Analysis of mode-field measurements using orthogonal polynomials

Mode-field measurements can be analyzed using a sum of orthogonal polynomials as the fitting function. This method is demonstrated theoretically and experimentally for the mode-field diameter (MFD) measurement of single-mode fibres using the transverse-offset (TO) technique. The fit error is reduced by an order of magnitude in comparison with an ordinary Gaussian fit, and is limited by instrumental noise. Using the Petermann 2 definition, expressions for the MFD and its estimated error are derived. The convergence of the method is demonstrated experimentally. It is shown that the MFD is independent of the chosen range of TO values. In the limit of a large range of equidistant X_i values, the orthogonal polynomials are Hermite-Gaussian polynomials. The transformation from TO field transmission coefficient to strip integrated far-field power can then be carried out easily, and the polynomial coefficients can be used for characterization of the field distribution