An off-axis pumped Nd:YAG/Cr4+:YAG laser under different degenerate cavity conditions has been thoroughly studied to generate high-pulse-energy geometric modes for further beam transformation. Because of the employment of Nd:YAG gain crystal provides a flexible choice of cavity length to achieve efficient passively Q-switched (PQS) operation, various PQS geometric modes with stable spatial structures are generated. Moreover, it is experimentally confirmed that the output energy and peak power of the PQS geometric modes can easily reach up to over 100 μJ and 10 kW with fairly stable pulse trains in pure linear polarization. By using an astigmatic mode converter (AMC) to transform the planar geometric modes into the circular geometric modes, various high-energy vortex beams with large angular momentum and diverse phase structures are successfully realized to offer a promising light source for further application. The propagation evolution of the transformed geometric modes through the AMC was also analyzed theoretically to offer useful insights for the formation of the geometric vortex beams.
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