Group refractive index via auto-differentiation and neural networks

In this article, using principles of automatic differentiation, we demonstrate a generic deep learning representation of group refractive index for photonic channel waveguides. It enables evaluation of group refractive indices in a split of second, without any traditional numerical calculations. Traditionally, the group refractive index is calculated by a repetition of the optical mode calculations via a parametric wavelength sweep of finite difference (or element) calculations. To the direct contrary, in this work, we show that the group refractive index can be quasi-instantaneously obtained from the auto-gradients of the neural networks that models the effective refractive index. We embed the wavelength dependence of the effective index in the deep learning model by applying the scaling property of the Maxwell's equations and this eliminates the problems caused by the curse of dimensionality. This work portrays a very clear illustration on how physics-based derived optical quantities can be calculated instantly from the underlying deep learning models of the parent quantities using automatic differentiation.