic mode evolution. Thanks to the waveguide mode converter designed by TO, the bending radius of the MRR with 2-µm-wide waveguide is reduced to an unprecedented level of only 10 µm, which is comparable to that of single mode waveguide. The fabricated MRR is also employed in microwave photonics, achieving ultra-narrow microwave filtering with wideband tunability, thus enabling high resolution mode selection in optoelectronic oscillator (OEO) with high flexibility. Furthermore, we also propose a novel method of stabilizing the resonant wavelength of MRR by employing an OEO. Results show that the wavelength stability is improved by two orders of magnitude. This research provides a versatile design methodology for ultrahigh-Q multimode MRRs with ultra-compact size. These advances open new possibilities for applications in microwave photonics, nonlinear photonics, large-scale photonic integration, and quantum photonics.