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Zhu RC, Wang JF, Qiu TS, Yang DK, Feng B et al. Direct field-to-pattern monolithic design of holographic metasurface via residual encoder-decoder convolutional neural network. Opto-Electron Adv 6, 220148 (2023). doi: 10.29026/oea.2023.220148
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Article Open Access
Direct field-to-pattern monolithic design of holographic metasurface via residual encoder-decoder convolutional neural network
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Abstract
Complex-amplitude holographic metasurfaces (CAHMs) with the flexibility in modulating phase and amplitude profiles have been used to manipulate the propagation of wavefront with an unprecedented level, leading to higher image-reconstruction quality compared with their natural counterparts. However, prevailing design methods of CAHMs are based on Huygens-Fresnel theory, meta-atom optimization, numerical simulation and experimental verification, which results in a consumption of computing resources. Here, we applied residual encoder-decoder convolutional neural network to directly map the electric field distributions and input images for monolithic metasurface design. A pretrained network is firstly trained by the electric field distributions calculated by diffraction theory, which is subsequently migrated as transfer learning framework to map the simulated electric field distributions and input images. The training results show that the normalized mean pixel error is about 3% on dataset. As verification, the metasurface prototypes are fabricated, simulated and measured. The reconstructed electric field of reverse-engineered metasurface exhibits high similarity to the target electric field, which demonstrates the effectiveness of our design. Encouragingly, this work provides a monolithic field-to-pattern design method for CAHMs, which paves a new route for the direct reconstruction of metasurfaces.-
Keywords:
- metasurface /
- holography /
- complex amplitude /
- deep learning /
- monolithic design
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References
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Supplementary information for Direct field-to-pattern monolithic design of holographic metasurface via residual encoderdecoder convolutional neural network 
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Zhu RC, Wang JF, Qiu TS, Yang DK, Feng B et al. Direct field-to-pattern monolithic design of holographic metasurface via residual encoder-decoder convolutional neural network. Opto-Electron Adv 6, 220148 (2023). doi: 10.29026/oea.2023.220148
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Figure 1.
Schematic diagram of CAHM monolithic design via REDCNN model
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Figure 2.
REDCNN model design and feature extraction. (a) The architecture and dimension of REDCNN model. (b) The downsampling process of feature encoder. (c) The upsampling process of feature decoder. (d) Feature transfer of different channels in encoding process. (e) Feature transfer of different channels in decoding process
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Figure 3.
Training and test of the REDCNN model. (a) The variation of MAE loss value in deep learning process. (b) The variation of MAE loss value in transfer learning process. (c) The error histogram of deep learning in training set. (d) The error histogram of deep learning in test set. (e) The error histogram of transfer learning in training set. (f) The error histogram of transfer learning in test set.
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Figure 4.
The comparison of predicted metasurface and real metasurface with error distributions. (a) Input images. (b) Phase profiles of metasurface. (c) Amplitude profiles of metasurface. (d) Theoretical electric field distributions calculated by diffraction theory. (e) Simulated electric field distributions.
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Figure 5.
Measurement verification and comparation of the metasurfaces. (a) Photograph of fabricated metasurface prototype. (b, c) Photograph of orthogonal metal gratings. (d) Photograph of real metasurface pattern. (e) Photograph of predicted metasurface pattern. (f) Electric-field measurement environment in microwave anechoic chamber. (g) Measured electric field distribution of real metasurface. (h) Measured electric field distribution of predicted metasurface. (i) The error of measured electric field distribution between the real and predicted metasurfaces
