The phase-matching condition in waveguides requires that the propagation constants of the interacting waves satisfy momentum conservation. In most cases, the device requires precise dispersion engineering, thus causing difficulties in fabrication.

In this paper, we experimentally demonstrate the observation of an efficient SHG in a nonlinear SMCOW. A single crystalline lithium niobate (LN) slab is used as the guiding layer. The difference between the small propagation constants of FW and SH is tuned to the phase-matching condition to encourage the SHG process. Moreover, the ultrahigh-order guided modes also ensure that both FW and SH resonate at the phase-matching condition. A theoretical analysis is also explored which agrees with experimental results well. We believe nonlinear effects in SMCOWs would be of practical importance in applications of highly-integrated photonic functionalities.