@article{936, author = {Zhuan-Fang Bi and Alejandro Rodriguez and Hila Hashemi and David Duchesne and Marko Loncar and Ke-Ming Wang and Steven Johnson}, title = {High-efficiency second-harmonic generation in doubly-resonant $\chi^(2)$ microring resonators}, abstract = {By directly simulating Maxwell{\textquoteright}s equations via the finite-difference time-domain (FDTD) method, we numerically demonstrate the possibility of achieving high-efficiency second harmonic generation (SHG) in a structure consisting of a microscale doubly-resonant ring resonator side-coupled to two adjacent waveguides. We find that > 94\% conversion efficiency can be attained at telecom wavelengths, for incident powers in the milliwatts, and for reasonably large bandwidths (Q \~{} 1000s). We demonstrate that in this high efficiency regime, the system also exhibits limit-cycle or bistable behavior for light incident above a threshold power. Our numerical results agree to within a few percent with the predictions of a simple but rigorous coupled-mode theory framework.}, year = {2012}, journal = {OE}, volume = {20}, number = {7}, pages = {7526{\textendash}7543}, url = {http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7526}, }