Unstable hybrid waveguide cavity optical field characteristics is an important theoretical problem in high power RF slab CO_{2} laser, together with key engineering design technology involving external optical path shaping,discharging gain and thermal stability, which also influence each other, determine the performance of the RF slab CO_{2} laser. Diffraction theory of non-parallel unstable resonator and mode theory of slab waveguide resonator are established, the output optical field, the loss and the mode identification characteristics of the two directions are studied. The main conclusions of this paper are summarized as follows:The application scope of the Rayleigh Sommerfeld diffraction integral is extended from plane aperture to reflective curved surface aperture in order to provide numerical calculation formula for analysis of non-paraxial cavity. The expression of one-dimensional condition is obtained by applying stationary phase method to two-dimensional diffraction formula.Theory model Slab waveguide cavity is established. In this model, slab waveguide is no longer regarded as a fundamental mode filter but involves higher order mode transmission. It can reflect the effect of modes' transmission in slab waveguide on its coupling with free space mode. Meanwhile, in the E1 mode approximation, a conclusion that 99.47% of the total energy can be coupled to the fundamental mode of Hermite Gaussian beam with waist radius of 0= 0.711(6 is demonstrated.Optical field properties of one-dimensional unstable cavity with circle and parabolic mirrors is investigated from four aspects involving diffraction loss?mode identification?mode cross and output optical field transmission characteristics which should be focus on when designing lasers. Diffraction loss of lowest order mode in Non-paraxial one-dimensional unstable cavity with parabolic mirrors in the condition of large Fresnel Number presents periodicity similar with paraxial cavity with spherical mirrors in the condition of small Fresnel Number. Its mode identification factor presents periodicity too,its value is greater than 1.06 in a wide range of change of equivalent Fresnel Number and its peak value is 0.01 higher than that of cavity with circle mirrors which locates right at the valley of diffraction loss. This advantage can be made best use of to provide more margins and eliminate the effect of the actual error of process parameters on the output mode when designing a resonator. The width of filter in external optical shaping system is computed to be about 0.8mm.A quantitative analysis with fundamental mode approximation of slab waveguide cavity is adopted and suitable coating material and polarization of output optical field is obtained. Taking higher eigenmodes into account, the data of variation of mode identification factor, transmission and coupling loss with waveguide length in the condition of both single pair of electrodes and double pairs of is obtained. The data suggests that when double pairs of electrodes is adopted, if mirrors takes reasonable large curvature radius?equal or more than 100mm?, selecting appropriate waveguide length can make the mode identification factor above 1.5 and control the loss between 2.5% and 5%. Additionally, the expansion coefficient based on slab waveguide cavity eigenmodes at the waveguide end can tell us that various of modes exist in slab waveguide, while the ratio of the higher order modes is very small.The research has important instruction significance for theoretical analysis and design of unstable waveguide hybrid resonator and improvement of the beam quality of RF slab CO_{2} laser. |