The crystal size and the reflectivity of S and P polarization components of the output coupling (RS and RP) are crucial for the operation of the monolithic single frequency ring laser. The working principle of single frequency operation of the monolithic ring laser was discussed by means of Jones matrix. In order to achieve high single frequency output power and high slope efficiency, RS and RP were determined by calculating the square eigenvalues and the differences of square eigenvalues of Jones matrix of the resonator as well as considering the optimum output coupling for given crystal size, magnetic field and pumping power. A fiber coupled diode laser was used as pumping source in experiment. Single frequency output power of 1.20 W with the slope efficiency of 47.4% was obtained when input pumping power was 2.83 W.