The phenomenon of mutual coupling in continuous aperture arrays (CAPAs) is studied. First, a general physical model for the phenomenon that accounts for both polarization and surface dissipation losses is developed. Then, the unipolarized coupling kernel is characterized, revealing that polarization induces anisotropic coupling and invalidates the conventional half-wavelength spacing rule for coupling elimination. Next, the beamforming design problem for CAPAs with coupling is formulated as a functional optimization problem, leading to the derivation of optimal beamforming structures via the calculus of variations. To address the challenge of inverting the coupling kernel in the optimal structure, two methods are proposed: 1) the kernel approximation method, which yields a closed-form solution via wavenumber-domain transformation and GaussLegendre quadrature, and 2) the conjugate gradient method, which addresses an equivalent quadratic functional optimization problem iteratively. Furthermore, the optimal array gain and beampattern are analyzed at the large-aperture limit. Finally, the proposed continuous mutual coupling model is extended to spatially discrete arrays (SPDAs), and comprehensive numerical results are provided, demonstrating that: 1) coupled SPDA performance correctly converges to the CAPA limit, while uncoupled models are shown to violate physics, 2) polarization results in anisotropic array gain behavior, and 3) the coupled beampattern exhibits higher directivity than the uncoupled beampattern.

翻译：本文研究了连续孔径阵列中的互耦现象。首先，建立了一个同时考虑极化和表面损耗效应的通用物理模型。随后，对单极化耦合核进行了表征，结果表明极化会引发各向异性耦合，并使传统用于消除耦合的半波长间距准则失效。接着，将存在互耦的连续孔径阵列的波束成形设计问题表述为一个泛函优化问题，并通过变分法推导出最优波束成形结构。为应对最优结构中耦合核求逆的挑战，提出了两种方法：1）核近似法，该方法通过波数域变换和高斯-勒让德积分获得闭式解；2）共轭梯度法，该方法通过迭代求解一个等价的二次泛函优化问题。此外，在大孔径极限下分析了最优阵列增益和波束方向图。最后，将所提出的连续互耦模型推广至空间离散阵列，并提供了全面的数值结果，表明：1）耦合空间离散阵列的性能正确收敛于连续孔径阵列极限，而无耦合模型则违背物理规律；2）极化导致阵列增益呈现各向异性行为；3）耦合波束方向图比无耦合波束方向图具有更高的方向性。