Mixing of argon-ion and carbon dioxide laser radiation in uniaxial rubidium chlorate crystals

Mixing in uniaxial RbCl${\mathrm{O}}_3$ of visible and infrared photons emitted, respectively, by an argon-ion and C${\mathrm{O}}_2$ laser has been examined at room temperature under conditions in which the two laser beams propagate collinearly in the single crystal. The intensity dependence of the Stokes (down-converted) and anti-Stokes (up-converted) mixed-phonon signals has been measured as a function of the propagation direction of the collinear C${\mathrm{O}}_2$ and argon-ion laser beams and has been found to vary by three orders of magnitude as $\theta$, the angle between the wave vector of the visible (or infrared) laser beam and the crystal $c$ axis varies from 0° to 90°. The mixed-photon signal intensity achieves its maximum value at a critical propagation angle ${\theta }_c$ at which phase matching is achieved. The functional dependence of ${\theta }_c$ on the C${\mathrm{O}}_2$-laser wavelength has been calculated and measured. The excellent agreement between experiment and theory provides an additional, yet independent, check of the dielectric functions of RbCl${\mathrm{O}}_3$ which have been determined previously from Raman scattering measurements. The polarization relationships between the mixed photons and the incident photons have been studied carefully and analyzed through both the second-order nonlinear susceptibility tensor and the Raman tensors. Group-theoretically-derived polarization selection rules are rigorously obeyed as evidenced by experimental depolarization factors in excess of 1000. Consistent with wave-vector selection rules, the mixed photons that emerge from the RbCl${\mathrm{O}}_3$ crystal are highly collimated along a specified direction. The mixing process, in addition to being viewed as a second-order nonlinear interaction, is treated as Raman scattering from angular-tunable optically pumped hot phonons and polaritons. Nonequilibrium steady-state pumped-polariton gains in excess of ${10}^8$ corresponding to equilibrium sample temperatures of the order of ${10}^{11}$ °K have beem measured and calculated. An extensive search was made for first-and second-order Raman scattering from the hot-polariton decay and scattering products. No such damping products were observed for reasons related principally to limitations in the minimum achievable measurement temperature.