Inverse design of digital nanophotonic devices using the adjoint method
Digitized adjoint method for high-efficiency inverse design of digital photonic devices.
Inverse design is an attractive and emerging approach to achieve ultra-compact, high-performance, and even new-function integrated silicon photonic devices. Inverse-designed integrated photonic devices can usually have two types of subwavelength structures, "analog" and "digital". For the analog subwavelength photonic device, the cell structure (called "pixel") has a fine size, and the device etched pattern usually has a complex boundary of "arbitrary" bending; its high degree of freedom in inverse design may theoretically achieve high-quality design goals, but the performance of the device is usually greatly affected by fabrication errors. For the digital subwavelength photonic device, the pixel size is generally about an order of magnitude larger, and the device etched pattern has relatively regular rectangular or circular boundaries; the inverse design of digital devices can use simple optimization algorithms to obtain excellent performance and large fabrication tolerance.
The gradient-descent-based adjoint method is indispensable to reduce the ultrafine-pixel-induced tremendous computational cost to a reasonable degree and make the inverse design of analog devices feasible because it could provide the topology or shape gradient information using only a forward and an adjoint (backward) 3D electromagnetic fields simulations regardless of the number of pixels. Unfortunately, the conventional adjoint method can be hardly applied to inverse design of digital devices because one cannot calculate the gradients of a digital pattern. Simple brute-force methods are usually used for optimization of digital patterns. However, the number of 3D simulations in brute-force methods will increase exponentially with the pixel number in a pattern, which may drastically limit the inverse design capability of digital nanophotonic devices.
The research group led by Professor Minming Zhang from Wuhan National Laboratory for Optoelectronics and Huazhong University of Science and Technology proposed and demonstrated a novel digitized adjoint method for high-efficiency inverse design of digital photonic devices.
The inverse design process comprises three stages. In the first stage, the adjoint method based on sensitivity analysis is employed to obtain an "analog" pattern with fixed geometric shapes but "grayscale" relative permittivities; in the second stage, a linear-biasing method is used to convert such analog pattern to a "quasi-digital" one in which the relative permittivities of most pixels are close to the two boundary values; in the third stage, the quasi-digital pattern is transformed into an easy-to-fabricated and high-performance N-ary digital pattern based on the equivalent medium theory and fabrication constraints. The researchers designed and experimentally demonstrated a single-mode 3-dB power divider and a dual-mode multiplexer to verify the efficiency and performance of the digitized adjoint method. Related research results are published in Photonics Research, Volume 8, Issue 4, 2020. (Kaiyuan Wang, Xinshu Ren, Weijie Chang, et al. Inverse design of digital nanophotonic devices using the adjoint method[J]. Photonics Research, 2020, 8(4): 04000528)
The digitized adjoint method takes the advantages of adjoint sensitivity analysis and digital subwavelength structure, which could overcome the efficiency bottleneck of the brute-force method that is restricted by the number of pixels of a digital pattern and improve the device performance by extending a conventional binary pattern to a multi-level one. Compared with the typical brute force optimization algorithm, the design efficiency of the digital adjoint method has been improved by nearly 5 times, and approximately the same experimental performances of devices have been achieved.
Professor Minming Zhang believes that this work may create a new way for the efficient and high-performance inverse design of compact digital subwavelength photonic devices, which will help to promote the design automation of inverse-designed integrated photonic devices and their practical applications in on-chip optical interconnection.
Further work will focus on the inverse design of integrated subwavelength photonic devices with complex topologies and novel functions, and exploring their advanced applications in on-chip all-optical signal processing and optical computing.
数字化伴随法实现光子器件逆向设计
数字化伴随法实现高效率数字型光子器件的逆向设计
逆向设计是实现超紧凑、高性能、新功能集成硅光子器件极具吸引力的新兴方法。逆向设计的集成光子器件通常分为“模拟型”和“数字型”两类亚波长结构。前者的单元结构（像素）尺寸精细，刻蚀图案通常具有“任意”弯曲的复杂边界；其逆向设计自由度高，理论上可以实现高质量的设计目标，但器件性能受工艺误差影响较大。后者的像素尺寸一般大一个数量级左右，刻蚀图案的轮廓是较为规则的矩形或圆形；其逆向设计可以采用更为简单的优化算法获得性能优良的器件，且工艺容差大，更易于制造。
基于梯度下降的伴随法是模拟型光子器件逆向设计必不可少的优化算法，它仅使用两次（正向和伴随）3D电磁场仿真就可以获得优化所有像素介电常数的梯度信息。不幸的是，因为我们无法计算大尺寸像素介电常数二进制变化的梯度，常规的伴随法无法应用于数字型光子器件的逆向设计。目前，数字型光子器件通常采用暴力算法进行优化设计。但是，这类方法中3D仿真的次数将随着图案中的像素数量呈指数增加，这可能会大大限制数字型光子器件的逆向设计能力。
武汉国家光电研究中心和华中科技大学光学与电子信息学院的张敏明教授领导的研究小组提出并验证了一种新颖的数字化伴随法，以实现高效率数字型光子器件的逆向设计。该方法分为三个阶段：第一阶段采用基于灵敏度分析的伴随法，获得几何形状固定的“灰度”优化图案；第二阶段采用线性偏置方法将第一阶段的“灰度”图案转换为“准数字”图案；第三阶段引入制造约束条件，并基于等效介质理论最小化性能劣化，将“准数字”图案转换为易于制造的多进制“数字”图案。
采用这种方法，研究人员逆向设计了硅基集成单模3 dB功分器和双模式复用器，并仿真和实验验证了该方法的效率和性能。相关研究结果发表于Photonics Research 2020年第8卷第4期上(Kaiyuan Wang, Xinshu Ren, Weijie Chang, et al. Inverse design of digital nanophotonic devices using the adjoint method[J]. Photonics Research, 2020, 8(4): 04000528），并被主编选为“On the Cover”。
数字化伴随法利用了灵敏度分析高效率和数字亚波长结构易制造的优点，不仅可以克服常规暴力优化算法的效率瓶颈，还将传统的二值化数字亚波长结构扩展到多值化结构，进一步减小了器件图案数字化过程中的性能衰退，获取更佳性能。相较于典型的暴力优化算法，数字化伴随法设计效率提高了近5倍，并实现了同等良好的器件实验性能。
张敏明教授相信，该工作为超小尺寸数字型亚波长光子器件的高效率、高性能逆向设计开辟了新途径，有助于推进逆向设计集成光子器件的设计自动化及其在片上光互连的实际应用。
进一步的工作重点在于将该方法应用于复杂拓扑、新奇功能的集成光子器件逆向设计，并探索其在片上全光信号处理、光计算的应用。