Photonic integrated circuits (PICs) based on silicon-on-insulator (SOI) platforms have attracted much attention due to their high integration density and compatibility with complementary metal-oxide-semiconductor transistor (CMOS) processes. Among the various integrated optical devices on the SOI platforms, optical couplers with arbitrary splitting ratios are widely used for power distribution, passive optical networks, and signal monitoring. Traditional device design methods are limited by the experience of designers and spend a lot of time on structural design and parameter optimization. In addition, when the design targets change, the structure often needs to be redesigned and optimized, which makes the design less efficient due to the large amount of repetitive work. In contrast, inverse design methods use intelligent algorithms to generate desired device structures, and they can effectively reduce design complexity and improve design efficiency. Specifically, the adjoint method is able to calculate the shape derivatives of all points in the space and requires only two simulation processes in each iteration. It can achieve design targets with fewer simulations and iterations, and further improve the design efficiency of devices. The device structures of inverse design can be divided into internal perforation type and boundary optimization type. Internally perforated devices have a large number of holes in their structures, and when light is transmitted in these devices, these holes tend to cause light reflection and thus lead to relatively large transmission losses. The boundary-optimized device structure mainly adjusts the boundary of devices, so it can avoid the existence of a large number of holes in the structure. In this paper, an inverse design method based on the adjoint method is adopted, and an efficient design method for realizing 1×2 optical couplers with arbitrary splitting ratios by optimizing the boundary shapes of devices is proposed. Various optical couplers with different splitting ratios are automatically designed to verify the feasibility. The analysis results show that the performance of the designed optical couplers has met the design targets, and characteristics such as small size, low insertion loss, and large bandwidth are obtained.

Optical couplers with arbitrary splitting ratios can be realized by optimizing the boundary shapes of devices through an inverse design method based on the adjoint method. First, the initial structure of optical couplers is defined, and multiple discrete boundary optimization points are inserted at both top and bottom boundaries of the devices. By using the adjoint method combined with gradient descent, the positions of the optimization points can be effectively adjusted in the y-axis direction to approach design targets. The boundary shape can be defined by fitting the optimized points into a curve through spline interpolation. By the adjoint method, the number of simulations is effectively reduced, and design efficiency is improved. Three optical couplers with splitting ratios of 1∶2, 1∶4, and 1∶8 (i.e., 3 dB, 6 dB, and 9 dB) are designed, and the characteristics such as splitting ratio, insertion loss, and fabrication tolerance are numerically analyzed. One of the couplers is fabricated through a commercial multi-project wafer (MPW) program. By measuring the power from output ports within a bandwidth range, the performance can be fully characterized.

Simulation results show that the splitting ratios of the three couplers are 1∶2, 1∶3.97, and 1∶8.17 at 1550 nm, which well match the design targets (Fig. 5). For all the couplers, the simulated insertion loss is less than 0.12 dB at 1550 nm. When the wavelength ranges from 1500 nm to 1600 nm, the splitting ratio deviations are kept within ±1 dB, and the insertion loss is less than 0.28 dB (Fig. 7). In addition, the fabrication tolerance of the three couplers is analyzed by controlling the width within ±20 nm, and the splitting ratio deviations are still kept within ±1 dB compared with the design targets, which indicates a stable performance (Fig. 8). Experimental tests show that the designed optical coupler with a splitting ratio of 1∶2 meets the design targets in a wavelength range of 1500-1565 nm, and the insertion loss is less than 0.9 dB (Fig. 10).

In summary, 1×2 optical couplers with arbitrary splitting ratios are efficiently designed by using the inverse design method based on the adjoint method. The simulation results show that when the wavelength ranges from 1500 nm to 1600 nm, the splitting ratio deviations of the three designed optical couplers are kept within ±1 dB, and the insertion loss is less than 0.28 dB. The experimental tests show that when the wavelength ranges from 1500 nm to 1565 nm, the designed optical coupler with a splitting ratio of 1:2 meets the design targets, and the insertion loss is less than 0.9 dB. Compared with recently designed optical couplers with arbitrary splitting ratios, the proposed design has advantages in small footprint and large operating bandwidth. The proposed design method paves the way for the efficient design of couplers with arbitrary splitting ratios, low insertion loss, and large operating bandwidth.