We consider a line-of-sight communication link between two holographic surfaces (HoloSs). We provide a closed-form expression for the number of effective degrees of freedom (eDoF), i.e., the number of orthogonal communication modes that can be established between the HoloSs. The framework can be applied to general network deployments beyond the widely studied paraxial setting. This is obtained by utilizing a quartic approximation for the wavefront of the electromagnetic waves, and by proving that the number of eDoF corresponds to an instance of Landau's eigenvalue problem applied to a bandlimited kernel determined by the quartic approximation of the wavefront. The proposed approach overcomes the limitations of the widely utilized parabolic approximation for the wavefront, which provides inaccurate estimates in non-paraxial deployments. We specialize the framework to typical network deployments, and provide analytical expressions for the optimal, according to Kolmogorov's $N$-width criterion, basis functions (communication waveforms) for optimal data encoding and decoding. With the aid of numerical analysis, we validate the accuracy of the closed-form expressions for the number of eDoF and waveforms.

翻译：我们考虑两个全息表面之间的视距通信链路。针对全息表面间可建立的正交通信模式数量（即有效自由度），给出了闭式表达式。该框架可应用于超越广泛研究的近轴场景的通用网络部署。通过采用电磁波前的四次近似，并证明有效自由度数量对应于由波前四次近似确定的带限核的Landau特征值问题实例，我们获得了这一结果。所提方法克服了广泛使用的波前抛物近似的局限性——后者在非近轴部署中会产生不准确估计。将该框架具体应用于典型网络部署，依据Kolmogorov $N$宽度准则，给出了用于最优数据编码与解码的基函数（通信波形）的解析表达式。通过数值分析，验证了有效自由度数量及波形闭式表达式的准确性。