Elliptical facet cylindrical optical fiber - Mathieu equation

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SUMMARY

The discussion centers on deriving equations for the evanescent field above an elliptical facet cylindrical optical fiber, referencing the Mathieu equation. The user seeks to understand how to model the fields for three modes within this specific fiber geometry, as outlined in the Optical Engineering journal (2007). The inquiry includes exploring the feasibility of fitting a function like "sinc" to describe the field distribution on the fiber surface.

PREREQUISITES
  • Understanding of the Mathieu equation and its applications in optical fiber modeling.
  • Familiarity with elliptical cylindrical geometries in optical fibers.
  • Knowledge of evanescent fields and their significance in waveguide theory.
  • Basic proficiency in mathematical modeling techniques for optical fields.
NEXT STEPS
  • Research the application of the Mathieu equation in optical fiber design.
  • Explore mathematical modeling techniques for evanescent fields in waveguides.
  • Investigate the use of sinc functions in optical field approximations.
  • Study the properties of elliptical cylindrical fibers and their mode structures.
USEFUL FOR

Optical engineers, physicists, and researchers involved in fiber optics design and analysis, particularly those focusing on advanced geometries and field modeling techniques.

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Let's say I have three modes in a fiber that is elliptical cylinder shaped (cylinder with elliptical facet), as in the image below (the source:Optical Engineering, 46(4), 045003 (2007)) so what is the equations that describe these fields..
 

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Just an idea came up to my mind, I need the equations to know the evanescent field above the waveguide... do you think it is possible to fit a function like "sinc" or similar to obtain filed on the surface? if yes how one can do it
 

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