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A theoretical model for optical parametric oscillation (OPO) with power-dependent pump reflections and arbitrary idler reflectivity is presented. After the differential coupled-wave propagation equations under the appropriate boundary conditions are solved, the general expression for conversion efficiency is derived. The characteristic behavior of the OPO efficiency as a function of input pump intensity is shown to evolve from pure singly resonant oscillation to pure doubly resonant oscillation as the idler reflectivity is gradually varied from 0% to near 100%. The optimal idler reflectivity depends on the specific values of the given OPO components and could be found with the general results presented.

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Using a real-time formalism of equilibrium and nonequilibrium quantum-field theory, we derive the reaction-rate formula for neutrino-conversion ($\nu \to \nu'$) process and $\nu \bar{\nu}'$ annihilation process, which take place in a hot and dense QED plasma with background (anti)neutrinos out of equilibrium. Also derived is the formula for the inverse processes to the above ones. Using the hard-thermal-loop resummation scheme, we include the contribution from the coherent processes. The decay/production of a neutrino causes an evolution of its spatial distribution. A scheme for dealing with this evolution is presented. For the case of isotropic neutrino distribution, numerical computation is carried out for the parameter region of type-II super-nova explosion. Defferential reaction rate exhibits characteristic peak structure, which comes from the coherent processes. The contribution from the above processes to the decay or damping rate of a parent neutrino $\nu$ is also studied.Comment: 27 pages and 13 figure

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