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An algorithm is proposed for the computation of resonator wavelength of vertical cavity surface emitting lasers by Cauchy's formula and the method of lines. To calculate the laser modes an implicit eigenvalue problem has been solved. A pole-free complex function has been developed which allows the determination of all roots within the observed complex area. To test the proposed method several wavelengths of a 1.55 μm laser have been computed and compared with direct and iterative algorithms.