Numerical analysis of primary rainbows from a homogeneous cylinder and an optical fiber for incident low-coherent light

- Spatial and spectral representations of scattered far field in the vicinity of multiple primary rainbows undergo qualitative as well as quantitative transformations in comparison with laser light scattering when a transparent fiber is illuminated by a beam of low-coherent light.
- A physical interpretation of macroscopic low-coherent scattering may refer to second-order refraction of light.
- By finding an optimal width of the spectral profile of the incident radiation it is possible to establish a causal physical relationship between the core diameter of a step-index fiber and the rainbow spectrum.

This work provides a numerical study of the scattering of low-coherent light by an infinite right circular cylinder and various types of optical fiber (with step- and graded-index profiles) in the vicinity of primary rainbows, caused by light that has been subjected to one internal reflection. The scattered intensity is analyzed in terms of the Fourier transform as well as in the time domain (by examining the impulse response of a fiber) with the aim to obtain a detailed information about the scattering process. The analysis reveals a wealth of information about the scattering process that is not obvious when a fiber is illuminated by a temporally coherent light source. The results also provide an idea for the characterization of the core size of step-index optical fibers.