The MIT Photonic-Bands (MPB) package is a free program for computing the band structures (dispersion relations) and electromagnetic modes of periodic dielectric structures, on both serial and parallel computers.
This program computes definite-frequency eigenstates (harmonic modes) of Maxwell's equations in periodic dielectric structures for arbitrary wavevectors, using fully-vectorial and three-dimensional methods. It is especially designed for the study of photonic crystals (a.k.a. photonic band-gap materials), but is also applicable to many other problems in optics, such as waveguides and resonator systems. (For example, it can solve for the modes of waveguides with arbitrary cross-sections.)
As complementary Meep package works for time-domain simulations, reflection/transmission spectra, etc. (MPB is frequency-domain; Meep is Time-domain.)
There are two common computational approaches to studying dielectric structures such as photonic crystals: frequency-domain and time-domain.
Meep (or MEEP) is a free finite-difference time-domain (FDTD) simulation software package developed at MIT to model electromagnetic systems, along with our MPB eigenmode package. Its features include:
Time-domain methods are well-suited to computing things that involve evolution of the fields, such as transmission and resonance decay-time calculations. They can also be used to calculate band structures and for finding resonant modes, by looking for peaks in the Fourier transform of the system response to some input. The main advantage of this is that you get all the frequencies (peaks) at once from a calculation involving propagation of a single field. There are several disadvantages to this technique, however. First, it is hard to be confident that you have found all of the states—you may have coupled weakly to some state by accident, or two states may be close in frequency and appear as a single peak; this is especially problematic in higher-order resonant-cavity and waveguide calculations. Second, in the Fourier transform, the frequency resolution is inversely related to the simulation time; to get 10 times the resolution you must run your simulation 10 times as long (although matters are improved by using more sophisticated signal-processing methods such as Harminv's). Third, the time-step size must be proportional to the spatial-grid size for numerical stability; thus, if you double the spatial resolution, you must double the number of time steps (the length of your simulation), even if you are looking at states with the same frequency as before. Fourth, you only get the frequencies of the states; to get the eigenstates themselves (so that you can see what the modes look like and do calculations with them), you must run the simulation again, once for each state that you want, and for a time inversely proportional to the frequency-spacing between adjacent states (i.e. a long time for closely-spaced states).
This program computes definite-frequency eigenstates (harmonic modes) of Maxwell's equations in periodic dielectric structures for arbitrary wavevectors, using fully-vectorial and three-dimensional methods. It is especially designed for the study of photonic crystals (a.k.a. photonic band-gap materials), but is also applicable to many other problems in optics, such as waveguides and resonator systems. (For example, it can solve for the modes of waveguides with arbitrary cross-sections.)
As complementary Meep package works for time-domain simulations, reflection/transmission spectra, etc. (MPB is frequency-domain; Meep is Time-domain.)
There are two common computational approaches to studying dielectric structures such as photonic crystals: frequency-domain and time-domain.
Meep (or MEEP) is a free finite-difference time-domain (FDTD) simulation software package developed at MIT to model electromagnetic systems, along with our MPB eigenmode package. Its features include:
Time-domain methods are well-suited to computing things that involve evolution of the fields, such as transmission and resonance decay-time calculations. They can also be used to calculate band structures and for finding resonant modes, by looking for peaks in the Fourier transform of the system response to some input. The main advantage of this is that you get all the frequencies (peaks) at once from a calculation involving propagation of a single field. There are several disadvantages to this technique, however. First, it is hard to be confident that you have found all of the states—you may have coupled weakly to some state by accident, or two states may be close in frequency and appear as a single peak; this is especially problematic in higher-order resonant-cavity and waveguide calculations. Second, in the Fourier transform, the frequency resolution is inversely related to the simulation time; to get 10 times the resolution you must run your simulation 10 times as long (although matters are improved by using more sophisticated signal-processing methods such as Harminv's). Third, the time-step size must be proportional to the spatial-grid size for numerical stability; thus, if you double the spatial resolution, you must double the number of time steps (the length of your simulation), even if you are looking at states with the same frequency as before. Fourth, you only get the frequencies of the states; to get the eigenstates themselves (so that you can see what the modes look like and do calculations with them), you must run the simulation again, once for each state that you want, and for a time inversely proportional to the frequency-spacing between adjacent states (i.e. a long time for closely-spaced states).
- Free software under the GNU GPL.
- Simulation in 1d, 2d, 3d, and cylindrical coordinates.
- Distributed memory parallelism on any system supporting the MPIGNU/Linux is fine). standard. Portable to any Unix-like system (
- Dispersive ε(ω) (including loss/gain) and nonlinear (Kerr & Pockels) materials.
- PML absorbing boundaries and/or perfect conductor and/or Bloch-periodic boundary conditions.
- Exploitation of symmetries to reduce the computation size — even/odd mirror symmetries and 90°/180° rotations.
- Complete scriptability — either via a Scheme scripting front-end (as in libctlMPB), or callable as a C++ library. and
- Field output in the HDF5 standard scientific data format, supported by many visualization tools.
- Arbitrary material and source distributions.
- Field analyses including flux spectra, frequency extraction, and energy integrals; completely programmable.
- Multi-parameter optimization, root-finding, integration, etcetera (via libctl).
A time-domain electromagnetic simulation simply takes Maxwell's equations and evolves them over time within some finite computational region, essentially performing a kind of numerical experiment. This can be used to calculate a wide variety of useful quantities, but major applications include:
- Transmission and reflection spectra — by Fourier-transforming the response to a short pulse, a single simulation can yield the scattering amplitudes over a wide spectrum of frequencies.
- 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 a system (including waveguide and cavity modes, and including losses).
- Field patterns (e.g. Green's functions) in response to an arbitrary source, archetypically a CW (fixed-ω) input.
Using these results, one can then compute many other things, such as the local density of states (from the trace of the Green's function). Meep's scriptable interface makes it possible to combine many sorts of computations (along with multi-parameter optimization etcetera) in sequence or in parallel.
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