A Fast Mode Calculation Method For Resonators Based On Differential Equation

Currently, the large-scale simulation platform for high-energy laser systems that China is studying is mainly composed of high energy laser output performance calculation module, inner optical system beam transmission simulation module, adaptive optical system simulation module, laser propagation in the atmosphere simulation module, and performance evaluation of Laser-matter Interaction module. And the function of high energy laser output performance calculation module is to use numerical method to obtain information on the characteristic mode of laser. The high energy laser systems usually have very high beam quality requirements, so beam quality is closely related to laser resonant cavity light field mode. Therefore, the high-energy laser output performance calculation module plays an important role in the simulation platform, and the calculation results will guide the overall design of the high energy laser system and cavity design.According to parabolic partial differential equation theory, the active unstable resonator mode calculation method based on differential equations was analyzed in this thesis. In order to overcome the defects in traditional finite difference method that a larger number of samples are required and the calculation is slow when calculate active unstable resonator mode, this thesis applied the mobile matrix method and coordinate transformation method. Using mobile matrix method would make the speed of calculating the active cavity mode will have significant improvement while maintain the same number of samples. And using the coordinate transformation method, the spherical wave transmission problem in Cartesian coordinate system can be transformed into the plane wave transmission problem in coordinate system, which makes it possible to reduce the required number of samples significantly. Through these improvements, the calculation algorithm is able to keep the traditional advantages such as the accuracy and credibility of the calculation results, while improve the computational efficiency greatly, which formed a fast algorithm suitable for active unstable resonator with large number of Fresnel. The correctness of the fast algorithm was verified by comparing the calculation results of Fresnel diffraction, Fraunhofer diffraction and non-uniform gain unstable resonator of some related reference papers.The influence of gain module's position on the output power in HF chemical laser, the gain module aspect ratio on output power and the extraction efficiency in MOPA HF chemical laser, were all analyzed using the active unstable resonator mode fast calculation method based on the differential equations proposed in this thesis. The influence of the output beam shaping on the output power and extraction efficiency in MOPA HF chemical laser was also analyzed. The results showed that the following measures could be taken for MOPA structure HF chemical laser in order to obtain greater output power: the distance between gain module and concave mirror of confocal unstable resonator should be as small as possible; gain module height moderate at perpendicular to the flow direction should be moderately increased. In addition, the main oscillator output with beam rotation 180°made the uniformity of beam intensity distribution be improved without affecting the output power and extraction efficiency in HF MOPA laser. The active unstable resonator mode fast calculation program in this thesis has been used in the optimal design of high-power HF laser.A differential algorithm based on the q parameter transmission was established, and it is can be used to calculate active stable cavity mode. Output optical field mode of the electrical stimulation stable cavity HF chemical laser was calculated using this algorithm, and the numerical results were compared with the experimental results to verify the correctness of the program.