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Phase conjugation with stimulated Brillouin scattering can be used to correctwavefront aberrations in high-power laser systems. Here, we consider suchprocess with cylindrical vector lasers beams. By using a vectorial approach anda modal decomposition, we obtain a differential matrix equation that enablesthe calculation of the structure of Stokes vector eigenmodes and theirBrillouin gain. The emphasis is put on the mode with the largest gain, whichcontributes the most to the Stokes beam. We show that the phase conjugation oforbital angular momentum in cylindrical vector beams is prevented fromhappening almost everywhere on the higher-order Poincar\'e sphere. Thisphenomenon is traced to the tendency of the Stokes beam to acquire apolarization structure similar to the incident pump beam, which constraints thepossible combinations of topological charges of the two orbital angularmomentum modes making up the Stokes cylindrical vector beams. However, near thepoles of the higher-order Poincar\'e sphere, the Stokes mode with the largestgain acquires an additional helical phase factor that produces the conjugatedtopological charge for the stronger circularly polarized component withoutaffecting the polarization structure. Experimental results are found to agreewith our theoretical predictions.

Inhibition of the phase conjugation of orbital angular momentum superpositions in cylindrical vector beams during stimulated Brillouin scattering