Study On The Resonator With Eigenvalue Method And Hollow Beam With Its Applications

Three parts are included in this dissertation.The first part is to introduce different methods for analyzing resonators and basic theory of diffraction in resonator. And an eigenvalue method (EM) is illustrated and developed to calculate the optical field in resonators. A new transit matrix of an optical resonator is obtained based on the Fresnel-Kirchoff diffraction integral equation. Each eigenvalue can directly derive one set of eigenvectors which just represents one mode distribution on the mirror, without hundreds of times of iteration. The EM has great advantages over others.The second part is to simulate the optical field in resonator with graded reflectivity mirror by using the software "Mathematics5.0" and hollow beam is obtained by reconstructing the optical resonator with graded reflectivity mirror. And two models, high-order Bessel-Gauss modes and hollow Gauss beams, have been proposed to describe hollow beams. The results for high-order Bessel-Gauss beams and hollow Gauss beams propagating through free space and lens focusing system are derived respectively by terms of Collins integral formula. The theoretical results are simulated by Mathematics respectively. All of the theoretical results are consistent well with the experimental results.The third part is the practical application-laser engraving system. The hardware and software of the system are introduced in detail. And the experimental data and results are discussed in this part. And the program in Mathematics is also introduced in detail.The main work of this dissertation focuses on analyzing the resonator by using eigenvalue method; and hollow beams are obtained experimentally and analyzed theoretically, which shows the hollow beams have great advantages and special characteristics. Two model, high-order Bessel-Gauss modes and hollow Gauss beams,are used to describe hollow beams. And the theoretical simulation results have been given to show the special characteristics of hollow beams; And the application of the hollow beam, laser engraving system, has been successfully developed, the hardware and the software of which are proved properly and efficiently.