The up-conversion and down-conversion process of the second-order nonlinear optical parametric process is a means to expand the laser wavelength range, in which the second harmonic generation and sum frequency generation in the up-conversion process can effectively produce short-wavelength visible lasers with high power and high optical quality. In this paper, an experimental model of injecting the fundamental frequency light field with polarization direction of e and wavelength of 1 438.9 nm into a double-ended optical cavity with a single-period structure (15.69m) is proposed theoretically. The fundamental frequency light passes through the crystal many times, which can improve the conversion efficiency of the output dual-wavelength laser. Class 0 quasi-phase matching with the largest second-order nonlinear polarization tensor is selected. In the same period of the polarized crystal, at the proper working temperature of the crystal, the second-harmonic light field of 719.45 nm and the third-harmonic light field of 479.63 nm can be generated, and the obtained two light fields are output from both ends of the double-ended frequency doubling cavity respectively. The periodic structure of the crystal is designed, and the phase difference caused by the dispersion phenomenon when the interacting light waves propagate in the crystal is well solved by using the quasi-phase matching technology, so that the two nonlinear optical processes corresponding to the second-harmonic light field and the third-harmonic light field meet the first-order quasi-phase matching and third-order quasi-phase matching conditions respectively in the same crystal polarization period. By using the refractive index equation, thermal dispersion coefficient equation and nonlinear optical phase matching condition and other related theories, the relationship between crystal polarization period, fundamental wavelength and temperature is calculated and analyzed. The conclusions obtained can not only provide a theoretical reference value for a single laser to generate dual-wavelength laser in single-period polarized crystal, but also have a certain experimental reference value for further understanding the interaction between laser and atom.