搜索

x
中国物理学会期刊

傅里叶域中的光线

CSTR: 32037.14.aps.68.20190839

Light rays in Fourier domain

CSTR: 32037.14.aps.68.20190839
PDF
HTML
导出引用
  • 建立普适的理论模型用于描述光线和光波场的关系是几何光学领域中重要的研究内容. 本文基于传统几何光学与傅里叶光学原理, 提出利用光波场的傅里叶角谱得到光束的光线模型, 反之可以根据光线模型反演光场的傅里叶角谱. 以Airy光束以及Cusp光束为例, 展示了利用傅里叶角谱构建光束光线模型的方法及其正确性; 进一步展示利用光线构建焦点处的光波场的傅里叶频谱分布, 然后通过逆变换得到光波场的空间分布, 并与Debye方法取得了相同的结果; 最后从空间坐标域以及空间频率域给出了光线模型的高维解释, 以聚焦光束、Airy光束以及二次梯度折射率波导中的光线为例展示了高维光线模型的物理内涵. 理论分析表明, 传统几何光学构建的光线模型只是高阶光线模型在实空间内的投影.

     

    Establishing a universal model to characterize the relationship between light rays and optical waves is of great significance in optics. The ray model provides us with an intuitive way to study the propagation of beams as well as their interaction between objects. Traditional ray model is based on the normal of a beam wave front. The normal vector is defined as the direction of ray. However, it fails to describe the relationship between light ray and optical wave in the neighborhood of focus or caustic lines/surface since light ray in those regions are no longer perpendicular to the wavefront. In this work, the ray model of a light beam is built according to its Fourier angular spectrum, where the positions of rays can be determined by the gradient of the phase of the Fourier angular spectrum. On the other hand, the Fourier angular spectrum of a light beam can be reconstructed through the ray model. Using Fourier angular spectra, we construct the ray model of two typical beams including the Airy beam and the Cusp beam. It is hard to construct ray model directly from the optical field of these beams. In this ray model, the information about ray including direction and position involves the propagation properties of light beams such as self-accelerating. In addition, we demonstrate that the optical field of the focused plane wave can be reconstructed by the ray model in Fourier regime, and the optical field in spatial domain can be obtained by inverse Fourier transform. Simulation results are consistent with the results from Debye’s method. Finally, the high-dimensional ray model of light beams is elaborated in both spatial and spectral regime. Combined with focused plane wave, Airy beam and rays in quadratic gradient-index waveguide, our results show that the ray model actually carries the information about optical field in both spatial and Fourier domain. Actually, the traditional ray model is just a spatial projection of the high-dimensional ray model. Hence, when traditional ray model fails at the focus or caustic lines/surface, it is able to obtain the spectrum of the corresponding optical field from the Fourier domain, and then obtain the field distribution in spatial domain by inverse Fourier transform.

     

    目录

    /

    返回文章
    返回