Simple module to find numerically the propagation modes and their corresponding propagation constants of multimode fibers of arbitrary index profiles.
What is it?
pyMMF is a simple module that allows finding the propagating modes of multimode fibers with arbitrary index profiles and simulates the transmission matrix for a given length. The solver can also take into account the curvature of the fiber (experimental). This code is not designed to compete with commercially available software in term of accuracy of the mode profiles/propagation constants or speed, it aims at quickly simulating realistic transmission matrices of short sections of fiber.
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Download the file and execute the following command.
python setup.py install
How does it work?
The sovler solve, for a given index profile, the transverse part of the scalar propagation equation. It finds the modes by numerically finding the eigenvalues of the transverse operator represented as a large but sparse matrix on a square mesh. The eigenvectors represent the mode profiles and the eigenvalues give the corresponding propagation constants. The solver needs to know how many modes you want to compute, if the number set is higher than the number of propagationg modes, it will only returns the propagating modes. More detailed explanations can be found is this two-part tutorial:
Example 1: Finding the modes of a graded index fiber (GRIN)
import pyMMF import numpy as np import matplotlib as pyplot
We first set the parameters of the fiber we want to simulate.
NA = 0.275 radius = 7 # in microns areaSize = 2.5*radius # calculate the field on an area larger than the diameter of the fiber npoints = 2**7 # resolution of the window n1 = 1.45 wl = 0.6328 # wavelength in microns curvature = None
We first create the fiber object
profile = pyMMF.IndexProfile(npoints = npoints, areaSize = areaSize)
We use the helper function that generates a parabolic index profile:
We then give the profile and the wavelength to the solver
solver = pyMMF.propagationModeSolver() solver.setIndexProfile(profile) solver.setWL(wl)
Run the solver
The solver needs to know how many modes you want to compute. We estimate the number of modes of a GRIN multimode fiber.
NmodesMax = pyMMF.estimateNumModesGRIN(wl,radius,NA)
To be safe, we ask for a bit more than the estimated number of modes previously calculated.
modes = solver.solve(nmodesMax=NmodesMax+10,boundary = 'close',curvature = curvature)
Ask for the number of propagating modes found by the solver (other modes are discarded).
Nmodes = modes.number
Display the profile of a mode
m = 10 plt.figure() plt.subplot(121) plt.imshow(np.real(modes.profiles[m]).reshape([npoints]*2)) plt.subplot(122) plt.imshow(np.imag(modes.profiles[m]).reshape([npoints]*2))