Shan Mingguang, Nastasa Viorel, Popescu Gabriel
Opt Lett. 2016 Jun 1;41(11):2490-2. doi: 10.1364/OL.41.002490.
The dispersion relation is fundamental to a physical phenomenon that develops in both space and time. This equation connects the spatial and temporal frequencies involved in the dynamic process through the material constants. Electromagnetic plane waves propagating in homogeneous media are bound by simple dispersion relation, which sets the magnitude of the spatial frequency, k, as being proportional to the temporal frequency, ω, with the proportionality constant dependent on the refractive index, n, and the speed of light in vacuum, c. Here we show that, for spatially broadband fields, an analog dispersion relation can be derived, except in this case the k-vector variance is connected with the temporal frequency through the statistics of the refractive index fluctuations in the medium. We discuss how this relationship can be used to retrieve information about refractive index distributions in biological tissues. This result is particularly significant in measurements of angular light scattering and quantitative phase imaging of biological structures.
色散关系对于在空间和时间中发展的物理现象至关重要。该方程通过材料常数将动态过程中涉及的空间和时间频率联系起来。在均匀介质中传播的电磁平面波受简单色散关系的约束，该关系将空间频率k的大小设定为与时间频率ω成正比，比例常数取决于折射率n和真空中的光速c。在这里，我们表明，对于空间宽带场，可以推导出类似的色散关系，只是在这种情况下，k矢量方差通过介质中折射率波动的统计与时间频率相关联。我们讨论了如何利用这种关系来获取有关生物组织中折射率分布的信息。这一结果在生物结构的角光散射测量和定量相成像中尤为重要。
