Abstract
Thanks to controlling the off-optical axis propagation in the monoclinic KGd(WO4)2:Nd biaxial crystal used as a laser gain medium, we exhibited remarkable crescent laser modes and mode switching, demonstrating the preservation of the conical diffraction. We revealed an optical singularity in addition to the optical axis: the directions of polarization changed abruptly to the highest emission cross-section mode, which leads to un-polarized lasing. The key explanation is a severe mode selection due to the threshold behavior of lasing. This is confirmed by a theoretical model taking into account a two-axes crystal rotation and including the conical diffraction behavior. The rotation around the two-fold b crystallographic axis of the frame, which makes the imaginary part of the dielectric susceptibility tensor diagonal, is exhibited.

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