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 setup.py install
See the ipython notebooks in
Some basic tests are included in
To run an example test,
tests/test_nonlinear_solvers.py, either call
python -m unittest tests/test_nonlinear_solvers.py
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
NPML: defines number of PML grids
[# on x borders, # on y borders]
pol: polarization, one of
zis 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
yrange: defines spatial domain in y [bottom-most position, top-most position] in units of
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,
numpy.ones(eps_r.shape) and a source
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) simulation.setup_modes()
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
simulation.setup_modes() must always be called after adding mode(s) in order to populate
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
Mz source term, depending on whether
pol is set to
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
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.
- 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
Fdfdobject to be reused later if one has the same
Abut a different
- 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