从多模近场耦合到Friis公式

中文摘要 AI 辅助

有限孔径之间的近场传播可以支持多个空间信道，而远场传输实际上是单模的，并遵循Friis传输公式。本文通过发射孔径与接收孔径之间的相互阴影区域，建立了这两种机制之间的直接联系。相互阴影决定了空间自由度的渐近数量，并且在近轴条件下，导出了一个简单的波束赋形距离，该距离为从多模传播过渡到有效单模传播提供了特征尺度。信道奇异值求和规则进一步表明，在该距离以下，增大间距主要减少所支持的空间信道数量，而其平均归一化强度近似保持不变。超过该过渡距离后，剩余信道强度按照传统的自由空间二次方功率定律衰减，从而恢复Friis传输公式。针对圆形孔径的数值结果展示了这一过渡、随孔径尺寸的缩放关系以及对发射和接收孔径的依赖性。相互阴影公式还将描述扩展到近轴条件之外。

英文摘要

Near-field propagation between finite apertures can support multiple spatial channels, while far-field transmission is effectively single mode and follows the Friis transmission formula. This letter establishes a direct connection between these two regimes through the mutual shadow area between the transmitting and receiving apertures. The mutual shadow determines the asymptotic number of spatial degrees of freedom and, in the paraxial regime, leads to a simple beamforming distance that provides a characteristic scale for the transition from multimode to effectively single-mode propagation. The channel singular-value sum rule further shows that, below this distance, increasing separation primarily reduces the number of supported spatial channels while their average normalized strength remains approximately constant. Beyond the transition, the remaining channel strength decreases according to the conventional free-space quadratic power law, recovering the Friis transmission formula. Numerical results for circular apertures demonstrate the transition, the scaling with aperture size, and the dependence on the transmitter and receiver apertures. The mutual-shadow formulation also extends the description beyond the paraxial regime.

发表机构

• Lund University（隆德大学）

机构由 AI 辅助整理，请以论文原文为准。