To date, remarkable advances have been made in quadratic optical parametric processes on the LNOI platform, which are crucial in both classical and quantum optics. Among them, second-harmonic generation (SHG) is one of the most prominent applications. For efficient SHG, it is necessary to satisfy energy and momentum conservations simultaneously. However, due to the material and waveguide structure dispersion, the momentum during wave mixing is naturally not conserved, i.e., phase mismatching. There are several phase matching mechanisms, which can be roughly divided into quasi-phase matching (QPM), intermodal phase matching (intermodal PM) and birefringent phase matching (BPM). QPM is a popular approach which uses the reciprocal lattice vector provided by periodic domain inversion to compensate the phase mismatch. The method can take advantage of the largest nonlinear coefficient and has a wide operation wavelength range upon QPM grating design. However, the periodic poling is material selective and only applicable to ferroelectric crystals. In addition, due to stronger dispersion, nonlinear wave mixings in LNOI waveguides requires smaller poling periods than their bulk counterparts. Also, period poling requires stringent domain uniformity where any discrepancy would decrease the actual conversion efficiency. These all impose difficulties to the poling technique. Furthermore, the type-0 phase matching scheme, usually adopted for QPM to utilize the largest nonlinear coefficient, suffers a limited wavelength tunability due to the relatively weak wavelength dependence on the thermo-optic coefficient. Another common method is intermodal PM, which is typically achieved by engineering the waveguide mode dispersion between the fundamental mode of pump and higher-order SH modes. Nevertheless, intermodal PM is intrinsically subject to poor spatial mode overlap, which inevitably degrades its conversion efficiency.

On the other hand, BPM can achieve the exact phase matching, which makes use of the birefringence displayed by nonlinear media. The refractive indices of fundamental wave (FW) and its second harmonic (SH) can be equal in a proper light propagation direction with respect to the optical axis under a specific polarization configuration, with one being ordinary wave and the other extraordinary wave. However, the spatial walk-off effect greatly limits their interaction length in long bulk crystals, leading to a limited conversion efficiency. Besides, BPM is a very restrictive condition to realize, and is rarely implemented in waveguides. To date, the method for BPM SHG at 1064 nm is mainly realized via temperature tuning in which the BPM condition is closely met naturally. Perfect BPM in the telecommunication band is hardly involved in LNOI waveguides.

Here, we propose and demonstrate a novel design of angel-cut LN ridge waveguides for SHG on the LNOI platform, which can access type-I BPM without need of periodic poling. A normalized conversion efficiency of 2.7%W-1cm-2 in the telecommunication C band is experimentally demonstrated. The approach effectively overcomes the spatial walk-off effect via the strong confinement of the waveguide, while possessing large mode overlap. It also gets rid of the complicated periodic poling of the LN waveguide. Besides, the strong thermo-optic effect in type-I phase matching scheme makes it possible to obtain a large wavelength tunability. The measured thermal tunability of the phase matching wavelength is 1.06 nm/K, making it easy to cover the whole telecommunication C band by temperature control. The proposed angle-cut ridge waveguide structure can be applicable for other on-chip birefringent platforms as well, particularly other materials whose periodic poling is challenging, which is of great promise for efficient frequency conversion on integrated nonlinear photonics.

Fig. 1. (a) Schematic of the waveguide structure, and simulated mode profiles for FW and SH waves in the ridge waveguide. (b) Numerically calculated BPM wavelength versus the propagation or cut angle at room temperature. (c) Effective indices of TM00 mode at FW (blue line) and TE00 mode at SH (red line) in the ridge waveguide, respectively.

Fig. 2. Measured SHG phase matching curve and power of the ridge waveguide.

Fig. 3. Measured SHG conversion efficiency spectra redshifts with increased temperatures at the linear rate of 1.06 nm/K.

This research is published by “Chuanyi Lu, Yuting Zhang, Jing Qiu, Yongzhi Tang, Tingting Ding, Shijie Liu, Yuanlin Zheng, and Xianfeng Chen, Highly tunable birefringent phase matched second-harmonic generation in an angle-cut lithium niobate-on-insulator ridge waveguide, Optics Letters, 47(5), 1081-1084 (2022)”.

Link：https://doi.org/10.1364/OL.449634