Formation Mechanism of Coherent Rainbows II

When white light laser is focused on liquids, colorful interference rings with different shapes, i.e. “coherent rainbows” can be seen. The formation mechanism of such coherent rainbows is described as follows. The laser heating changes the local temperature distribution of the liquid, which affects the refractive index locally and thus the optical path difference, i.e. thermal lens effect which may cause the laser to go off at large angles. The curvature of the laser wavefront and the convection and bubbles in the liquid can also play some roles as reported here. The wave front curvature results in the asymmetry of the coherent rainbows in the near of the focal point because the wave front curvature in front of the focal point is negative and the wave front curvature in the rear of the focal point is positive. The coherent rainbow has an oval shape with up-down asymmetry because convection in the locally heated liquid leads to an asymmetric temperature distribution. We construct a function including wave front curvature and thermal lens effect, and obtain the relationship between the size of the coherent rainbows and the position of the sample. As a result of the liquid instability induced by the laser heating, the temperature distribution in the liquid is no longer axisymmetric, thus, the focal length of the transverse and longitudinal thermal concave lens are no longer the same. The fitting results accord well with the experimental observations that the coherent rainbows change faster (slower) in front of (rear) the focal point and the longitudinal and transverse dimension of the coherent rainbow are different. Many tiny bubbles are generated in water in the center of the laser beam, forming a local “black barrier” which explains the observation that there are diffraction rings and Poisson-type bright spots in the dark area of the coherent rainbows. The coherent rainbows can be observed in many liquids where the shape and number of rings of coherent rainbows depend on liquid properties such as density, viscosity and thermal conductivity.