We present the design and analysis of a nonlinear optical waveguide that enables simultaneous second-harmonic generation (SHG) and polarization rotation within a single device. We explore the effect of introducing a birefringent nonlinear crystal into the waveguide structure to enhance polarization rotation. The waveguide core is made of a z-cut Lithium Niobate ( \(\text {LiNbO}_3\) ) crystal with a triangular cross-section. Through optimization of the core dimensions, perfect phase matching is achieved between the fundamental transverse electric ( \(\text {TE}_0\) ) mode at a pump wavelength of 1550 nm, and the fundamental transverse magnetic ( \(\text {TM}_0\) ) mode at the second-harmonic wavelength. Starting from Maxwell’s equations, the coupled-mode equations that describe the coupling among different modes along the device are addressed. Using electric field profiles determined from simulation, we compute the nonlinear coupling coefficient and obtain the conversion efficiency by numerically solving the coupled-mode equations. Numerical calculations reveal a SHG efficiency of \(68.5\% W^{-1}cm^{-2}\) using the undepleted pump approximation , surpassing previously reported designs and enabling direct conversion between fundamental modes.
