# LP Mode Solver

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This small Matlab library contains functions for finding and plotting all the LP modes of a step-index fibre under the weakly guided approximation. The function find_LP_modes numerically solves the eigenvalue equation:

where $J_l$ is a Bessel function of the first kind of order $l$, $K_l$ is a Bessel function of the second kind of order $l$ and

where $V$ is the fibre V number and $u$ is the parameter to be solved.

The images below are example amplitude and intensity plots of an LP mode.

### Version History

Release 1 : Original Release
Release 2 : Bug fix in plot_all_LP_modes which was incorrectly choosing which modes were rotationally degenerate