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"Design and simulated performance of transmissive phase elements for intra-cavity beam shaping", by Jinsong Liu and M. R. Taghizadeh, Journal of Optics A: Pure and Applied Optics, 5(3): 216-220, 2003.

Intra-cavity transmissive diffractive-phase elements (DPEs) for super-Gaussian (SG) beam shaping which have excellent simulation performance are reported for the first time. The propagation of the angular spectrum is used as the basis for the simulation, and Fox-Li analysis is used to simulate the performance of the designed DPEs. The simulation shows that the iteration equation for the design of transmissive DPEs is basically convergent although it may oscillate during the first ~100 iterations. The irradiance mean square errors (MSEs) of the circular and the square output beam fitted to a 12th-power SG beam are 1.21 x 10-3 and 7.15 x 10-4 respectively when the iteration number is 10 000. Smaller MSEs, 5.400 x 10-4 for the square output, can be obtained by choosing the designed beam to be an SG function of one or two orders higher than the required one. The DPEs with 64-phase-level quantized profile have slightly worse performance than the continuous profile elements do, and the irradiance MSEs are 1.23 x 10-3 and 9.29 x 10-4 respectively.

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