光子晶体的自动微分反求设计
Inverse design of photonic crystals through automatic differentiation
摘要：
光子学中基于逆设计的方法已经在设计小尺寸、高性能的光学器件方面取得了显著的成果。伴随变量法，它允许有效的计算梯度，发挥了重要作用，在这一成功。然而，基于梯度的优化还没有被应用到模式扩展的方法，这是最常见的方法来研究周期性的光学结构，如光子晶体。这是因为，在这种模拟中，伴随变量方法不能像标准的有限差分或有限元时域或频域方法那样明确定义。在这里，我们克服了这一点，通过使用自动微分，这是一个推广的伴随变量的方法，以任意计算图形。我们实现了平面波的扩展和导模的扩展方法，使用自动微分库，并表明，任何模拟输出的梯度可以有效地计算和并行相对于所有输入参数。然后，我们使用这种实施方案，以优化的光子晶体波导的色散，和超小腔的品质因数的锂酸盐平板。这将光子逆向设计扩展到一个全新的模拟类别，并更广泛地强调了自动微分在未来跟踪和优化复杂物理模型的重要性。
英文摘要：
Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has played a major role in this success. However, gradient-based optimization has not yet been applied to the mode-expansion methods that are the most common approach to studying periodic optical structures like photonic crystals. This is because, in such simulations, the adjoint variable method cannot be defined as explicitly as in standard finite-difference or finite-element time- or frequency-domain methods. Here, we overcome this through the use of automatic differentiation, which is a generalization of the adjoint variable method to arbitrary computational graphs. We implement the plane-wave expansion and the guided-mode expansion methods using an automatic differentiation library, and show that the gradient of any simulation output can be computed efficiently and in parallel with respect to all input parameters. We then use this implementation to optimize the dispersion of a photonic crystal waveguide, and the quality factor of an ultra-small cavity in a lithium niobate slab. This extends photonic inverse design to a whole new class of simulations, and more broadly highlights the importance that automatic differentiation could play in the future for tracking and optimizing complicated physical models.
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