Realizing the Talbot Effect of Ring Laser Array With Gyrator Canonical Transformation

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 ability 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 intensity of the sub-images is identical, and the phase difference between adjacent sub-images is π/2. 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-images is offset half a cycle along the angular direction. Moreover, the sub-images with twice the number of the emitters are presented at three quarters of the Talbot distance. The light intensity of the sub-images is identity and the phase difference between adjacent sub-images is -π/2. 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 for the study of the external cavity phase locking of ring laser arrays and for applications in the field of high brightness coherent laser and quantum measurement.