In this paper, a high-efficiency Denisov-type launcher, a hardcore of quasi-optical mode converters in high-power gyrotron oscillators, is investigated. Based on integral expression of Bessel functions and geometric optics, the propagation of EM wave in circular waveguides, the syntheses of amplitude and phase of nine modes are analyzed in detail. A generalized method for designing the launcher with a dimpled waveguide wall operating in different modes is demonstrated. This method shows how to select a set of appropriate coupled modes to synthesize the Gaussian-like distribution on the inner wall of the launcher. A program is developed and its accuracy is confirmed by a high-power gyrotron at 140 GHz, in TE28,8 mode theoretically. Numerical calculations show a good agreement with reported results.