Lithium niobate on insulator (LNOI) is an interesting material for high-density photonic integrated circuits because of the high refractive-index contrast between lithium niobate (LN) and silicon dioxide, which also retains the excellent optical properties of LN. Based on LNOI, many photonic devices with outstanding performances have been demonstrated such as tunable frequency combs and high-frequency electro-optical modulators driven by low voltage. To link to off-chip systems, low-loss coupling between an LNOI waveguide and a conventional single-mode fiber (SMF) is necessary. At present, two mainstream methods are edge coupling and grating coupling. However, the edge couplers with low alignment tolerance can only be located on the edge of the chip and require intensive post-fabrication processing, such as cleaving and facet polishing. In contrast, grating couplers with relaxed fiber-positioning tolerances can be located at any point on the chip to facilitate wafer-level testing anywhere on the chip. Reports of grating couplers fabricated on LNOI so far either have low coupling efficiency or require additional layers to realize high coupling efficiency. Therefore, it is important to identify ways to improve the performance of LNOI without additional layers.

We propose a novel strategy that allows designing low-loss apodized gratings on LNOI, where the filling factor is linearly varied while periods are tuned according to Bragg condition. Our apodized grating coupler consists of ten apodized diffraction units with filling factors and pitches both varying along the x-axis, followed by several uniform diffraction units with fixed filling factors and periods [Fig. 2(c)]. The apodized grooves are designed to reduce the modal mismatch and the reflection from the interface between the waveguide and grating coupler and improve upward transmission. The uniform grooves are employed to guarantee that almost all the lights are scattered upwards rather than transmitted through, and the filling factors and periods are the same as the tenth apodized diffraction unit. According to this design idea, only the linear apodization factor R of the filling factor and the etching depth e should be optimized. Due to the limitations of the process, the cross-section of the waveguide fabricated on LNOI is not an ideal rectangle, but a trapezoidal shape with an etching inclination angle of about 65°. Thus the reasonably extended Bragg condition is adopted to tune the grating periods of the apodized grating coupler with an etching inclination angle.

As shown in Fig. 3(b), by nesting the linear apodization factor R(0-0.06) and etching depth e (280-400 nm), the highest coupling efficiency of 81.3% (0.90 dB) for the TE polarization at 1550 nm is obtained. It represents the best performance ever reported in the literature for LNOI without a reflection layer. As shown in Fig. 4, this scheme not only improves the upward transmission but also increases the overlap integration between the upward diffraction field and the SMF mode field, which greatly improves the coupling efficiency. Considering the etching inclination angle of the waveguide in the actual process, the grating periods of the apodized grating coupler with etching inclination angles are also tuned based on the reasonably extended Bragg condition, and the optimized coupling efficiency is as high as 60.0% (2.22 dB), which is smaller than 81.3% (0.90 dB). The reasons are as follows. First, the grooves become wider when the etching inclination angle is introduced, which leads to enhanced light diffraction ability in the first few periods and makes the upward diffraction field deviate from the Gaussian field. Second, the introduction of the etching inclination angle decreases the optical impedance matching between the waveguide and the grating section, causing more optical power to be reflected into the waveguide. Further, according to the actual etching effect and smallest etching gap, this design method can be applied to design grating couplers with any etching inclination angle, which paves the way for experiments.

In this study, we propose a new design strategy for apodized grating couplers with low coupling loss. This method changes the filling factors and periods spontaneously and improves the upward transmission and the overlap integration between the upward diffraction field and the SMF mode field. For the TE mode at 1550 nm, the upward transmission is 84.3% and the coupling efficiency is 81.3% (0.90 dB), which is the highest grating coupling efficiency obtained so far based on LNOI without a reflective layer. Then, considering the actual etching inclination, the model is optimized based on the extended Bragg conditions. For the TE mode at 1550 nm, the coupling efficiency reaches 60.0% (2.22 dB), which guides subsequent experiments. Additionally, as the process iterates with a bigger etching inclination angle and a smaller gap that can be etched, this method can design a low-loss apodized grating with any etching inclination angle.