Research of errors of the approximated solutions for weakly guiding circle optical waveguides on model refractive index profiles

Roman V. Andreev; Denis E. Praporshchikov; Vladimir A. Burdin

doi:10.1117/12.634562

6 June 2005 Research of errors of the approximated solutions for weakly guiding circle optical waveguides on model refractive index profiles

Roman V. Andreev, Denis E. Praporshchikov, Vladimir A. Burdin

Author Affiliations +

Proceedings Volume 5854, Optical Technologies for Telecommunications; (2005) https://doi.org/10.1117/12.634562
Event: Optical Technologies for Telecommunications, 2004, Samara, Russian Federation

Abstract

In the given work results of the theoretical analysis of errors of the approximated calculation methods for transfer parameters of weakly guiding single-mode optical fibres are submitted, namely a Gaussian approximation method and approach for small values of the normalized frequency. Errors were defined by testing for a modeling step refractive index profile of weakly guiding optical fibre for which a strict decision is exist. As a result of differentiation of the known characteristic equation for a step optical fibre analytical expressions for the first and second derivatives of a square waveguide parameter U² and, accordingly, derivatives of a distribution constant of a waveguide have been received. Calculations of dependences of a square waveguide parameter U² a distribution constant for a basic mode of a step fibre and their derivatives from the normalized frequency for area of small values V, great values V and area of changes V near to unit are executed. Calculations were made both on the basis ofthe strict approach, and on the basis of the approximated solutions. In result dependences of errors of the approximated solutions are received depending on the normalized frequency, allowable scopes for considered approximation are determined.

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Roman V. Andreev, Denis E. Praporshchikov, and Vladimir A. Burdin "Research of errors of the approximated solutions for weakly guiding circle optical waveguides on model refractive index profiles", Proc. SPIE 5854, Optical Technologies for Telecommunications, (6 June 2005); https://doi.org/10.1117/12.634562

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