We present a digitized adjoint method for realizing efficient inverse design of "digital" subwavelength nanophotonic devices. We design a single-mode 3-dB power divider and a dual-mode demultiplexer to demonstrate the digitized adjoint method for single-object and dual-object optimizations, respectively. The optimization comprises three stages, a first stage of continuous variation for an "analog" pattern, a second stage of forced permittivity biasing for a "quasi-digital" pattern, and a third stage for a multi-level digital pattern. Compared with conventional brute-force method, the proposed digitized adjoint method can improve the design efficiency by about 5 times, and the performance optimization can reach approximately the same level using the ternary pattern. The digitized adjoint method takes the advantages of adjoint sensitivity analysis and digital subwavelength structure and creates a new way for efficient and high-performance design of compact digital subwavelength nanophotonic devices. This method 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, which may be attractive for inverse design of large-scale digital nanophotonic devices.

中文翻译：

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用于数字纳米光子器件逆向设计的数字化伴随方法

我们提出了一种数字化伴随方法，用于实现“数字”亚波长纳米光子器件的高效逆向设计。我们设计了一个单模 3-dB 功率分配器和一个双模解复用器，以分别演示用于单目标和双目标优化的数字化伴随方法。优化包括三个阶段，“模拟”模式的第一阶段连续变化，“准数字”模式的强制介电常数偏置的第二阶段，以及多级数字模式的第三阶段。与传统的brute-force方法相比，所提出的数字化伴随方法可以将设计效率提高约5倍，并且性能优化可以达到与使用三元模式大致相同的水平。数字化伴随方法利用伴随灵敏度分析和数字亚波长结构的优点，为紧凑型数字亚波长纳米光子器件的高效、高性能设计开辟了新途径。这种方法可以克服强力方法受数字模式像素数限制的效率瓶颈，并通过将传统的二进制模式扩展到多级模式来提高设备性能，这可能对逆向设计具有吸引力大规模数字纳米光子器件。