Effects of a partially coherent beam on periodic bottle beam

In this paper, we propose how to generate the periodic bottle beam by using a partially coherent beam. Firstly, a spatially completely coherent beam is transformed into a partially coherent beam by a rotating ground glass. Secondly, after passing through the double-axicon system, the parallel beam is converted into two Bessel beams which have the same optical frequencies but different radial wave vectors. Finally, the partially coherent periodic bottle beam can be generated by two interfering Bessel beams. Based on the interference theory, an analytical expression can be obtained for calculating the distribution of light intensity in the image and spot diagrams in spectral degree of coherence for the optical field with 0.9. By doing this calculation, the proposed optical system can be made to generate a partially coherent periodic bottle beam with the oscillation period of 2.5 mm. Before further investigating the effect of field coherence on the periodic bottle beam, we may also calculate the distribution of light intensity in the images and spot diagrams in the spectral degree at 0.83, 0.7, 0.5 and 0.2, respectively. Results show that the intensity contrast ratio between the dark focus and the surrounding periodic regions can be reduced with the decrease of the spatial coherence degree. In this case, the period of the bottle beam and the central dark focus size will not be affected. We have also designed and carried out an experimental generation of the periodic bottle beam and measured its focusing properties. In the experiment, we can control the coherence in the incident field by controlling the size of the circular aperture located behind the rotating ground-glass disk. When the size of the circular aperture is 0.1 (or 0.2) mm, the value of the coherence degree of the incident optical field is 0.9 (or 0.83). The two different coherence degrees of the partially coherent bottle beam have been measured by CCD. Experimental results show that the obtained bottle beams are of the same period of 2.5 mm. The measured diameters of the two different coherence degrees of the central spots (maximum sizes of the dark spot) are both 15 m. Experimental results also show that the spectral degree of coherence cannot affect the shape and size of the periodic bottle beam except the contrast of it. Therefore, the experimental results agree well with the theoretical results.