2-D Near-Field Shaping Synthesis by Eigen-Function-Informed Neural Networks

This letter presents Eigen-function-informed Neural Networks (ENN) for fast two-dimensional (2-D) near-field shaping synthesis. Differing from the traditional nonlinear neural networks, the proposed ENN is a linear neural network developed with the 2-D Fast Fourier Transform (2-D FFT) and eigen-function-informed neurons, aiming to solve linear electromagnetic problems. The training process optimizes weights of eigen-function-informed neurons based on the eigenfunctions instead of the desired shaped near-field intensity. Thanks to the orthogonality between eigenfunctions, the eigen-function-informed neurons are not cross-connected, which allows them to train and compute in parallel. Once trained, the ENN can rapidly synthesize arbitrarily desired fields within the spatial frequency range of (-k<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>, k<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>) in the near-field region of antenna arrays. Simulation results demonstrate the successful realization of various field distributions at a wavelength-scale distance, confirming the effectiveness of the proposed method.