Quasi-Phase-Matched Four-Wave Mixing Enabled by Grating-Assisted Coupling in a Hybrid Silicon Waveguide

Phase matching must be performed to realize four-wave mixing (FWM) in a silicon waveguide, which is challenging when a signal wavelength is highly deviated from an idler wavelength. To solve this problem, quasi-phase-matching (QPM) based on grating-assisted directional coupling (GADC) in a hybrid structure is theoretically investigated. The proposed system consists of a silicon strip with periodic width modulation as the grating and a silicon nitride strip that is vertically aligned to the silicon strip. GADC occurs between the TE
_S
mode (mainly confined in the silicon strip) and TE
_N
mode (mainly confined in the silicon nitride strip) at an idler wavelength. This phenomenon compensates for the phase mismatch occurring in FWM among the TE
_S
modes at the pump, signal, and idler wavelengths. Results of analysis of the hybrid structure show that the TE
_S
and TE
_N
modes at an idler wavelength of 2.1177
$\mu \text{m}$
are efficiently generated with the TE
_S
modes at a pump wavelength of 1.58
$\mu \text{m}$
and signal wavelength of 1.2601
$\mu \text{m}$
. Moreover, the signal TE
_S
mode can be efficiently implemented with the pump TE
_S
mode and idler TE
_N
mode. Owing to the GADC characteristics, the conversion bandwidth of the signal is 0.8 nm; however, the signal wavelength can be thermally tuned, with a temperature change of 50 °C corresponding to a signal wavelength change of 3.6 nm. The hybrid structure with the GADC-based QPM can be used to generate and detect mid-infrared light with well-developed O-band and L-band devices.