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**Meep** is a free and open-source software package for [electromagnetics](https://en.wikipedia.org/wiki/Electromagnetism) simulation via the [finite-difference time-domain](https://en.wikipedia.org/wiki/Finite-difference_time-domain_method) (**FDTD**) method spanning a broad range of applications.
**Key Features**
- **Free and open-source software** under the [GNU GPL](https://en.wikipedia.org/wiki/GNU_General_Public_License).
- Complete **scriptability** via [Python](Python_Tutorials/Basics), [Scheme](Scheme_Tutorials/Basics), or [C++](C++_Tutorial) APIs.
- Simulation in **1d, 2d, 3d**, and **cylindrical** coordinates.
- Distributed memory [parallelism](Parallel_Meep) on any system supporting [MPI](https://en.wikipedia.org/wiki/MPI).
- Portable to any Unix-like operating system such as [Linux](https://en.wikipedia.org/wiki/Linux), [macOS](https://en.wikipedia.org/wiki/macOS), and [FreeBSD](https://en.wikipedia.org/wiki/FreeBSD).
- **Precompiled binary packages** of official releases via [Conda](Installation.md#conda-packages).
- Variety of arbitrary [material](Materials) types: **anisotropic** electric permittivity ε and magnetic permeability μ, along with **dispersive** ε(ω) and μ(ω) including loss/gain, **nonlinear** (Kerr & Pockels) dielectric and magnetic materials, electric/magnetic **conductivities** σ, **saturable** gain/absorption, and **gyrotropic** media (magneto-optical effects).
- [Materials library](Materials#materials-library) containing predefined broadband, complex refractive indices.
- [Perfectly matched layer](Perfectly_Matched_Layer/) (**PML**) absorbing boundaries as well as **Bloch-periodic** and perfect-conductor boundary conditions.
- Exploitation of [symmetries](Exploiting_Symmetry) to reduce the computation size, including even/odd mirror planes and 90°/180° rotations.
- [Subpixel smoothing](Subpixel_Smoothing.md) for improving accuracy and shape optimization.
- [Custom current sources](Python_Tutorials/Custom_Source.md) with arbitrary time and spatial profile as well as a [mode launcher](Python_Tutorials/Eigenmode_Source.md) for waveguides and planewaves, and [Gaussian beams](Python_User_Interface.md#gaussianbeamsource).
- [Frequency-domain solver](Python_User_Interface.md#frequency-domain-solver) for finding the response to a [continuous-wave](https://en.wikipedia.org/wiki/Continuous_wave) (CW) source as well as a [frequency-domain eigensolver](Python_User_Interface.md#frequency-domain-eigensolver) for finding resonant modes.
- ε/μ and field import/export in the [HDF5](https://en.wikipedia.org/wiki/HDF5) data format.
- [GDSII](Python_User_Interface.md#gdsii-support) file import for planar geometries.
- Field analyses including [discrete-time Fourier transform (DTFT)](Python_User_Interface.md#field-computations), [Poynting flux](Python_Tutorials/Basics.md#transmittance-spectrum-of-a-waveguide-bend), [mode decomposition](Python_Tutorials/Mode_Decomposition.md) (for [S-parameters](Python_Tutorials/GDSII_Import.md#s-parameters-of-a-directional-coupler)), [energy density](Python_User_Interface.md#energy-density-spectra), [near to far transformation](Python_Tutorials/Near_to_Far_Field_Spectra.md), [frequency extraction](Python_Tutorials/Basics.md#modes-of-a-ring-resonator), [local density of states](Python_Tutorials/Local_Density_of_States.md) (LDOS), [modal volume](Python_User_Interface.md#field-computations), [scattering cross section](Python_Tutorials/Basics.md#mie-scattering-of-a-lossless-dielectric-sphere), [Maxwell stress tensor](Python_Tutorials/Optical_Forces.md), [absorbed power density](Python_Tutorials/Basics.md#absorbed-power-density-map-of-a-lossy-cylinder), [arbitrary functions](Field_Functions.md); completely programmable.
- [Adjoint solver](Python_Tutorials/Adjoint_Solver.md) for **inverse design** and **topology optimization**.
- [Visualization routines](Python_User_Interface.md#data-visualization) for the simulation domain involving geometries, fields, boundary layers, sources, and monitors.
Time-Domain Simulation
----------------------
A time-domain electromagnetic simulation simply evolves [Maxwell's equations](https://en.wikipedia.org/wiki/Maxwell's_equations) over time within some finite computational volume, essentially performing a kind of **numerical experiment**. This can be used to calculate a wide variety of useful quantities. Major applications include:
- **Transmittance and Reflectance Spectra** — by Fourier-transforming the response to a short pulse, a single simulation can yield the scattering amplitudes over a broadband spectrum.
- **Resonant Modes and Frequencies** — by analyzing the response of the system to a short pulse, one can extract the frequencies, decay rates, and field patterns of the harmonic modes of lossy and lossless systems including waveguide and cavity modes.
- **Field Patterns** (e.g. Green's functions) — in response to an arbitrary source via a [continuous-wave](https://en.wikipedia.org/wiki/Continuous_wave) (CW) input (fixed-ω).
Meep's scriptable interface makes it possible to combine many sorts of computations along with multi-parameter optimization in sequence or in parallel.
[Tutorial/Basics](Python_Tutorials/Basics.md) provides examples of the various kinds of computations.
Download
--------
The [source repository](https://github.com/NanoComp/meep) is hosted on GitHub. Gzipped tarballs of tagged versions are in [Releases](https://github.com/NanoComp/meep/releases). The release history is in [NEWS](https://github.com/NanoComp/meep/blob/master/NEWS.md). Installation instructions are in [Installation](Installation.md).
Documentation
-------------
For a list of topics, see the left navigation sidebar. For new users, the most important items to review are the [Introduction](Introduction.md), [Tutorial/Basics](Python_Tutorials/Basics.md), and [FAQ](FAQ.md).
This documentation is for the master branch of the [source repository](Download.md#github-source-repository). Note that certain features described in this documentation may therefore be *unavailable* if you are using a [tagged release](https://github.com/NanoComp/meep/releases).
### Discussion Forum
For questions regarding setting up simulations, analyzing results, installation, etc., use the [Discussions](https://github.com/NanoComp/meep/discussions) page on GitHub.
As an additional resource, archives of the [meep-discuss mailing list](https://www.mail-archive.com/meep-discuss@ab-initio.mit.edu/), which is no longer active, are available which include postings from 2006-2021. These archives can also be accessed using a [newsgroup reader](https://en.wikipedia.org/wiki/List_of_Usenet_newsreaders) via the NNTP interface address: `news.gmane.io/gmane.comp.science.electromagnetism.meep.general`.
### Bug Reports and Feature Requests
For bug reports and feature requests, please file a [GitHub issue](https://github.com/NanoComp/meep/issues).
Acknowledgements
----------------
The Meep project is maintained by the developer community on [GitHub](https://github.com/NanoComp/meep). [Acknowledgements](Acknowledgements.md) provides a complete listing of the project contributors.
Support and Feedback
---------------------
If you have questions or problems regarding Meep, you are encouraged to query the [mailing list](https://www.mail-archive.com/meep-discuss@ab-initio.mit.edu/).
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