In the He-Ne laser with an integrated cavity made of zerodur, the inner face performance of the gain tube is limited by
the machining techniques, which tends to influence the beam propagation and transverse mode distribution. In order to
improve the beam quality and select out the fundamental mode, an aperture is usually introduced in the cavity. In the
process of laser design, the Fresnel-Kirchhoff diffraction integral equation is adopted to calculate the optical field
distributions on each interface. The transit matrix is obtained based on self-reproducing principle and finite element
method. Thus, optical field distribution on any interface and field loss of each transverse mode could be acquired by
solving the eigenvalue and eigenvector of the transit matrix. For different-sized apertures in different positions, we could
get different matrices and corresponding calculation results. By comparing these results, the optimal size and position of
the aperture could be obtained. As a result, the feasibility of selecting fundamental mode in a zerodur He-Ne laser by a
circular aperture has been verified theoretically.
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