Power normalization with the TFSF source can be slightly confusing, particularly when the data is normalized by the power injected by the source.
This issue is best illustrated with an example. The following screenshots shows a Mie scattering simulation, where a small gold sphere is illuminated by a planewave using the TFSF source. The goal of the simulation is to measure the amount of power absorbed by the particle when it is illuminated by a plane wave.
After running the 3D Mie scattering simulation, it is possible to calculate and normalize the amount of power absorbed by the particle in several slightly different ways. The script usr_TFSF_mie_absorbed_power_script.lsf will reproduce the following figures when applied to the 3D Mie scattering simulation file.
Power in Watts
One option is to calculate the absorption in units of Watts. In this particular simulation, we can see that the particle absorbs about 2.7e-17 W of power at 530nm (for a planewave with an amplitude of 1V/m).
When the data is presented in this form (i.e. power in Watts), the data is straightforward to understand and interpret.
Power normalized to the source power
Alternatively, the data can be normalized to the power injected by the source.
This type of normalization is quite common. For example, the 'transmission' script function automatically normalizes the power transmission data to the source power. While this normalization is often very convenient, it is not well suited to simulations using the TFSF source. The fundamental problem is that an ideal plane wave has infinite power (since it has infinite extent), while a single particle must absorb a finite amount of power. Obviously it is not meaningful to normalize a finite quantity by an infinite one!
To avoid the problem of having infinite source power, we define the source power of the TFSF source as the amount of power injected by the primary injection plane of the source (the plane of the source with the Blue and Pink arrows). It is important to notice that this definition means the source power is proportional to the source size (if the X span of the source is doubled, then the source power will double).
This definition can lead to some non-intuitive results. For example, in the associated figure, notice that the absorbed power at 530nm is greater than 1! This appears to violate power conservation (i.e. the particle absorbed more power than what the source injected). The simulation result is actually correct and does not mean the simulation is violating any conservation laws. Instead, it simply demonstrates that normalizing the data to the source power is not appropriate in this situation.
To understand why the absorption is larger than 1 in this simulation, we can plot the Poynting vector near the nano-particle when it is illuminated by a plane wave (see figure). The Poynting vector shows the direction of power flow near the particle. The nanoparticle outline and TFSF source are also shown. Notice how the nanoparticle affects the poynting vector, causing it to bend in toward the particle. Power is flowing towards the particle through the sides of the TFSF in addition to the primary injection plane. The source power calculation does not include this additional 'side power', which leads to the absorption being larger than the source power.
To reiterate, the simulation results will be correct when the TFSF source is setup as shown in the screenshot. It is capable of correctly simulating the system, even when power is flowing in through the sides of the source. The only issue is that the source power normalization only accounts for the power injected from the primary injection plane, not the sides.
It is worth noting that even if the power measurements are less than 1, this is still not a very useful way to normalize the results, since they depend on the source size. If the source size is doubled, the transmission data will be halved, even though the actual physical quantity (eg the power absorbed by the particle) is independent of the size of the TFSF source.
Normalized to source intensity (cross section units)
As explained above, normalizing power measurements to the source power is not recommended. Instead, it is more meaningful to normalize power measurements to the source intensity (Watts / m^2). This returns the data a cross section, in units of Area.
To apply this normalization, simply divide the absorbed power (Watts) by the source intensity (Watts/m^2) to get the absorption cross section in units of m^2.
It is interesting to notice that at 530nm, the absorption cross section is larger than the geometrical area of the TFSF source, which is why the 'source power normalization' produced values larger than 1. The absorption cross section is also much larger than the geometrical cross section of the nanoparticle.
3D Mie scattering example