Optimization of Grating Couplers for Vertical Emission Lasers using Adjoint Method and Topology Optimization

The efficient coupling of light from planar photonic integrated circuits to external optical fibers or free-space optics remains a significant bottleneck in the deployment of silicon photonics and vertical emission laser systems. Traditional uniform grating couplers suffer from limited coupling efficiency and restricted bandwidth due to mode mismatch and significant backreflections. This paper presents a comprehensive study on the design and optimization of highefficiency vertical emission grating couplers utilizing the adjoint method combined with topology optimization. Unlike conventional parameter sweeping approaches that are limited to predefined geometric shapes, topology optimization allows for the free distribution of dielectric material within a design domain, enabling non-intuitive organic geometries that manipulate the optical field with high precision. We establish a computational framework that integrates finite-difference time-domain simulations with gradient-based optimization algorithms to maximize the figure of merit, defined as the vertical coupling efficiency into a Gaussian mode. The study rigorously addresses fabrication constraints, such as minimum feature sizes, to ensure themanufacturability of the generated designs. Our results demonstrate that topology-optimized couplers can achieve coupling efficiencies exceeding those of apodized gratings by a significant margin, while maintaining robust operation across a wide spectral bandwidth. These findings suggest that inverse design methodologies are essential for the next generation of high-performance vertical emission devices.