Analysis of a right-angle conical reflector resonator by the transfer matrix method

A resonator with a right-angle conical reflector has been proposed to produce high-power CO₂ laser beams. To analyze eigenfields of the right-angle conical reflector resonator, this paper adopts and demonstrates the transfer matrix method. In this paper, the mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. The calculation results reveal that the right-angle conical reflector resonator could be used for a high-power CO₂ laser to achieve low-order modes. However, the beam quality is reduced due to the residual blind-hole, which is in accord with the experimental result.