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：研究了连续孔径阵列（CAPA）中的互耦合现象。首先，建立了考虑极化与表面耗散损耗的广义物理模型。随后，表征了单极化耦合核，揭示了极化会引发各向异性耦合，并使得传统半波长间距规则失效。接着，将含耦合的CAPA波束成形设计问题建模为泛函优化问题，通过变分法推导了最优波束成形结构。针对最优结构中耦合核求逆的难点，提出了两种方法：1）核近似法，通过波数域变换与高斯-勒让德求积得到闭式解；2）共轭梯度法，通过迭代求解等效二次型泛函优化问题。进一步分析了渐进大孔径条件下的最优阵列增益与波束方向图。最后，将所提连续互耦合模型推广至空间离散阵列（SPDA），并给出全面的数值结果，表明：1）耦合SPDA性能正确收敛于CAPA极限，而未耦合模型违反物理规律；2）极化导致各向异性阵列增益特性；3）含耦合波束方向图比未耦合波束方向图具有更高指向性。