Thin-film lithium niobate (TFLN) photonic integrated circuits are driving the development of next-generation optoelectronic technologies. Due to the indirect bandgap nature of lithium niobate, the TFLN photonic integrated chips typically require off-chip light sources. Thus, grating couplers are key components for enabling efficient coupling between external light sources and the integrated chip. Existing research on TFLN grating couplers has primarily focused on oblique incidence configurations. While uniform gratings under angled incidence can achieve higher coupling efficiencies, they are less favorable during coupling and packaging processes due to the difficulty in accurately controlling the incident angle, which may introduce additional coupling losses. Vertical incidence is advantageous for device packaging; however, it often suffers from significant back-reflection caused by second-order Bragg diffraction. To mitigate this effect, efficient vertical coupling can be achieved by designing dual-layer gratings or incorporating a bottom reflector. However, such approaches often involve complex fabrication steps and may induce additional optical losses in other on-chip components. Therefore, it is of great significance to develop efficient vertical grating couplers on TFLN using standard films without metallic reflectors by carefully designing the grating structure and adopting relatively simple fabrication procedures. Such an approach will facilitate the integration of TFLN photonic chips with off-chip light sources.

This study presents the design of a non-uniform grating with a spatially varying period and duty cycle to achieve efficient vertical coupling. The grating structure is optimized using the L-BFGS-B algorithm, which is based on gradient descent. To ensure consistency between the design and the experimental results, the initial structural parameters are determined. A linearly tapered grating is then constructed to enable preliminary vertical coupling. The simulations are conducted using the finite-difference time-domain (FDTD) method with perfectly matched layer (PML) boundary conditions. The objective function in the inverse design is defined as the coupling efficiency of the vertical grating coupler, and a minimum feature size constraint of 300 nm is applied based on current fabrication capabilities. During optimization, the algorithm adjusts the widths of each grating tooth and trench according to the objective function, with gradients estimated via two FDTD simulations per iteration. The structural parameters are updated iteratively under the feature size constraint, and the process is repeated until 250 iterations are completed. After several rounds of simulation validation, 250 iterations are found to be sufficient to obtain the optimal structural parameters. Following the completion of the design optimization, simulations are also conducted to evaluate the impact of fabrication errors on the grating coupling efficiency.

Simulation results indicate that the designed vertical grating coupler achieves a coupling efficiency of -1.9 dB at 1550 nm. The grating is fabricated using electron beam lithography and ion beam etching. Scanning electron microscope (SEM) images reveal that the grating surface and sidewalls are clean and smooth. After fabrication, the device is characterized using the fiber-to-chip vertical coupling setup. Experimental measurements indicate a peak coupling efficiency of -4.3 dB near 1550 nm. The discrepancy between the measured and simulated results is mainly due to a fabrication-induced structural deviation of approximately 20 nm. Future improvements in fabrication processes may further enhance the device performance. In the 1525?1575 nm wavelength range, the measured spectral response aligns well with the simulation results. The vertical grating coupler proposed in this work is designed via an inverse design approach and fabricated using a simple process involving only a single lithography and etching step, without the need of heterogeneous material integration or metal reflectors. The measured coupling efficiency of -4.3 dB meets the basic requirements for photonic device testing and research. The 3 dB bandwidth of 25 nm is sufficient to support applications in lithium niobate based nonlinear photonic chips where single-wavelength lasers are used as the input light sources.

This work presents a vertical grating coupler on TFLN, designed using an inverse design method. The grating period and duty cycle are optimized using a gradient descent algorithm, and the coupler is fabricated through a single-step etching process. In the 1550 nm communication band, the fabricated coupler achieves a vertical coupling efficiency of -4.3 dB and a 3 dB bandwidth of approximately 25 nm. A deviation from the simulated efficiency (-1.94 dB) is observed, primarily due to fabrication limitations. Further performance improvements are expected with process optimization. The developed vertical grating coupler provides a practical and efficient solution for integrating off-chip light sources with TFLN photonic chips.