Modes, beams, coherence, and orthogonality

Anthony E. Siegman

doi:10.1117/12.259904

20 November 1996 Modes, beams, coherence, and orthogonality

Anthony E. Siegman

Proceedings Volume 2870, Third International Workshop on Laser Beam and Optics Characterization; (1996) https://doi.org/10.1117/12.259904
Event: Third International Workshop on Laser Beam and Optics Characterization, 1996, Quebec City, Canada

Abstract

Loss-guided optical waveguides have propagation operators which are linear but not self-adjoint. The eigenmodes of such nonHermitian systems are then not orthogonal but rather are biorthogonal to a set of adjoint functions. If one wishes to expand an arbitrary wave in the eigenmodes of the system, it is tempting to find the expansion coefficients using the biorthogonality relation to obtain quadrature integrals between the propagating wave and the adjoint functions. We show however that a minimum least-square error expansion is obtained not by using these adjoint integrals, but by a more complex procedure based on inverting the eigenmode orthogonality matrix. For the particular case of Hermite-Gaussian functions having a complex-valued scale factor, expansions using the adjoint coefficients fail to converge under a wide range of circumstances, whereas the minimum-error coefficients converge and give much smaller errors under all circumstances.

Citation Download Citation

Anthony E. Siegman "Modes, beams, coherence, and orthogonality", Proc. SPIE 2870, Third International Workshop on Laser Beam and Optics Characterization, (20 November 1996); https://doi.org/10.1117/12.259904

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