Propagation losses at 10.6 µm in hollow-core rectangular waveguides for distributed feedback applications

Eigenvalue equations for the TE and TM modes propagating in a rectangular hollow-core waveguide are derived. The solutions to the eigenvalue equation are used to determine the theoretical losses for the lowest even order mode propagating in a rectangular waveguide whose cross-sectional dimensions are suitable for distributed feedback at 10.6 μm. Waveguide materials such as gold, BeO, glass, and germanium are analyzed. It is shown that by using gold for the top and bottom waveguide regions with BeO for the side walls, loss as small as 1.19 dB/m can be obtained with a cross-sectional dimension 0.1 mm × 0.8 mm. Using external discharge pumping the authors have created an active medium with gain in excess of 17 dB/m in a 0.08 mm hollow-core slab waveguide. Loss calculations indicate the feasibility of succesfully constructing a conventional electric discharge waveguide laser for DFB operation at 10.6 μm. Using a BeO-glass combination with cross-sectional dimensions 0.1 mm × 1 mm, a loss of 2.75 dB/m is calculated. It is also shown that a TEA waveguide laser could be built using the side walls for electrodes. This would result in a DFB waveguide laser at 10.6 μm with 2.75 dB/m loss and a cross section 0.1 mm × 2 mm. These results indicate that with good fabrication techniques and with the application of distributed feedback, it may be possible to construct a CO2waveguide laser with a significantly reduced waveguide cross section.