Off-axis pumped Nd:YAG/Cr4+:YAG lasers under degenerate cavity conditions are explored to achieve high-pulseenergy geometric modes for beam transformation. The employment of Nd:YAG crystal promises efficient passively Qswitched (PQS) operation with a flexible cavity length to ensure various PQS geometric modes with stable structures can be generated. 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. Various high-energy vortex beams carrying large angular momentum and diverse phase structures are achieved by converting the planar geometric modes into the circular ones to offer promising light sources for potential applications.
Theoretical wave functions are analytically derived to formulate the propagation evolution of the Hermite-Gaussian (HG) beams transformed by single lens astigmatic mode converter with arbitrary angle. The derived wave functions are associated with the combination of the rotation transform and the antisymmetric fractional Fourier transform. The derived formula are validated by the mode conversions of high-order HG beams generated by an off-axis diode-pumped solidstate laser. In addition to validation, the creation and evolution of vortex structures in the transformed HG beams are numerically manifested. The present theoretical model can be applied not only to characterize the evolution of the transformed beams but to design the optical vortex beams with various forms.
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