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Pure Python implementation of the finite difference frequency domain (FDFD) method for electromagnetics
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fdfdpy fixed flux bug, also gave flux probe nonlinear option Oct 11, 2018
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This is a pure Python implementation of the finite difference frequency domain (FDFD) method. It makes use of scipy, numpy, matplotlib, and the MKL Pardiso solver. fdfdpy currently supports 2D geometries


python install


See the ipython notebooks in notebooks.

Unit Tests

Some basic tests are included in tests/

To run an example test, tests/, either call

python -m unittest tests/


python tests/



The Simulation class is initialized as

from fdfdpy import Simulation
simulation = Simulation(omega, eps_r, dl, NPML, pol, L0)
  • omega : the angular frequency in units of 2 pi / seconds
  • eps_r : a numpy array specifying the relative permittivity distribution
  • dl : the spatial grid size in units of L0
  • NPML : defines number of PML grids [# on x borders, # on y borders]
  • pol : polarization, one of {'Hz','Ez'} where z is the transverse field.
  • L0 : (optional) simulation length scale, default is 1e-6 meters (one micron)

Creating a new Fdfd object solves for:

  • xrange : defines spatial domain in x [left-most position, right-most position] in units of L0
  • yrange : defines spatial domain in y [bottom-most position, top-most position] in units of L0
  • A : the Maxwell operator, which is used later to solve for the E&M fields.
  • derivs : dictionary storing the derivative operators.

It also creates a relative permeability, mu_r, as numpy.ones(eps_r.shape) and a source src as numpy.zeros(eps_r.shape).

Adding sources is exciting!

Sources can be added to the simulation either by manually editing the 2D src array inside of the simulation object,

simulation.src[10,20:30] = 1

or by adding modal sources, which are defined as planes within the 2D domain which launch a mode in their normal direction. Modal source definitions can be added to the simulation by

simulation.add_mode(neff, direction, center, width)
  • neff : defines the effective index of the mode; this will be used as the eigenvalue guess
  • direction : defines the normal direction of the plane, should be either 'x' or 'y'
  • center : defines the center coordinates for the plane in cell coordinates [xc, yc]
  • width : defines the width of the plane in number of cells

Note that simulation.setup_modes() must always be called after adding mode(s) in order to populate simulation.src.

Solving for the electromagnetic fields

Now, we have everything we need to solve the system for the electromagnetic fields, by running

fields = simulation.solve_fields(timing=False)

simulation.src is proportional to either the Jz or Mz source term, depending on whether pol is set to 'Ez' or 'Hz', respectively.

fields is a tuple containing (Ex, Ey, Hz) or (Hx, Hy, Ez) depending on the polarization.

Setting a new permittivity

If you want to change the permittivity distribution, reassigning eps_r

simulation.eps_r = eps_new

will automatically solve for a new system matrix with the new permittivity distribution. Note that simulation.setup_modes() should also be called if the permittivity changed within the plane of any of the modal sources. <- I'll make this happen automatically later -T


Primary fields (Hz/Ez) can be visualized using the included helper functions:

simulation.plt_re(outline=True, cbar=True)
simulation.plt_abs(outline=True, cbar=True, vmax=None)

These optionally outline the permittivity with contours and can be supplied with a matplotlib axis handle to plot into.

To Do


  • xrange, yrange labels on plots.
  • set modal source amplitude (and normalization)
  • Add ability to run local jupyter notebooks running FDFD on parallel from server.
  • Save the factorization of A in the Fdfd object to be reused later if one has the same A but a different b.
  • Allow the source term to have (Jx, Jy, Jz, Mx, My, Mz), which would be useful for adjoint stuff where the source is not necessarily along the z direction.
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