The page provides further information on the correct usage of the TFSF source.
Understanding the TFSF source
The TFSF source is an advanced version of the plane-wave source designed primarily for particle scattering simulations, where the particle may be in a homogeneous medium or on a multi-layer substrate. When adding a TFSF source to a simulation, the most visible difference between the TFSF source and all other sources is that it appears as a 3D box, rather than a 2D plane. As shown in the above figure, one side of the source will be the Injection plane. The source will inject a plane wave from this side of the source. This aspect of the source is very similar to all other sources.
The slightly confusing aspect is that the source will then 'subtract' the same plane wave when it arrives at one of the boundaries of the source. This is much easier to understand with an example. The following screenshots show the behavior of the TFSF source in free space. Notice that the fields are injected at one edge, and are then 'subtracted' at the other edge. Also notice that the fields are zero in the 'Scattered field' region, since there are no scattering objects inside the source. The subtraction happens at the boundaries of the source and a reference 1D line at the top right corner of the TFSF boundary is used to determine the index profile of all the boundaries. For this reason, it is important to make sure the Reference corner (yellow line in the above figure), always goes through the substrate and NOT the feature for which we want to calculate scattering.
Simple example of TFSF with empty space
Simulating empty space is always a good starting point. The second figure shows a movie of Ez(t). The plane wave was injected along the left edge and propagates in the positive X direction. The third figure shows results from a frequency monitor of the CW fields. An intensity of 1 is measured within the TFSF source, while 0 is measured outside. There were no structures to cause any scattering, so the field remained an ideal plane wave inside, with an amplitude of 1. Similarly, the fields are zero in the scattered field region since there were no scattering objects in the simulation.
Orientation of the source with respect to the structure
When adding a TFSF source to your simulation, ensure the following conditions are satisfied:
- The scatterer must be completely inside the TFSF source. The boundaries of the source cannot extend through the scattering object.
- The injection axis of the source must be normal to the substrate. In other words, all sides of the TFSF source must 'see' the same refractive index profile along the direction of propagation. The following figures show one example of a valid setup and one example of an invalid setup.
VALID: The injection axis is normal to the Gold and Glass layers. Also, each side of the source 'sees' the same refractive index profile (Air - Gold - Glass) along the direction of propagation, from the Injection plane to the End plane.
NOT VALID: The injection axis is not normal to the substrate. Also, the upper side of the source 'sees' a refractive index of air, while the lower side 'sees' the substrate index.
Extending through simulation boundaries
In most cases, the TFSF source should not be extended through the simulation boundaries. The only exception is that the TFSF can be extended through Periodic or Bloch boundaries.
VALID: Extending source through PML boundaries
NOT VALID: Extending source through PML boundaries
VALID: Extending source through Periodic boundaries
The TFSF supports the use of non-uniform mesh within the source. However, for best results, the mesh should be uniform in the directions normal to the direction of propagation. For example, if the source is injecting along the z-axis, the x,y mesh should be uniform within the TFSF source. This detail is particularly important when the source angle is non-zero. See the "Particle on a surface at non-normal incidence" section below for more information.
Non-normal angles of incidence
When using non-normal angles of incidence, please take the following precautions
- Remember that the angle of incidence is still wavelength-dependent, as with other beam and plane wave sources. Please see Plane waves - Angled injection for more details.
- For best results, you should use a mesh override region over the entire x, y, and z span of the source so that the mesh is uniform over the source.
- For normalization, please note that the sourceintensity is defined with respect to the principle injection plane of the source. There may be a factor of cos(theta) that needs to be applied to your result. Please see the section Cross sections and normalization.
Tips for testing your setup
The best way to test your setup is to temporarily disable the particle or defect, run your simulation, and perform your subsequent analysis. This will allow you to determine the noise floor and immediately see if something is wrong with your setup. For example, if you are measuring the scattering and absorption cross-section of a particle on a surface, you should expect to find a scattering and absorption cross-sections of 0. In most cases, your defect or particle will have a mesh override region so that the mesh will not change when the defect is disabled. Typically the magnitude of the electric field in the scattered field region without a defect should be approximately 1e-7 when the incidence field amplitude is on the order of 1.
The simulation setup with a TFSF source at a non-normal angle of incidence.
The magnitude of the electric field with the particle disabled on a log scale. Note that the field in the scattered field region is on the order of 1e-7, while the field in the total field region is on the order of 1.
The magnitude of the electric field with the particle enabled on a log scale. We now have confidence that the scattered field (on the order of 1e-3 to 1e-1) is correct and well above the noise floor.
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 show a Mie scattering simulation, where a small gold sphere is illuminated by a plane-wave 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 plane-wave 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 an 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 set up 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.
Power normalization and energy conservation
Power normalization and energy conservation with the TFSF can be non-intuitive. For example, you may find that power transmission measurements depend on the size of the source. It is also possible to find situations where power measurements are greater than 100%. While this may be non-intuitive, it is simply a normalization issue and does not indicate a simulation error. In these situations, it is usually more physically meaningful to normalize to the source intensity, rather than the power injected by the source. See the sourceintensity script function or contact Lumerical support for more information. See the Understanding source normalization in the TFSF source for additional information.
Periodic structures and the TFSF source
The plane wave source is generally the best source for periodic simulations. The TFSF source should only be used in situations where scattering in the specular (zeroeth order) direction is of interest.
The figures below show how the same structure can have different simulation outcomes when simulated using different sources, TFSF source, and plane wave source. TFSF source is used for the top cases, where the plane wave source is used for the bottom cases. The structure simulated is the same, periodic, and the FDTD simulation object employs the periodic boundary conditions, except along the axis of injection. Note that the sources extend through the FDTD simulation regions to avoid diffraction along edges.
TFSF source is used in both cases. The two examples differ in the region of the structure that the TFSF source region and the FDTD simulation object are over. In the left image, the reference corner is going through the substrate, while, in the right image, the reference corner goes through the feature (assuming that the protruding part of the structure is the feature).
The subtraction happens at the boundaries of the source and the reference 1D line, which is at the top right corner of the TFSF source region (marked with the solid yellow line). As the reference corner goes through the simulation structure at different parts in these two example cases, even though the object simulated is exactly the same, the collected result of monitors outside the TFSF source region will differ.
Plane-wave source is used in both cases. Both simulations will return exactly the same data.
Scattering object in free space
This is a typical setup for Mie scattering.
A scattering object (circle with n= 1.5) is located inside the source. Any light scattered from the object will propagate through the source boundary, into the scattered field region.
Movie of Ez(t). We can now see scattering from the circle.
A frequency monitor records the CW fields. The electric field intensity profile is now much more complicated because of scattering from the circle. The TFSF source continues to subtract the ideal plane wave at the edge of the source. Only scattered fields will pass into the region outside the TFSF source.
Multi-layer stack with gap
The TFSF source can be used in systems with substrates and multi-layer stacks. The injection direction does not have to be normal to the surface. Also, you should extend the substrate/stack completely through the source and boundaries.
This example shows a 3 layer stack composed of Air - Gold - Glass, with a small gap in the gold layer. If you are interested in using the TFSF source with substrates or multi-layer stacks, you should first run a simulation without any gaps or scattering object, to ensure you understand the behavior of the TFSF source.
Movie of Ez(t). Notice that most of the reflection from the Gold interface is automatically removed by the injection plane of the source. Only scattering from the gap will pass through the edge of the source.
A frequency monitor records the CW fields. Once again, notice that the reflection from the Gold layer is removed by the source. Only light scattered from the gap will pass through the edge of the source.
Particle on a surface at non-normal incidence
The TFSF source can be used in systems with substrates and multi-layer stacks. This example shows how the source can be used to measure the scattering and absorption cross-sections at non-normal incidence. Please see Cross sections and normalization for details on normalization of the cross-section.
This example shows a gold particle on a surface. Note that the mesh override regions extend completely outside the source region in the x and y directions to ensure that the x and y meshes are uniform over the region of the source. The z mesh can be graded. In this example, the source and the cross-section object "scat" have been increased in size for clarity in the movie but both could be brought inside the uniform mesh override region to save memory. The source is at a nominal angle of 10 degrees, which means that the angle of incidence is actually wavelength-dependent, however, the small change in angles has been ignored in the analysis.
Movie of |E(t)|2. Notice that only the field scattered by the gold particle can be seen in the scattered field region. The light reflected by the silicon substrate is removed.
The scattering and absorption cross-sections can be calculated. A frequency monitor records the CW fields.
The TFSF source supports dispersive (absorbing) materials.
The simulation volume is composed of Silicon. At 600nm, the index of Silicon is approximately n=3.9 + i0.02, which will create substantial absorption as the fields propagate. No scattering object is present.
Movie of Ez(t).
A frequency monitor records the CW fields. Notice that the field intensity decays, due to absorption. Also, notice that the fields outside the source are still zero since there is no scattering object within the source.