fdfd_suite

This package contains a comprehensive list of two-dimensional finite-difference frequency-domain (FDFD) programs used to simulate how electromagnetic waves interact with various dielectric/metal geometries.

It can efficiently calculate the field patterns in both TE and TM polarizations in the following simulations:

Scattering: Compute how electromagnetic waves scatter off of a dielectric/metal object
Resonator mode: Compute the natural resonating modes and frequencies of a 2D dielectric geometry
Photonic crystal: Compute the modes supported by a periodic structure
Modulator: Compute the steady-state field profile of an active device whose refractive index is modulated in time
Waveguide mode: Compute the modal profile of a waveguide given its 2D cross section geometry

This repository contains the following folders:

class: This folder contains the class definitions for each FDFD simulation. These classes are used to instantiate a particular simulation.
examples: This folder contains a list of examples that set up various types of FDFD simulations. The files can be used as a template for starting your own simulation.
flux: This folder contains the programs for calculating the Poynting flux given a field distribution
helper: This folder contains the helper functions in the FDFD solvers, including assigning permittivity distribution, calculating various finite-difference operators, and so on.
solver: This folder contains the implementations of the FDFD algorithm
vis: This folder contains the visualization programs used for plotting the permittivity distribution, field patterns, and making a movie out of the field patterns.

How to set up a basic simulation

The easiest way to learn how to use this package is to take a look at the sample programs in the example folder. Below is a short tutorial on what you can do with the fdfd_suite.

Add folders to path

First, add all folders to path.

clear, close all; clc; 
addpath('../class', '../flux', '../helper', '../solver', '../vis');

Instantiate a particular solver

Direct solve of an electromagnetic simulation with a source: fdfd = fdfd_solve();
Resonator mode solver: fdfd = fdfd_modes();
Photonic crystal geometry: fdfd = fdfd_blochX_modes();
Spatiotemporal modulation of permittivity: fdfd = fdfd_mf_solve();
Waveguide cross section modes: fdfd = fdfd_wg_modes();

Initialize simulation properties

While most solvers have their unique properties, the properties below are common to almost all solvers and should be initialized first.

fdfd.L0: Length scale. e.g. 1e-6 = microns
fdfd.wvlen0: Operating wavelength in units of L0
fdfd.xrange: Simulation domain limit in the x direction in units of L0, [xmin, xmax]
fdfd.yrange: Simulation domain limit in the y direction in units of L0, [ymin, ymax]
fdfd.N: Number of cells, [Nx, Ny]
fdfd.pol: Polarization, either "TE" or "TM"
fdfd.Npml: Number of absorbing layers at the boundaries, i.e. PMLs, [Npmlx, Npmly]

Add permittivity blocks

To add various dielectric or metal structures, use the function

fdfd.add_eps(block_type, block_loc, block_val);

block_val: value of the permittivity.
block_type: choose from 'rect', 'circ', 'poly', 'custom'
- 'rect': Rectangular block. block_loc = [x_min, y_min, x_length, y_length].
- 'circ': Circular block. block_loc = [x_center, y_center, radius].
- 'poly': Polygonal block. block_loc = [vertex1; vertex2; ... vertexN].
- 'custom': Custom block. block_loc = @(x, y) boolean function of coordinates x, y.

Set up the permittivity distribution

Simply call

fdfd.eps_setup();

To visualize the permittivity distribution, run

fdfd.vis_structure();

Set up the source

To add a source to a simulation, use the function fdfd.source_setup(src_type, src_loc, src_params)

src_type: choose from 'point', 'tfsf', 'modal'

src_type = 'point': Point source
- src_loc = [x_coord, y_coord]
- src_params = src_amplitude
src_type = 'tfsf': Total field scattered field source
- src_loc = [x_min, y_min, x_length, y_length];
- src_params = [src_amplitude, src_angle]. Note: src_angle (in degrees) is measured from the lower left corner with respect to the x-axis.
src_type: 'modal': Modal line source for a waveguide
- src_loc = [x_center, y_center];
- src_params = {orientation, mode, num_points};
  - orientation = 'v' for vertical, 'h' for horizontal
  - mode = order of the waveguide mode. e.g. mode = 0 is for either TE0 or TM0 mode
  - num_points = number of points above and below the center of the source.

Run the simulation

Call the function

fdfd.simulate();

Upon finishing, the appropriate Ex, Ey, Ez, Hx, Hy, and Hz fields are stored in the fdfd object

Visualize the field patterns

There are three functions for visualization.

fdfd.visreal(field): Visualize the real part of the field
fdfd.visabs(field): Visualize the amplitude of the field
fdfd.moviereal(field, Ncycle, Nfpc): Create a movie of with the field.
- Ncycle: (Optional) number of cycles of the movie
- Nfpc: (Optional) number of frames per cycle

Poynting vector

The "poynting(obj)" function can be used to calculate the Poynting vector density of the simulation domain. After a simulation is completed, you can call the following function to compute the Poynting vector of the simulation domain.

[Sx, Sy] = poynting(fdfd);

Specialized simulations

For more specialized simulations (spatiotemporal modulation, photonic crystal band structure, etc), please refer to the examples folder to see how the simulations are set up.

Please let me know if you have questions!

Also, if you would like to have additional functionalities for your simulations, I'd be happy to discuss with you to see what I can do.

-Jerry, 2/19/2018

YuJerryShi / fdfd_suite