| We have carried out thoroughly theoretical investigation of the conversion efficiency and the field distribution of the second harmonic generation (SHG) and the third harmonic generation (THG) on the Flattened Gaussian beam. The field distribution of the Flattened Gaussian beam across the waist plane is flattened. For several applications it is of great value. We have studied and simulated the theory of the conversion efficiency of the Flattened Gaussian beams SHG and THG on the crystal CsLjB6Oio, and compared it with that of the Gaussian beam, and computed the field distribution of the Flattened Gaussian beam s harmonic wave. In the section 1 , we have introduced the background and the recent advance of the Flattened Gaussian beam ; In the section 2 , For the first time, we have calculated the type- I and type- II SHG conversion efficiency and simulated curves versus the crystal length , the pumping light polarization rate , the order of the Flattened Gaussian beam and the pumped power intensity , we obtained that the highest efficiency was influenced by the order and the polarization rate of the pumped Flattened Gaussian beam . At the same time we obtained that the SHG conversion efficiency of the Flattened Gaussian beam is higher than that of the Gaussian beam under the same condition ; In section 3 ,we have computed the theoretical conversion efficiency of the THG on the Flattened Gaussian beam , where we also have worked out the type- I and type-11(1) THG conversion efficiency curves versus the same effectors, and found the Flattened Gaussian beams THG conversion efficiency is higher than that of the Gaussian beam too; In the section 4, we have simulated the field distribution of the SHG and THGwave on the Flattened Gaussian beam. |