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Once the simulation has been set up, it will look as in the screen shot below. The nanowire is the circle in the center of the simulation region. There are two yellow boxes of monitors which surround the nanowire. In between the two monitor boxes there is a third box with grey lines. This box shows the region of Total-field scattered-field (TFSF) source.

 

TFSF source is a type of plane wave source, mostly used in particle scattering. The pink arrow shows the direction of propagation (k vector), and the blue arrow shows the polarization (E field vector). In the region inside the grey box, the total fields (incident plane wave field + any fields scattered by particle) are calculated. In the outside of TFSF box, only the fields scattered by the particle exist, which are referred to them as "scattered fields".  You can find more information about TFSF sources in the Sources section.

 

Because we use the TFSF source,  the power scattered by the nanowire can be computed by measuring the power flow through a box of monitors located outside of the source (ie. in the scattered field region). The power absorbed by the nanowire is equal to the net transmitted power through the box of monitors in the total field region. In the analysis group the power towards outside of the box is calculated, so the result has a negative sign. The real absorbed power is positive  thus in the script file one can see the extra negative sign.

 

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In the graphical user interface (CAD), orange lines show the FDTD mesh which can be observed by clicking icon_viewmesh (click it again the FDTD mesh will disappear). There are two different regions: A graded mesh region (automatic mesh) and a mesh override region (uniform). When using automatic meshing, the mesh size is based on the refractive index. A higher index material will have a smaller mesh size, inversely proportional to the index. When a material has a complex index, both the real and imaginary parts are considered by the automatic mesh algorithm. However, accurate modeling of small geometric features, particularly when there is a high index contrast between materials combined with curved or angled interfaces, sometimes requires a finer mesh than is created by the automatic mesh algorithm. In these cases, a mesh override region  can be used, as in this example, to manually define a finer mesh (the "mesh" object ) where it is needed, which is uniform.

 

The above screen shot does not show the full simulation region. Although we are not interested in obtaining any data outside of the largest yellow monitor box shown above, the simulation span is set to be much larger. We set the simulation to be larger because the boundaries are PML. PML absorbs incident radiation, but it can reflect evanescent fields. Hence, the PML should be placed far enough away from the structure so that it does not interact with evanescent fields. In this case, the PML is about a full wavelength from the structure. In general, half wavelength is recommended for initial simulations.

 

The Ag (Silver) material used for the nanowire is defined with experimental data (the squares in the figure below), rather than an analytic model.  A material model (solid line in the figure below) is automatically calculated based on the experimental refractive index data over the source bandwidth. We can check the material fit in the Material Explorer before running the simulation.  The material fit, named FDTD model in the legend, can be adjusted by changing the Max coefficients and Tolerance parameters in the Material Explorer. If the solid lines have artificial spikes or the rms is too big, users can modify the fit parameters.

 

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We can see from the above plot that the material data has an index that is on the same order of magnitude as the background index of 1. In particular, from about 340nm, the real part of the refractive index is around 0.2. This will need much finer mesh. Thus we set the fine mesh size to 1nm. In addition, the real part of the permittivity (one can choose "permittivity" in "vertical axis") is smaller than 1, we can change the mesh refinement option to "conformal variant 1" to take full advantage of the conformal meshing feature. Note that "conformal variant 1" is a good option here because there is low index contrast, however "conformal variant 1" is not always a good option for metals (the default conformal variant 0 will revert to staircasing for interfaces involving metals and PECs). Please see Mesh refinement and Conformal mesh for more detail.

 

Note that in the screenshot of the simulation above, there is a yellow cross. This cross gives the location of a time domain monitor. Time domain monitors are used in FDTD simulations to check that the fields have decayed by the end of the simulation, or to record the transient signals. If the fields have not properly decayed, the simulation results can be incorrect. By default, FDTD has a simulation time of 1000fs and shuts off the simulations early if the field strength has decayed to a user defined fraction of the peak field intensity (the "auto shutoff min" in FDTD--> Advanced options). Below, you can see a plot of the x component of the E field. Notice that the simulation shuts off early at 32fs.

 

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Results

Scattering, absorption and extinction cross-sections can be computed analytically for the nanowire. We have precalculated the theoretical result for this specific material and saved it in the associated file, nanowire_theory.csv, from the first page of this getting started example. In the script of the analysis groups, the transmission of each monitor is first calculated through transmission function. The total power is the product of total transmission out of the box  and the source power by use of the sourcepower function.  

 

Below, the leftmost figure shows the cross-sections obtained from the FDTD simulation in comparison with the analytic results.  Clearly there is very good agreement (we used much finer mesh size than the auto-graded mesh of about 20nm in "Mesh Accuracy 2").  The second figure shows the same results from FDTD, but analytic results for a radius of 24 and 26 nm.  Since the simulation used a 1nm mesh, it is reasonable to expect the FDTD results to be accurate within these results. We can see from the figure that this is true.

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The above image shows that the maximum extinction occurs near 345nm. To show the field profile at this wavelength, the profile monitor is added and set to record this wavelength. Also the mesh size is modified to be 0.5nm to give more accurate result. After re-run the simulation, we can plot |Ey|^2 at z=0 as shown in the image below.

 

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You may notice that the cross-section results do not change if we use mesh size of 1nm. Therefore, if you are only interested in the cross sections, it is not necessary to use a finer mesh.

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