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

Phase conjugation with stimulated Brillouin scattering can be used to correct wave-front aberrations in high-power laser systems. Here, we consider such a process with cylindrical vector lasers beams. By using a vectorial approach and a modal decomposition, we obtain a differential matrix equation that enables the calculation of the structure of Stokes vector eigenmodes and their Brillouin gain. The emphasis is put on the mode with the largest gain, which contributes the most to the Stokes beam. We show that the phase conjugation of orbital angular momentum in cylindrical vector beams is prevented from happening almost everywhere on the higher-order Poincar\'e sphere. This phenomenon is traced to the tendency of the Stokes beam to acquire a polarization structure similar to the incident pump beam, which constrains the possible combinations of topological charges of the two orbital angular momentum modes making up the Stokes cylindrical vector beams. However, near the poles of the higher-order Poincar\'e sphere, the Stokes mode with the largest gain acquires an additional helical phase factor that produces the conjugated topological charge for the stronger circularly polarized component without affecting the polarization structure. Experimental results are found to agree with our theoretical predictions.