Talbot effect of ring laser array realized by Gyrator canonical transformation

Abstract

We propose a ring laser array structure and study the Talbot effect. By comparing with the one-dimensional laser array, the near-field distribution of the identical intensity of the ring laser array without edge effect is obtained, which can be more conducive to improving the capability of the external cavity phase locking of lasers. In this paper, Talbot effect and self imaging condition of ring laser array in polar coordinates are calculated by using Gyrator canonical transformation. The sub-image distribution at the fractional Talbot distance is further analyzed. The optical profile and phase distribution of the ring laser array at the fractional Talbot distance are simulated, which are mutually verified with the theoretical calculation results. At a quarter of the Talbot distance, the number of sub-images is twice that of the emitters. The light intensities of the sub-images are identical, and thedifference in phase between adjacent sub-images is <inline-formula><tex-math id="M1">\begin{document}${\pi }/{2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20222412_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20222412_M1.png"/></alternatives></inline-formula>. At half of the Talbot distance, the number of sub-images is the same as that of the emitters, while the spatial position of sub-image is shifted by half a cycle along the angular direction. Moreover, the sub-images with twice the number of the emitters are present in three quarters of the Talbot distance. The light intensities of the sub-images are identical and the difference in phase between adjacent sub-images is <inline-formula><tex-math id="M2">\begin{document}$- {\pi }/{2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20222412_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20222412_M2.png"/></alternatives></inline-formula>. Further, the Talbot images with the same spatial and phase distribution as the emitters are generated along the angular direction at the Talbot distance. The optical profile and phase distribution of one dimensional laser array at the fractional Talbot distance are also simulated by FDTD Solutions for comparison. It is found that the edge effect of one-dimensional laser array leads to the uneven distribution of near-field light intensity, in which the intensity of light spot on the edge of array is significantly lower than that in the center of array. While the Talbot sub-images of ring laser array with identical light intensity are obtained. Therefore, We consider that the ring laser array can effectively eliminate the edge effect. The results are helpful in studying the external cavity phase locking of ring laser arrays and its applications in the field of high brightness coherent laser and quantum measurement.