Introduction

High index contrast silicon or III-V photonics is used to drive modern integrated optics towards achieving more functionality in a smaller device and energy footprint, and tighter integration with micro-electronics. Scaled-up integrated photonic circuits with dozens of electrically-driven or active (e.g., laser or detector) components have been densely integrated within a few squared millimeters \cite{Lee_2014,Sun_2013}. However, nonlinear optical (NLO) devices are difficult to scale-up, for a few different reasons.
Crystalline lithium niobate (LiNbO3 or LN) has been an attractive material for nonlinear optics (NLO) due to its wide transparency window, low loss, and its large second-order nonlinear coefficient, d33 \cite{2005} (five times higher than that of AlN \cite{Jung_2016}, for example). However, NLO devices based on LN (and similar materials) mostly use waveguides with titanium indiffusion or annealed proton exchange to create a relatively weak core-cladding index difference \cite{Amin_1997,Schreiber_2001,Schreiber_2001a}, resulting in a large modal effective area, large minimum bending radius and low nonlinear efficiencies. Thus, a long and straight device is typically used to generate appreciable amounts of power by second-harmonic generation or wavelength conversion. Unlike the square footprints achieved in silicon or III-V photonics (which are amenable to microelectronics packaging), LN NLO devices tend to be narrow in one dimension (tens of microns) and very long in the other (several centimeters) \cite{Schreiber_2001a}
This work presents and studies a way to overcome this limitation. As a representative case study, we design and simulate an NLO LN device for wavelength conversion from 1550 nm to 750 nm wavelengths. Two aspects of our approach enable the improved structure: (a) a high-index contrast material, silicon carbide (SiC), is used as a "ridge" to load a thin slab of LN, thus enabling a confined mode with a small effective area Aeff at both the fundamental and second-harmonic wavelengths with (simultaneously) low loss, low dispersion, and ease of fabrication; and (b) bends are designed to periodically compensate for walk-off, thus enabling a very compact device with simplified poling and packaging requirements. High conversion efficiencies are predicted even with realistic assumptions for loss, disorder as affecting the periodic poling, and imperfect fabrication of bends.
Thanks to advances in crystal ion slicing over the past twenty years \cite{Levy_2004,Rabiei_2004} and the introduction of commercially available LN thin films on handle (abbreviated as LNOI), a new class of optical waveguides has recently emerged, wherein a semiconductor or glass rib material is bonded or deposited to a LN thin film to form a hybrid waveguide. These hybrid devices have used Si ribs on LN (Si-LN) to make all-optical interferometers \cite{Weigel_2016} and electro-optic modulators \cite{Chen_2014}, and SiN-LN to make nonlinear optical (NLO) waveguides \cite{Chang_2016} and electro-optic modulators \cite{Jin_2016}. While SiN-LN hybrid waveguides are useful for nonlinear conversion into the visible regime, the low refractive index of SiN (n\(\approx\)2) compared with LN (n\(\approx\)2.13 along the crystal axis) prevents the SiN-LN structure from being used in more complex geometries. Conversely, Si-LN devices are useful because of the high index of Si. By changing the width of the high-index Si rib, the optical mode can be confined in the Si to make low-loss, low-radius bends and complex waveguiding devices that require such bends \cite{Weigel_2016}. Yet the low bandgap of Si (1.1 eV) prevents the hybrid Si-LN waveguide from being used for nonlinear processes in the visible regime.