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 + <i>k</i><sup>2</sup>)<i>Ẽ</i>(<i>x</i>, <i>y</i>, <i>z</i>) = 0 is transformed into a solvable three-dimensional eigenvalue problem by the separation of the propagation factor exp(−<i>ikz</i>) from the phasor amplitude <i>E</i>˜(<i>x</i>, <i>y</i>, <i>z</i>) 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
(000.4430) General : Numerical approximation and analysis
(140.3410) Lasers and laser optics : Laser resonators
(140.3580) Lasers and laser optics : Lasers, solid-state
(140.4780) Lasers and laser optics : Optical resonators
(140.6810) Lasers and laser optics : Thermal effects
Konrad Altmann, Christoph Pflaum, and David Seider, "Three-Dimensional Finite Element Computation of Laser Cavity Eigenmodes," Appl. Opt. 43, 1892-1901 (2004)