*Deep Learning Enabled Nanophotonics DOI: http://dx.doi.org/10.5772/intechopen.93289*

#### **Figure 5.**

*Advances and Applications in Deep Learning*

GAN has been found to overcome the above limitations effectively. GAN is originally proposed in the computer vision. It is capable of creating artificial images that even cannot be distinguished from true images by the computers [15]. GAN has been successfully applied to the design of subwavelength scale metallic nanostructures and multifunctional dielectric metasurface [13, 16]. The operation principles of GAN in the design of metasurface are described as follows. The unit cell of the metasurface is divided into N\*N (i.e., N = 32, 64) pixel images while the thickness of structure and period of the unit cell is fixed. There are two neural networks in GAN: generator and discriminator. The generator networks try to create the image so that it cannot be differentiated to the real image. In contrast, the discriminator networks are trained to distinguish the image produced by the generator from the real image sets. The competing process between these two networks leads to the creation of artificial images that cannot be distinguished from the real one. In fact, the topology optimisation method or deep learning approach does not always work alone. They can be combined together to build up a new generative network. Such a generative network has been proposed to optimise the efficiency of metagrating at large angle across a broadband wavelength range because it took both the advantages of GAN and adjoint-based topology optimisation [17]. Although GAN requires less training sets, the training data may be optimised first and thus demand more computation source. More recently, global topology optimisation networks (GLOnets) was proposed by Jiang et al. from Stanford [18, 19]. It incorporates the adjoint-based optimisation into the generative neural networks. Unlike DNN and GAN methods, it does not require pre-calculation of training data based on the electromagnetic solver. Instead, it adopts the generator networks followed by the adjoint-based topology optimiser, allowing for direct learning the physical relationship between geometry parameters of the device and electromagnetic response, as shown in **Figure 4f**. Such a global optimiser does not only reduce the computation time but also further improve the efficiency of metagrating at large angles com-

pared to the topology optimisation method (See **Figure 4g**).

Another example of deep learning's application in nanophotonics is to design plasmonic chiral metamaterials [20, 21]. Chirality corresponds to the structure– property of an object which cannot superpose to its mirror image by any combination of rotation and translation. It shows different response under the illumination of left circular polarisation (LCP) and right circular polarisation (RCP) incidence. This concept is originated from molecules or ions in chemistry. However, the optical chirality in nature is extremely weak due to the small interaction volume in the visible wavelength. The emergence of metamaterials makes it possible to realise a strong optical chiral response. It is well established that a pair of rotating gold splitring resonators (SRRs) separated by a dielectric spacer can induce strong chirality. The question of how to optimise the chirality at the given frequency still remain unanswered because so many parameters involved make it difficult to find out the optimal design [20]. The advent of machine learning approach provided the possibility of processing many parameters at once in a reasonable short time. Ma et al. developed a deep learning-based model to design and optimise three-dimensional plasmonic chiral metamaterials at the desired wavelength. The structure they considered is shown in **Figure 5a**. The period of the unit cell is fixed as 2.5 μm while the thickness and width of gold SRR are set as 200 nm and 50 nm, respectively. Other parameters, such as length of top and bottom SRR (*l*1 and *l*2), top and bottom dielectric space layer (*t*1 and *t*2), and the twisted angle α between two SRRs, are set as input parameters. For output parameters, 201 points are sampled in the reflection

**2.4 Design of chiral metamaterials by deep learning**

**72**

*(a) Schematic drawing of unit cell for chiral metamaterials. (b) Architecture of neural network used for the inverse design of chiral metamaterials. (c) Reflection spectra calculated from numerical simulation and predicted from DNN. (d) Chirality spectra for both numerical simulation and DNN prediction. (e) Schematic drawing of unit cells of structure used for inverse design. (f) Schematic of BoNet for optimisation of the farfield spectrum. (g) BoNet predicted and experimental verification of far-field circular dichroism spectra at the desired wavelength of 650, 700, 750 and 800 nm.*

spectrum from 30 to 80 THz. Here, four characteristic reflection spectra that include RLL (LCP-input: LCP-output), RLR (LCP-input: LCP-output), RRR (RCPinput: RCP-output) and chirality spectrum are investigated as output parameters. **Figure 5b** shows the structure of DNN that consists of primary networks (PN) and auxiliary network (AN). Both networks have a forward path and an inverse path. For the forward path of PN, the huge mismatch of dimension between input parameters (1 × 5) and output parameters (3 × 201) makes it hard to converge. This is especially obvious around the resonant frequency. To avoid this issue, a neural tensor network followed by the unsampled module is used. Instead of using DNN with fully connected layers that are formed by simply linear recombination from previous neurons, the first hidden layer is replaced as the neural tensor network to model second-order relationships because the input parameters are not independent with each other. **Figure 5c** compares the reflection spectra obtained from electromagnetic simulation and prediction of PN. The excellent agreement can be found for most wavelengths except around resonant wavelengths. This issue is well addressed by introducing another AN which learns the relationship between structural parameters and chirality spectrum. The results are shown in **Figure 5d**. After finishing the training both PN and AN, one can construct any chirality spectrum feature by single or double resonances as well as optimise the chirality at predefined spectrum. Note that such networks are not the only one which can design and optimise the chiral metamaterials. Li et al. developed a self-consistent framework termed BoNet (Bayesian optimisation (BO) and CNN) [21], which can conduct selflearning on the optical properties of nanostructure (i.e., near field and far-field). The unit cell of structure, as shown in **Figure 5e**, is divided into 40 × 40 pixels, where the empty area is denoted as 0, and the gold brick area is denoted as 1. Other parameters, such as period and thickness, are fixed. DNN used here is composed of convolution layers followed by several fully connected layers (see **Figure 5f**). Successful training on the BoNet can help to optimise the chirality at an arbitrary

wavelength in the visible wavelength range. **Figure 5g** shows the chirality spectra of measurement and prediction from BoNet. The discrepancy can be attributed to the tolerance of fabrication and measurements.
