https://github.com/fancompute/fdfdpy
Pure Python implementation of the finite difference frequency domain (FDFD) method for electromagnetics
https://github.com/fancompute/fdfdpy
eigenvalues eigenvectors electromagnetics fdfd finite-difference frequency-domain modal-calculations optics python-fdfd
Last synced: 23 days ago
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Pure Python implementation of the finite difference frequency domain (FDFD) method for electromagnetics
- Host: GitHub
- URL: https://github.com/fancompute/fdfdpy
- Owner: fancompute
- License: mit
- Created: 2018-03-05T21:29:09.000Z (almost 8 years ago)
- Default Branch: master
- Last Pushed: 2018-11-05T22:12:15.000Z (over 7 years ago)
- Last Synced: 2024-08-11T11:26:02.544Z (over 1 year ago)
- Topics: eigenvalues, eigenvectors, electromagnetics, fdfd, finite-difference, frequency-domain, modal-calculations, optics, python-fdfd
- Language: Jupyter Notebook
- Homepage:
- Size: 1.4 MB
- Stars: 53
- Watchers: 6
- Forks: 17
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
# fdfdpy
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
## Installation
python setup.py install
## Examples
See the ipython notebooks in `notebooks`.
## Unit Tests
Some basic tests are included in `tests/`
To run an example test, `tests/test_nonlinear_solvers.py`, either call
python -m unittest tests/test_nonlinear_solvers.py
or
python tests/test_nonlinear_solvers.py
## Structure
### Initialization
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)
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
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
### Plotting
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
#### Whenever
- [ ] 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.