Occasionally the results of an FDTD simulation will show normalized transmission values greater than one, which is, in general, incorrect for linear simulations. This article will discuss a few of the more common causes of this issue and how they can be fixed.
Note that while this article specifically addresses transmission values greater than one, the issues discussed here can also be sources of inaccurate transmission results in general. If you suspect that your transmission results are inaccurate, you should consider if these issues are relevant for your simulation.
Simulation Ends Before Autoshutoff
One of the more common causes of this issue is the simulation ending before the light leaves the simulation region. Generally we would like the simulation to end when it reaches the autoshutoff level, which is a measure of the energy left in the simulation region. However, the simulation can also end when the “simulation time” is reached, while there is still a significant amount of energy left in the simulation. This causes artifacts in the transmission spectra which appear as “oscillations” or “ripples” that can increase the transmission to values greater than one. For example, here are the transmission results for a varFDTD ring resonator simulation with different simulation times:
In this plot, the 2500 fs simulation has large ripples in its transmission spectrum. Increasing the simulation time reduces the amplitude of these ripples.
You can see how your simulation is ending by looking at the “Simulation status” result of the FDTD solver object. A result of 1 indicates the simulation ran for the full simulation time, and 2 indicates that the simulation ended by reaching the autoshutoff level. You can also see how the simulation ended by looking at the log file. If your simulation is ending because the simulation time is being reached, increase the simulation time until the simulation is able to reach the autoshutoff level. If the autoshutoff level is reached and the problem persists, you may have to decrease the autoshutoff level as well.
This is generally the most common cause of transmission results greater than one, and is particularly relevant for resonator structures.
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Purcell Enhancement of Dipole Sources
The source power used to normalize transmission results when dipole sources are used is the power emitted by the dipole in a homogeneous environment. The power emitted by the dipole may change if it is placed inside a more complex environment due to the Purcell enhancement. Note that this is not an error, because the actual power emitted by the dipole is changing.
You can renormalize your results using the dipolepower script command, which will return the actual power emitted by the dipole:
transmission("monitor")*sourcepower(f)/dipolepower(f)
Here the sourcepower command returns the power emitted by the dipole in a homogeneous medium (which is used to normalize the transmission results by default) and “f” is a vector of frequencies. Note that in dispersive materials with a non-zero imaginary part of the permittivity or with a very high mesh density, the dipolepower command will return incorrect results, and a box of monitors around the dipole must be used to obtain the power emitted by the dipole.
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Understanding dipoles in non-homogeneous materials
Improper Source Injection
Various errors can occur when sources inject the input pulses into the simulation domain. Scattering can occur at the injection plane, in particular for mode sources, broadband sources or sources at an angle. This can also happen when using an imported source with an electric field profile that does not propagate. This scattering can throw off the power normalization used for the transmission measurements, leading to inaccurate results.
Similar to the Purcell enhancement of dipole sources, if fields are reflected back into the source plane they can interfere with the injection of the source pulse, affecting the transmission result normalization. You can fix this issue by moving the source away from any reflecting surfaces, or adding a monitor in front of the source to measure the actual power emitted by the source and renormalizing your results.
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Optical Sources - Import Source - Physics & Applications
Reflections from PML
Ideally PML boundaries will absorb all light incident upon them. However, this may not always be the case, for various reasons. Light reflected from PML boundaries can cause transmission values greater than one. This can also happen if you are using stabilized PML boundaries, which are less efficient than the standard PML BCs. If you suspect that this may be the cause of error in your simulation, increase the number of layers in the PML boundaries. If your simulation is periodic or you are using a source with a high angle of injection, use the steep angle PML profile for your boundaries.
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PML boundary conditions in FDTD and MODE
Materials With Gain
If the materials in your simulation have gain, this can increase the power in the simulation and cause the power transmitted through the monitors to be greater than one. If you don’t intend to have materials with gain, check the material fits in the Material Explorer to make sure your materials do not have gain.
Note that gain outside the bandwidth of the simulation can still affect the simulation. When checking the material fits for gain, you should extend the frequency range of the plotted fits beyond the simulation bandwidth.
TFSF Source Normalization
The TFSF source normalization works differently than the other sources, which can result in transmission results greater than one. Note that this is not necessarily an error, however typically cross-section results are used with TFSF sources rather than results normalized to the source power.
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Tips and best practices when using the FDTD TFSF source