整形波如何在散射介质中传播
How Shaped Waves Propagate in Scattering Media
- Institut Langevin（朗之万研究所）
- ESPCI Paris（巴黎高等物理化工学院）
- PSL University（巴黎文理研究大学）
- CNRS（法国国家科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出矩阵输运方程，用于描述波前控制的相干波在散射介质中的传播，并解析推导传输本征通道的能量与电流分布，经波动方程数值验证，为复杂介质中的相干波控制提供新框架。
AI中文摘要：
辐射传输方程为描述散射介质中的波传播提供了强大的框架。然而，它无法描述入射波前被有意定制的相干波。在此，我们基于矩阵传输方程建立了波前控制波的输运理论。与传统辐射传输传播标量辐射度不同，我们的理论传播一个保留相位信息并服从非线性传输方程的复数二乘二矩阵，尽管底层波动力学是线性的。我们利用该矩阵传输方程推导了任意扩散系统中传输本征通道从闭合到开放的能量和电流密度的空间分布。值得注意的是，这些分布可以用同一介质中随机波的常规辐射传输方程的解解析地表达。该理论进一步扩展到能量损失，包括吸收和泄漏到不受控制的通道，揭示了复杂结构中传输本征通道的对称性破缺。通过与波动方程的数值解进行验证，我们建立了矩阵输运作为描述和控制复杂介质中相干波传播的框架。
英文摘要：
The radiative transport equation provides a powerful framework for describing wave propagation in scattering media. However, it cannot describe coherent waves whose incident wavefront is deliberately tailored. Here we establish a transport theory for wavefront-controlled waves based on a matrix transport equation. Unlike conventional radiative transport, which propagates a scalar radiance, our theory propagates a complex two-by-two matrix that retains phase information and obeys a nonlinear transport equation, despite the underlying wave dynamics being linear. We use this matrix transport equation to derive the spatial profiles of the energy and current densities of transmission eigenchannels, from closed to open channels, in arbitrary diffusive systems. Remarkably, these profiles can be expressed analytically in terms of the solution of the conventional radiative transport equation for a random wave in the same medium. The theory further extends to energy loss, including absorption and leakage into uncontrolled channels, revealing symmetry breaking of transmission eigenchannels in complex structures. Validated against numerical solutions of the wave equation, we establish matrix transport as a framework for describing and controlling coherent wave propagation in complex media.
