Intelligent algorithms: new avenues for designing nanophotonic devices

Summary of intelligent algorithms and their applications for designing nanophotonic devices

Nanophotonic devices, which take photons as information carries, play key roles in next-generation photonic chip. The design of multifunctional and practical devices has always been one of the core topics of nanophotonic devices. However, traditional design methods rely on human experience and physical inspiration for structural design and parameter optimization, so they often consume a lot of computing resources to obtain excellent results, and the structure type is not abundant enough.

In recent years, the application of intelligent algorithms in the field of nanophotonic devices develops rapidly. It is universal and efficient in designing nanophotonic devices with different materials, different structures, different modes and different wavelengths. Using intelligent algorithms to design nanophotonic devices can break the limit of traditional methods and predict new structures. Therefore, intelligent algorithms provide new avenues in designing nanophotonic devices.

Intelligent algorithms are practical alternative techniques for solving varieties of challenging engineering problems, which are methods inspired by natural phenomena or laws. People use intelligent algorithms to solve practical problems by learning or imitating natural principles. In many practical applications, intelligent algorithms are used to deal with various challenging problems. Whether it is an intricate continuous problem or a discrete problem to be optimized, intelligent algorithms can be applied under both cases and find feasible solutions in a short time.

It shows that the avenues of designing nanophotonic devices based on intelligent algorithms will be an important direction for the future development of nanophotonics. Intelligent algorithms are important core techniques for parameter tuning and computer-aided design of devices, which can establish a clear and intuitive physical scene for the devices working principle. The design efficiency can be greatly improved by using the appropriate algorithm, and the best performance of the device can be expected. Therefore, the study of intelligent algorithms is of great practical significance to the design of nanophotonic devices.

Recently, Prof. Cuicui Lu et al. from Beijing Institute of Technology are invited to review the intelligent algorithms for designing nanophotonic devices from the design principle and applications. They expect to give a comprehensive summary for the applications of intelligent algorithms in designing nanophotonic devices. The research results are published in Chinese Optics Letters, Vol. 19, No. 1, 2021 (Lifeng Ma, Jing Li, Zhouhui Liu, Yuxuan Zhang, Nianen Zhang, Shuqiao Zheng, Cuicui Lu. Intelligent algorithms: new avenues for designing nanophotonic devices [Invited] [J]. Chinese Optics Letters, 2021, 19(1): 011301).

One of the group members Zhouhui Liu said "in the recent two years, we have realized the smallest on-chip wavelength router and polarization routers by using the finite element method and genetic algorithm. We now try to combine more optimization algorithms together, such as simulated annealing algorithm, topology optimization, and more efficient multi-functional nanophotonic devices are expected to be realized."

In this review, a variety of intelligent algorithms are discussed in detail. The deep learning methods, the gradient-based inverse design method, swarm intelligence algorithms [including genetic algorithm (GA), particle swarm optimization (PSO) and ant colony algorithm (ACA)], individual inspired algorithms [including the simulated annealing algorithm (SAA), the hill climbing algorithm and tabu search (TS)] and some other algorithms [including the direct binary search (DBS) algorithm, topology optimization, and Monte Carlo method] are introduced from the research background or concept to the applications for designing nanophotonic devices. Some representative application examples of nanophotonic devices are listed under each mentioned intelligent algorithm. The intelligent algorithms and their applications for designing nanophotonic devices are summarized and analyzed.

Compared with the traditional design methods, the intelligent algorithms are universal and efficient. For example, the advantage of deep learning is that after training, it has less computational cost and is more likely to find better optimal solutions than traditional algorithms. In addition, compared with traditional algorithms, the deep learning methods can realize inverse design more easily. ANN has many typical structures and strong flexibility. According to the design requirements in the training process, we can choose the appropriate neural network for optimal design.

The gradient-based inverse design method can automatically design nanophotonic devices and only require the user to input high level parameters. This method can provide large parameter space and design devices using full space parameters of manufacturable devices, which often requires less simulation than GA or PSO because they do not rely on parametric scanning or random perturbations to find the minima. This method can be used to design any passive, linear photonic device. However, the implemented design usually presents a continuous terrain, and some tiny structural components may be formed during the inverse design process, which presents a challenge to sample making.

Swarm intelligence algorithms have certain robustness and strong evolutionary or search ability. For instance, GA can not only solve single-objective optimization problem, but also plays a greater role in multi-objective optimization problems. It has the characteristics of group search and is suitable for solving complex optimization problems, such as the need to optimize multiple system parameters at the same time. Moreover, GA is scalable and easy to be combined with other algorithms. The researchers also introduced some other intelligent algorithms, such as individual inspired algorithms, which can give a better solution in a certain acceptable time, but cannot be guaranteed to be optimal.

All intelligent algorithms have their own advantages and disadvantages, and this review explains the developing trend of using intelligent algorithms through the analysis and summary of the principles and applications of intelligent algorithms, especially in the future design of nanophotonic devices. As the need for nanophotonic devices to achieve more functions is further strengthened, the intelligent algorithms, especially the more popular method (e.g., deep learning methods) with higher efficiency and better effect, will continue playing a significant role in the design of nanophotonic devices to implement complex functions and improve the performance of nanophotonic devices. This will provide an avenue for the realization of photonic chips in the future.

As for the utilization of intelligent algorithms, multiple algorithms can be adopted simultaneously to provide efficient and optimal solutions during the design process of nanophotonic devices, rather than just one algorithm. In addition, when too many algorithms are difficult to choose, the more reports some algorithms appear in, the more frequently they have been used, which may be a reference for similar problems.

智能算法：纳米光子器件设计新途径

智能算法及其在设计纳米光子器件方面应用的概括

在下一代光子芯片中，以光子为信息载体的纳米光子器件发挥着关键作用。多功能且实用的纳米光子器件的实现一直是纳米光子学领域的核心课题之一。然而，传统的设计方法需要利用以往经验和物理启发来进行结构的设计和参数的优化，通常其需要消耗大量的计算资源才能获得良好的结果，并且还存在结构类型不够丰富的缺点。

近年来，源于自然规律和现象的智能算法在纳米光子器件领域的应用中发展迅速。一方面是因为其在设计不同材料、不同结构、不同模式和不同波长的纳米光子器件方面具有通用性和高效性。另一方面是因为利用它来设计纳米光子器件不仅可以打破传统设计方法的局限性，还可以预测新的结构。并且，在许多实际应用中，其常用于处理各种具有挑战性的问题，例如无论是优化复杂的连续问题还是离散问题，它都可以在较短时间内找到可行的解。

研究表明，利用智能算法设计纳米光子器件将是未来纳米光子学发展的一个重要方向。因为智能算法是调整参数和计算机辅助设计的重要核心技术，其能够为器件的工作原理建立清晰直观的物理情景，再采用适当的算法可以很大程度地提高设计效率，并获得期望的具有最佳性能的器件。因此，智能算法的研究对纳米光子器件的设计具有重要现实意义。

最近，北京理工大学的路翠翠研究员等受邀撰写相关综述，给出了智能算法在纳米光子器件设计方面的全面总结。该综述作为封面文章发表在Chinese Optics Letters 2021年第1期上（Lifeng Ma, Jing Li, Zhouhui Liu, Yuxuan Zhang, Nianen Zhang, Shuqiao Zheng, Cuicui Lu. Intelligent algorithms: new avenues for designing nanophotonic devices [Invited] [J]. Chinese Optics Letters, 2021, 19(1): 011301）。

来自该课题组的刘舟慧说：“最近两年，我们通过将有限元方法和遗传算法结合，已经实现了基于算法的国际最小尺寸的片上波长路由器件和偏振路由器件，目前我们在前期基础上正在通过将模拟退火、拓扑优化等多种优化算法相结合的方式，来实现高效的多功能纳米光子器件。”

该综述对各种智能算法进行了详细的讨论。从智能算法设计纳米光子器件的研究背景、概念及应用等方面介绍了深度学习算法、基于梯度的逆向设计方法、群体智能算法(包括遗传算法(GA)、粒子群优化(PSO)和蚁群算法(ACA))、个体启发算法(包括模拟退火算法(SAA)、爬山算法和禁忌搜索(TS))以及一些其他算法(包括直接二元搜索算法(DBS)和蒙特卡罗法)。

在介绍每一种智能算法时都列举了具有代表性的纳米光子器件的设计实例，并对这些智能算法及其在设计纳米光子器件方面的应用进行了总结和分析。与传统的设计方法相比，智能算法具有通用性和高效性。

深度学习方法

在深度学习方法中，一旦经过训练，它会比传统的算法花费更少的计算成本，并且更可能找到更好的优化结果。此外，与传统的算法相比，深度学习方法更容易实现逆向设计。人工神经网络具有许多典型的结构和较强的灵活性。根据训练过程中器件的设计要求，可以选择合适的神经网络进行优化设计。

基于梯度的逆向设计方法

基于梯度的逆向设计方法只需要用户输入高质量参数就可以自动地对纳米光子器件进行设计。该方法可以提供较大的参数空间，以及利用器件的全参数空间进行设计。此外，其不需要依赖于参数扫描或随机扰动的方式来寻找最小值，因此通常会比遗传算法或粒子群算法进行更少的仿真。因此，这种方法可用于设计任何无源线性光子器件。然而，在逆向设计过程中可能会形成一些非常小的结构形状，这给器件的制备带来了挑战。

群体智能算法

群体智能算法具有一定的稳建性（Robustness）和较强的进化或搜索能力。例如遗传算法不仅可以解决单目标优化问题，还可以在多目标优化问题中发挥重要作用。它具有群搜索的特点，适用于求解复杂的优化问题，比如需要同时优化多个系统参数的问题。此外，遗传算法具有可扩展性，易于与其他算法相结合。

个体启发算法

个体启发算法可以在一定的可接受时间内给出更好的解，但不能保证是最优的解。

此外，该综述还介绍了其他的智能算法，包括DBS和蒙特卡罗法。

这项工作通过对智能算法的原理和应用进行分析和总结，阐述了智能算法的发展趋势，特别是其在未来纳米光子器件设计中的应用。随着对多功能纳米光子器件的需求进一步加强，智能算法尤其是越来越流行的高效且效果更好的方法（例如深度学习方法），将在设计具有复杂功能的纳米光子学器件和提高纳米光子器件的性能等方面继续发挥重要的作用，这为未来光子芯片的实现提供了一条新的途径。

同时，路翠翠研究员指出，“在应用智能算法设计纳米光子器件的过程中，可以同时采用多种算法来实现高效和最优设计，而不必局限于一种算法。优化过程也可以分多步进行优化，将一种算法优化的结果作为另一种算法的初始结构，多次优化达到目标。”