# Inverse Design of Distributed Bragg Reflectors Using Deep Learning
## 1 Introduction  
The application of optical devices is extremely broad, and over the last few decades, their prevalence has grown due to the advances in manufacturing techniques and computation power [1]. Metamaterials and nanophotonics can control the light-matter interaction precisely, enabling them to be used for a wide variety of applications. Their numerous applications include invisibility cloaking [2], structural and sustainable colour generation [3, 4], high-resolution printing, anti-reflectors [5], bio-sensors [6] and nanophotonic lasers [7]. Distributed Bragg Reflectors (DBRs) are one of the classical optical systems, and are formed of alternating layers with different refractive indices, where each material interface gives rise to a partial reflection of the incident light waves [8]. A typical DBR is formed of an alternating \(\lambda/4\) structure of high and low refractive index materials [9]. There are a number of applications for DBRs in photonics, such as LEDs and vertical-cavity surface-emitting lasers [10]. There exist several numerical methods and corresponding computer programs that serve to predict the responses of these thin-film structures, and over time, this information has been collated into a number of libraries. However, in practice, it is common to desire a response that has not yet been associated with a particular structure. This poses a need for inverse design (ID), which proves far more complex than direct structural analysis [11]. Traditional ID methods have yielded successful results, and are often highly accurate for small-scale modelling; however, when handling a large number of parameters, these methods simply are not feasible due to their complexity and time cost [12]. For these reasons, Machine Learning (ML) has moved to the forefront of pioneering inverse design methods [13]. ML employs a range of algorithms to analyse large amounts of data and map complex relationships between information, in order to make future predictions about new data [11, 14]. Although the input data are still produced through simulations, thiscomputational cost occurs only once and the burden can be spread across several devices in parallel [15]. Additionally, the analytical as opposed to the numerical approach adopted by ML algorithms is far more efficient, allowing huge amounts of data to be analysed in a relatively small amount of time [4]. Table 1 presents a summary of the most prevalent inverse design methods in the literature, and their associated drawbacks. Within recent years, the tandem approach has become the most popular method of addressing non-uniqueness. To give a more comprehensive overview, a tandem network is established first with an Inverse Design Neural Network (IDNN), the output of which acts as the input of a forward modelling network, as shown in Figure 1.  
This forward model (sometimes referred to as the simulation neural network (SNN) [16] to distinguish between the forward design and forward propagation) has been pretrained, meaning that its parameters are locked throughout the tandem model training. The calculated network loss is taken as the difference between the desired spectral response (fed into the inverse model as an input), and the predicted spectral response given by the pretrained forward model [15]. Any structure produced by the inverse model is directly fed into the pretrained SNN, which is known to converge. In taking this approach, we can minimise the non-uniqueness problem, as, regardless of the predicted material structure, the model will be assessed only on its ability to produce a structure with the desired spectral response [15].