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The properties of standard Laguerre–Gaussian beam (sLGB) and elegant Laguerre–Gaussian beam (eLGB) through the misaligned complex hard edge apertures (MCHEAs) are investigated. Analytical formulae for the far field distributions of sLGBs and eLGBs through the different hard edge apertures are derived based on the generalized Huygens–Fresnel diffraction integral equation. The propagation properties and beam qualities of sLGBs and eLGBs are studied comparatively. It is shown that the divergence angle of sLGBs with the low order modes is less than that of eLGBs. However, the energy distributions of eLGBs with the high order modes after through the multiple hard edged apertures are more convergent in comparison with sLGBs, and eLGBs have the better beam quality than sLGBs. The study results are useful for the propagations and applications of sLGBs and eLGBs through the complex optical systems.

Using misalignment matrix of optical components, the change law of the single-pass diffraction loss with the discharge tube and resonator mirror misalignment of two-dimensional axisymmetric-fold combination cavity CO 2 laser are researched and analyzed. The change curves with misalignment angle are also calculated and simulated numerically in this paper. The results show that when the laser parameters are ascertained, the single-pass diffraction loss is less than 0.1, the misalignment angle range of discharge tube and resonator mirror are obtained, and it is beneficial to the adoption of resonator and instruction for installation.

A method of reflection-injection phase-locking used on two-dimensional axisymmetric-fold combination resonator (ASFC) CO2 laser has been proposed. The structure characteristics and the method of phase-locking have been introduced. The expression of output light intensity distribution has been deduced by matrix theory and Collins Formula and the output light intensity distribution has been numerically calculated and simulated. Comparing the output light intensity distribution in the case of phase-locking with that of non-phase-locking. The result shows that this method of phase-locking greatly improve the characteristics of output beam.

Based on the phase-locking principle of Gaussian beam, the phase-locking mechanisms of the spherical wave from axisymmetric concentric cavity (ASCC) CO2 laser are analyzed. And then we study the variety laws of the equiphase surfaces and the light spots of the injected beam. The numerical calculations show that the injected beam could be considered as a spherical wave approximately in the ASCC. The phase-locking of the spherical wave is different from the phase-locking of the Gaussian beam; there are different field distributions between Gaussian beam and spherical wave. And the phase-locking method could improve the maximum value of the light intensity, the encircled energy reflects the degree of phase-locking.

The experimental proof of the light output on the two-cone axisymmetric-folded combination (ASFC) CO 2 laser has been performed. The output power from the centre discharge tube is 26.7 W, and that of one couple of folded discharge tubes is 40.5 W. Seventeen beams can be obtained from the device, which are from the folded cavities with axes placed in the inner and outer cones, respectively. Therefore, the ASFC CO 2 laser with more discharge tubes can be fabricated and much higher output power can be obtained.