Intra-cavity lossless phase retrieval for a nondegenerate on-demand laser via an extra-cavity-like scheme

We present a universal framework for intra-cavity phase retrieval in nondegenerate laser systems, employing a single lossless pure-phase hologram to achieve on-demand spatial mode generation at the source. By integrating mode-reproducing dynamics into a canonical extra-cavity phase retrieval pipeline, joint optimization is enabled for the holographic patterns and loose-state phase distribution on the output coupler. Experimental results showcase the generation of arbitrary intensity profiles, including square flat-top, "X"-shaped, and club-shaped beams. Experimental analysis confirms that precise mode discrimination is achieved via distinct diffractive losses during free-space propagation, rather than local losses imposed on the hologram. Additionally, counter-propagating tailored beams are realized, and interference experiments validate their coherence.