Resonators are a staple in optical physics, from the classic Fabry–Perot cavity to the resonances found in multilayer coatings. But in the realm of integrated optics, where light beams are routed on the surface of a chip, it is generally not feasible to build cavities from mirrors coated on interfaces perpendicular to the propagation axis. Rather, ring geometries form a more natural cavity architecture that takes advantage of finesse or quality factors being governed not by the reflection of a mirror but by the coupling between two guided modes. Through evanescent coupling, the transmission leakage from a resonant ring to a coupled waveguide can be made very small, equivalent to trapping light in a conventional cavity with a high-reflectivity mirror.
Consider that a ring resonator with a feedback of R=2/3 can lead to light multipassing the ring by a factor of 10. The consequence of this is that light on resonance is delayed—much like in demonstrations of slow light in atomic media, albeit with engineered atoms at the micrometer scale. Of course, nothing comes free, and the increased path length is accompanied by a corresponding decrease in bandwidth. Indeed, the key metric for slow-light enhancement, the delay-bandwidth product, remains constant so the only way to increase it is by cascading many resonators together in series. In each resonator, not only is the path length increased but concurrently the intensity is amplified by a factor of 10. In combination, these effects can dramatically enhance nonlinear optical interactions. For instance, the enhancement factor can be 100 for self-phase modulation or even 10,000 for four-wave-mixing-based wavelength conversion. But again, the really interesting behavior occurs in systems of cascaded resonators. Depending on how they are wired, directly or indirectly, interconnected sequences of microresonators are respectively termed CROWs or SCISSORs. These structures can display exotic propagation characteristics such as photonic bandgaps—both direct and indirect, with feedback that can be local to the rings and/or distributed across many rings. Moreover, interaction between high group¬velocity dispersion and enhanced nonlinear effects can be used to engineer novel functionalities such as pulse trapping and compression at the chip level.
For these reasons it is easy to fall in love with rings of circulating power. But even after two decades of research, the state-of-the-art can be sobering. To surmount bending losses, high lateral-index contrasts must be employed. Since scattering losses scale as the square of the permittivity difference, small structural imperfections can lead to significant losses—even 10 nm edge roughness can be detrimental. Systems of multiple interconnected resonators are even more sensitive to these losses. As a result, demonstrations of multiple interconnected resonators have been scarce.
The properties of a resonator cascade of course depend on the individual resonators but often in a nontrivial manner. Since they are typically fabricated all at once, characterizing them independently may not be readily achievable. Akin to a multilayer coating where the properties of each layer are inaccessible, cascades are generally probed in a black-box-like fashion. Of particular importance is knowledge of each resonator’s coupling coefficients, losses, and optical path length. Predicting these values from design and as-built models is problematic since evanescent coupling is exponentially sensitive to gaps that are difficult to characterize at the 10 nm scale. Losses due to scattering can be inferred from atomic force microscopy measurements of sidewall roughness but with significant error bars. Optical path lengths dictating spectral resonances can vary because of subtle variations in waveguide dimensions.
To test their method, Cooper et al. fabricated a 10-element cascade of ring resonators in a silicon-on-insulator platform. Ordinarily, the resonators would only be coupled by a single common waveguide, but for testing purposes, each resonator was also coupled to a tap waveguide. This allowed the circulating power in each resonator to be measured with a lensed fiber and detector repositioned at each tap waveguide output. The team then compared these buildup factors with the values inferred from imaging the light scattered vertically from each ring. By sweeping the spectrum of the probe source, the resonance structure of each resonator was then determined. The agreement between methods was quite good, indicating that the image-processing approach can safely be trusted to yield the same results as the laborious process of measuring the power at each tap. The results clearly reveal the challenge of realizing identical resonators. Each resonance spectrum is a unique fingerprint with poor overlap among the cascade. With this knowledge however, postfabrication trim knobs (thermal heaters for instance) might be able to tweak the system into a desired configuration.
The potential applications for microring resonators have been around for a long time, and the fabrication is finally catching up. But the next giant leap in the field requires gaining control over the fabrication process or at least managing errors with postcorrections, and that is where a rapid and accurate diagnostic technique becomes indispensible.
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