非均匀介质中的时间调制重聚焦
Time-modulated refocusing in inhomogeneous medium
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中文总结 AI 辅助
针对非均匀耗散介质中瞬时时间镜无法产生平衡点焦点的问题，通过麦克斯韦-德拜场分解与半经典模式约化，提出一种均衡源侧增益的时间调制方法，实现了点源场的相干重聚焦。
中文摘要 AI 辅助
在非均匀耗散介质中，不同射线经历的往返衰减不同，因此瞬时时间镜可能回溯射线却无法产生平衡的点焦点。针对该问题，我们研究了由包围非均匀德拜介质（含欧姆电导率）的薄壳的短脉冲调制产生的、经微局部选择的反向传播横磁分量。对麦克斯韦-德拜场的精确分解分离了脉冲产生的回波，半经典模式约化得到标量回波算子，其主符号分离了时间脉冲响应、壳调制和累积材料损耗。分析表明，波传播中存在几何畸变和振幅衰减，几何畸变在出射和返回分支间抵消，而物理衰减保留。利用已知无损耗反向传播算子，通过调制前测量计算的归一化定向能量，包含与回波算子主符号相同的主导衰减因子，其倒数定义了平滑、非负、物理上可容许的调制，无需完整衰减模型即可将选定源侧增益均衡至相对O(h)误差。采用该调制后，点源产生的场具有与定向衰减无关的焦尺度主轮廓，在源处有唯一最大值且返回时间相干；在每个固定焦窗口内，最大值在空间和时间上的位移至多为O(h²)，空间半振幅面积为O(h²)。
英文摘要
In an inhomogeneous dissipative medium, different rays experience different round-trip attenuation, so an instantaneous time mirror may retrace rays without producing a balanced point focus. We solve this problem for a microlocally selected back-propagating transverse-magnetic component generated by a short pulsating modulation of a thin shell surrounding an inhomogeneous Debye medium with Ohmic conductivity. An exact decomposition of the Maxwell--Debye field isolates the pulse-generated return, and a semiclassical mode reduction yields a scalar returned operator whose principal symbol separates the temporal pulse response, shell modulation, and accumulated material loss. Our analysis shows that geometric distortion and amplitude attenuation are both involved in wave propagation, but the geometric distortion cancels between the outgoing and returning branches, whereas physical attenuation remains. A normalized directional energy, computed from pre-modulation measurements using the known lossless backward propagator, contains the same leading attenuation factor as the returned symbol. Its reciprocal defines a smooth, nonnegative, physically admissible modulation that equalizes the selected source-side gain up to a relative $O(h)$ error without requiring a complete attenuation model. With such a modulation, the field generated by a point source has a focal-scale leading profile independent of directional attenuation, with a unique maximum at the source and coherent return time. In every fixed focal window, the maximum is displaced by at most $O(h^2)$ in space and time, and the spatial half-amplitude area is $O(h^2)$.
发表机构
- City University of Hong Kong（香港城市大学）
- Jilin University（吉林大学）
机构由 AI 辅助整理，请以论文原文为准。
