On-demand design of spectrally sensitive multiband absorbers using an artificial neural network

Sunae So; Younghwan Yang; Taejun Lee; Junsuk Rho

doi:10.1364/PRJ.415789

Abstract

We report an approach assisted by deep learning to design spectrally sensitive multiband absorbers that work in the visible range. We propose a five-layered metal-insulator-metal grating structure composed of aluminum and silicon dioxide, and we design its structural parameters by using an artificial neural network (ANN). For a spectrally sensitive design, spectral information of resonant wavelengths is additionally provided as input as well as the reflection spectrum. The ANN facilitates highly robust design of a grating structure that has an average mean squared error (MSE) of 0.023. The optical properties of the designed structures are validated using electromagnetic simulations and experiments. Analysis of design results for gradually changing target wavelengths of input shows that the trained ANN can learn physical knowledge from data. We also propose a method to reduce the size of the ANN by exploiting observations of the trained ANN for practical applications. Our design method can also be applied to design various nanophotonic structures that are particularly sensitive to resonant wavelengths, such as spectroscopic detection and multi-color applications.

Metamaterial perfect absorbers (MPAs) have ultra-thin structures that can absorb almost all incident light [1, 2]. This property has been exploited in several prominent applications such as thermal emitters [3], photovoltaics [4], spectroscopy [5], and sensors [6]. To achieve perfect absorption, MPAs have been developed as a variety of nano-structured devices that can control and manipulate the electromagnetic wave at the subwavelength scale. These structures are composed of either resonators [2, 7] that couple to electric and magnetic fields, or of metal-insulator-metal (MIM) structures [8, 9] that localize the electromagnetic fields inside the dielectric waveguide. Most proposed MPAs have one single resonant absorption peak in a single structure.

Multiband absorbers that exhibit multiple resonances in a single structure would be beneficial for spectroscopic or multi-color applications [10, 11]. Therefore, approaches to integrate several resonators into a single structure have been proposed [12 - 14]. In these structures, each component excites a single resonance at each corresponding wavelength, and thereby yields overall multiband or broadband resonances. However, the approaches usually yield large or complex structures. In contrast, multiband absorbers can also be achieved using a relatively simple method of stacking several sets of MIM structures [15, 16]. In particular, MIMs that have the structured top layers can provide much higher absorption of light, because the top structured layers can enhance the localized field inside the waveguide layer as well as the coupling of the incident light with the guided mode. Still, designing multiband absorbers for targeting multiple wavelengths of interest using MIM is not straightforward. In addition, the design process becomes more complicated for tasks that involve multiple designs, i.e., the design process must be repeated case-by-case for target tasks. This problem also applies to cases in which multiple design tasks must be applied to design general photonic devices. Efficient and flexible design methods are being sought.

Along with the rapid development of a machine learning technology, the design problem in nanophotonics has been mitigated recently with the capability of learning complex functions from the data [17 - 19]. These methods introduce artificial intelligence to represent the intricate functions and, thereby, to allow non-intuitive inverse designs in nanophotonics without the need to solve computationally expensive electromagnetic problems [20 - 25]. However, the approach that uses deep learning generally entails high computational cost to obtain sufficient data for use in training and optimizing the network, i.e., the network itself, including the number of neurons and layers, should be optimized for the task at hand. Therefore, the overall computational cost easily exceeds that of other design methods for a single design. However, these up-front costs are incurred only once, so the method can provide subsequent on-demand designs within a few seconds.

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This paper presents an efficient and spectrally sensitive design method that uses an artificial neural network (ANN) for multiband absorbers. A five-layered MIM grating structure is used for a multiband absorber, and its geometric parameters are designed using an ANN. An ANN is developed to design structures and focuses particularly on target resonant wavelengths. The developed ANN retrieves the geometric parameters from a given target input spectrum and spectral resonant wavelengths. The trained ANN is tested to evaluate its ability to design structures when given unseen optical properties, and then the designed structures are evaluated by finite difference time domain (FDTD) numerical simulation. The effective design capability of the developed network for multiple design tasks is investigated by achieving on-demand optical properties at various target wavelengths. We also show that the trained ANN can learn physical knowledge from the data by analyzing design results on gradually changing target wavelengths of the inputs. Finally, we demonstrate a method to reduce the size of an ANN through an observation for practical applications.

Figure 1.Schematic of the designing grating structures for multiband absorbers. (a) A schematic of ANN for designing grating structures. The network is composed of two artificial neural networks of design network and pre-trained spectrum network. The design network both takes the input reflection spectra and resonant wavelengths, and the pre-trained spectrum network takes design parameters to evaluate the optical reflection spectra of the designed structures. (b) A schematic and (c) an example of optical property of a perfect multiband absorber under investigation. Yellow markers indicate resonant wavelengths.

Figure 2.(a) Scanning electron microscope image of a designed grating structure with a scale bar of 1 μm. (b) Target reflection spectrum (black solid line) and designed optical properties obtained from the FDTD simulation (red dotted line) and experiment (yellow dotted line). Grating parameters with [P, G_r, h₁, h₂,

h_{sub}

] = [245 nm, 120 nm, 42 nm, 113 nm, 195 nm] are designed by the network. (c) Examples of test results are shown. Black solid lines and red dotted lines are the input and target reflection spectra, respectively, and yellow markers are indexed resonant wavelengths.

Figure 3.(a) Target (black solid line) and designed reflection spectrum. Magnetic field distribution (color maps) and electric displacement (arrow surfaces) at the resonant wavelengths of (b) 450 nm, (c) 525 nm, and (d) 600 nm.

Figure 4.Design of multiband absorbers with (a) single, (b) double, and (c) triple resonances. The first column shows the target input spectra, and the second column shows the designed responses. The red lines indicate target resonant wavelengths. The third column shows the histogram of the MSE for a total of 51 input spectra. The insets show the average MSE of the test input.

Figure 5.Comparison between two networks fed with and without spectral resonant wavelengths. The left is the target input spectra; the middle and the right are the predicted response of the networks without and with spectral information, respectively. The red lines are target resonant wavelengths.

Figure 6.Analysis on output parameters for gradually changing target resonant wavelengths. (a) Target spectra with gradually changing resonant target wavelengths and (b) corresponding designed responses. For given varying input spectra, the designed parameters of (c) grating height and substrate height and (d) period and grating width.

Figure 7.Network pruning results. Visualization of the trained weights in (a) the original network and (b) the pruned network. For each layer (

L n, n = 1, 2, \dots, 7

), the number of neurons is indicated. MSE histogram of the test data for (c) the original network and (d) the pruned network.

Figure 8.Design of multiband absorbers with (a) single, (b) double, and (c) triple resonances using the reduced network. The first column shows target input spectra, and the second column shows the designed response. The red lines indicate target resonant wavelengths. The third column shows the histogram of the MSE for a total of 51 input spectra.

We have proposed a method that uses deep learning to design spectrally sensitive multiband absorbers. By feeding additional spectral information of resonant wavelengths, the developed ANN achieved a highly robust and accurate design of multiband absorbers. We have also analyzed the results of the designed outputs when the resonant wavelength was gradually changed. For gradually redshifting inputs, the designed parameters of the substrate height and period tended to increase, in correspondence to physical intuition. The results suggest that the trained network can well grasp and learn physics by analyzing data. We envision that this can also be applied to other nanophotonic problems and may solve complex light-matter interactions that are even beyond our knowledge. Finally, we proposed a systematic method that uses observation of the trained network to guide its pruning. The method is expected to significantly reduce the computational cost involved in network reduction. The method could be extended to other research fields that use ANNs. In this study, we considered designing one structure for one given spectrum, but it is worth noting that multiple candidates could be designed by using deep learning algorithms for multi-output regression. We believe considering several design candidates would be beneficial for fabrication when the target design becomes much more complex.

Acknowledgment. Y. Y. acknowledges a fellowship from the Hyundai Motor Chung Mong-Koo Foundation.