Efficient inverse design of optical multilayer nano-thin films using neural network principles: backpropagation and gradient descent.

Optical multilayer thin films have a wide range of applications due to their ability to manipulate transmissive or reflective wavelengths by adjusting the thickness of composed layers, enabling diverse uses. Although their light weight, flexible nature and ease of fabrication position them as promising components for future devices, determining their optimal layer thickness for the desired functionality demands extensive simulations, leading to inefficient utilization of computational resources and time. To overcome these challenges, inverse design methods, leveraging machine learning and deep learning, are being explored. However, these methods necessitate learning processes, despite the presence of well-established formulas that elucidate these phenomena. Furthermore, deriving accurate answers for conditions not included in the learning process proves to be challenging. This paper introduces an innovative inverse design approach that utilizes the backpropagation of a networked transfer matrix, effectively explaining the characteristics of optical multilayer thin films. By exploiting the chain rule of the network, this method calculates gradients to discern how each layer thickness influences the outcomes. Consequently, the optimal thickness is determined without the need for an additional learning process. Mathematical elucidation of the operational principle of this approach is precisely described. Optimization of computing resource utilization through network configuration reduces the calculation time compared to conventional methods. The efficacy of this method is demonstrated through its application in the inverse design of transmissive and reflective films, verifying its potential for enhancing efficiency and accuracy in optical multilayer thin-film design and manufacturing processes.