A new method for computing eigenmodes of a laser resonator by the use of finite element analysis is presented. For this purpose, the scalar wave equation (Δ + k
2)Ẽ(x, y, z) = 0 is transformed into a solvable three-dimensional eigenvalue problem by the separation of the propagation factor exp(-ikz) from the phasor amplitude Ẽ(x, y, z) of the time-harmonic electrical field. For standing wave resonators, the beam inside the cavity is represented by a two-wave ansatz. For cavities with parabolic optical elements, the new approach has successfully been verified by the use of the Gaussian mode algorithm. For a diode-pumped solid-state laser with a thermally lensing crystal inside the cavity, the expected deviation between Gaussian approximation and numerical solution could be demonstrated clearly.
© 2004 Optical Society of America
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