Geodesic
Hadiation from the open resonator with the axis symmetry weakly curved mirrors
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 158-165

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Eigen oscillation of the resonator with the axis symmetry weakly curved mirrors are considered in the paper. Sommerfeld radiation condition and Dirichlet boundary condition on the mirrors are supposed to satisfy. The asymptotic formulae for the eigen-values are obtained. Imaginary part of the eigen-values describes dissipation of the energy. 
@article{ZNSL_1983_128_a17,
     author = {M. B. Tabanov},
     title = {Hadiation from the open resonator with the axis symmetry weakly curved mirrors},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {158--165},
     publisher = {mathdoc},
     volume = {128},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a17/}
}
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M. B. Tabanov. Hadiation from the open resonator with the axis symmetry weakly curved mirrors. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 158-165. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a17/