2007 | OriginalPaper | Buchkapitel
Round-Trip Operator Technique Applied for Optical Resonators with Dispersion Elements
verfasst von : Nikolay N. Elkin, Anatoly P. Napartovich, Dmitry V. Vysotsky, Vera N. Troshchieva
Erschienen in: Numerical Methods and Applications
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
The round-trip operator technique is widely used for dispersionless optical resonators beginning from pioneering studies of Fox and Li. The resonator modes are determined as eigenfunctions of the round-trip operator and may be calculated by means of numerical linear algebra. Corresponding complex eigenvalues determine the wavelength shifts relative to reference value and threshold gains. Dispersion elements, for example, Bragg mirrors in a vertical cavity surface emitting laser (VCSEL) cause a dependence of the propagation operator on the wavelength and threshold gain. We can determine the round-trip operator in this case also, but the unknown values of the wavelength and threshold gain enter into the operator in a complicated manner. Trial-and-error method for determination of the wavelength shifts and the threshold gains is possible but it is rather time consuming method. The proposed approximate numerical method for calculation of resonator modes is based on the solution of linear eigenvalue problem for the round-trip operator with reference wavelength and zero attenuation. The wavelength shifts and threshold gains can be calculated by simple formulae using the eigenvalues obtained and the computed effective length of the resonator. Calculations for a cylindrical antiresonant-reflecting optical waveguide (ARROW) VCSEL are performed for verification of the model.