Abstract The laser transition cross sections of YAP:Nd crystals are calculated by using group theory. The values of these cross sections for general elliptically polarized light are shown to be determined by three parameters. The theoretical results are verified by experiments and demonstrated by the construction of a wave length variable laser. We analysed two laser structures in which the transmission matrices are U-matrices, and calculated the polarizations and frequencies of their eigenmodes. Experimental results agree with the theory well. The results obtained in our work can be used in construc-tion of a single longitudinal mode laser with enhance output and to suggest a new method of modulation for lasers.