Full Vectorial Description of Second Harmonic Generation in Silicon Nitride Waveguides Integrated with MoS₂ Monolayers

Hybridly integrating 2D materials onto silicon-based integrated photonic waveguides and cavities is an emerging field, with numerous potential nonlinear optical applications, such as on-chip optical frequency conversion [1] and entangled photon-pair generation [2]. Although previous studies have demonstrated second harmonic generation (SHG) in on-chip silicon-based devices through integration with 2D transition metal dichalcogenides (TMDs) [3], their theoretical description of the process has largely overlooked the nonlinear modal interaction that considers both the tensorial nature of the TMD's second-order susceptibility and the full vectorial nature of the electro-magnetic fields. With such a simplistic, yet widely used, approach, nonlinear interaction would be negligible with modes for which the main electric field component is orthogonal to the 2D material. This work investigates SHG in silicon nitride (SiN) waveguides (WGs) integrated with a MoS<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> monolayer, as illustrated in Fig. 1(a-b). We present an experimental characterization of the frequency-conversion process (Fig. 1(c-f)), which demonstrates an enhancement in SH power in WGs incorporating a monolayer of MoS<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> compared to those without it, even for pump and signal modes for which the main electric field component is orthogonal to the MoS<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> flake. We provide a thorough theoretical description of the nonlinear modal interaction [4]. Jointly accounting for the full vectorial nature of the involved fields and the tensorial nature of the second-order susceptibility of the MoS<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>, our model shows that the electric field components along the waveguide axis play a fundamental role in nonlinear interactions between pump and/or signal modes with polarization orthogonal to the MoS<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> flake. As a consequence, the model is successfully able to reproduce the experimental results and to predict up to 5 orders of magnitude frequency conversion enhancement, upon optimization of the device.