Improvement And Numerical Analysis Of Optical Resonators In High-power CO₂ Lasers

This paper focuses on two kinds of resonator in high-power CO₂ gas lasers— Gaussian-reflectivity plano-concave resonator and seven-folded resonator with circular diaphragms to acquire laser beams with high power and good quality and promote application of high-power laser in the field of hardening treatment on material surface. Since self-reproducing principle is suitable for most resonators at large, in this paper the iterative method to solve integral equation is improved. First of all, by virtue of FFT (Fast Fourier Transform), the eigenmode integral equation is iteratively calculated and analyzed. Secondly, based on numerical dispersal and self-reproducing principle, the integral equation is transformed to the finite-sum matrix equation for eigenmodes. Finally, by solving the finite-sum matrix for eigenvectors and eigenvalues, eigenmode patterns and their losses in two resonators proposed above are discussed.The laser heat treatment on a metal surface is impacted by the quality of laser beams. Consequently, new technologies must be adopted to improve the quality of laser beams. In this paper, in the first place, the effect of power density distribution of laser on laser heat treatment is analyzed. Secondly, the necessity and approach to improve the resonator of a high-power transverse-flow CO₂ laser are described according to the measured results of power density distributions of the high-power transverse-flow CO₂ lasers.It is necessary to review traditional scalar diffraction theory and generalized Collins' formula because scalar diffraction theory plays an important role in the research of mode-fields in a diffraction-limited optics system and resonator. In this paper, spatial fields in a coherent optics system are numerically simulated by use of scalar diffraction theory and Collins' formula, respectively. Moreover, spatial tracing method of laser fields is summarized to study transverse-mode fields in resonators.In order to simulate transverse-mode fields in resonators, analytical methods for resonators are studied thoroughly as follows: first, according to diffraction integral theory, the traditional Fox-Li iterative method is discussed; second, based on the spatial tracing method, angular spectra theory and FFT, the Fox-Li iterative method is improved and the calculating instance for mode-fields in the seven-folded resonator with circular diaphragms is given; third, by means of scalar diffraction theory or Collins formula, after dividing an optics system into some serial subsystems along the diffraction-limited interface(s) and dispersing the overall field into tiny elements across the mirror, the finite-sum matrix equation is derived by introducing self-reproducing principle; in the end, by use of the QR method, transverse mode fields in the circular confocal resonator and the symmetric resonator are numerically analyzed by solving the matrix for all eigenvectors and eigenvalues. The computedresults indicate that by use of the QR method for all eigenvectors and eigenvalues of the matrix, transverse mode fields and losses in the laser resonator can be calculated quickly and exactly.By means of the finite-sum matrix method, eigenmode fields in the Gaussian-reflectivity plano-concave resonator and the seven-folded resonator with circular diaphragms are numerically investigated, and the numerical results of field distributions and losses in two high-power CO2 laser resonators are given. It is shown that the Gaussian-reflectivity plano-concave resonator and the seven-folded resonator with circular diaphragms can easily output the fundamental-mode laser beams, respectively. Therefore, laser beams with high power and good quality can be obtained by using two resonators above.Finally, heat actions of fundamental-mode Gaussian beams, square beams transformed from fundamental-mode beams and HJ-3 high-power transverse-flow CO2 laser beams are compared, which leads to the conclusion that under suitable velocity the homogeneous hardening strap can be acquired on the material surface after the fundamental-mode Gaussian beams passing through the square transforming device. As a result, the homogeneous hardening strap of heat treatment can be guaranteed by using two new resonators and acquiring the fundamental-mode output.