This section discusses how to obtain and understand the vector field components and polarization of far-field projections.
[[Note]]: The descriptions and examples of the far-field projection calculation on this page are primarily intended for users of FDTD. For users interested in calculating far-field projections with MODE, these descriptions are basically still correct, although some subtle differences do exist.
For some far-field projections, it is important to calculate the vectorial components of the electric field in order to determine the polarization properties. In this section, we will focus on the script commands farfieldvector3d and farfieldpolar3d. The concepts dealt with here can also be applied to the two-dimensional commands farfieldvector2d and farfieldpolar2d . We will continue to study the far-field example file described in Simple example.
[[Note]]: The descriptions and examples of the far-field projection calculation on this page are primarily intended for users of FDTD. For users interested in calculating far-field projections with MODE, these descriptions are basically still correct, although some subtle differences do exist.
These commands return three complex components of the electromagnetic field. All the properties of the polarization of the field can be determined from the amplitudes and phases of these components.
The difference between farfieldvector3d and farfieldpolar3d is the coordinate system for defining the components of the electric field. farfieldvector3d uses a cartesian coordinate system and farfieldpolar3d uses a spherical coordinate system.
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The script file performs a projection in both coordinate systems. The results are shown below.
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farfieldvector3d |
farfieldpolar3d |
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Ex  |
Er  |
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Ey  |
Etheta  |
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Ez  |
Ephi  |
The results in spherical coordinates are the easiest to interpret. Er is 15 orders of magnitude smaller than the other components. We expect that Er should be zero because in the far field the electric field is perpendicular to the direction of propagation. The small non-zero terms are due to numerical rounding error on double precision numbers. The polarization of the original source is P polarized. Therefore we expect that at the center of the beam, Ephi is zero and this is clearly the case on the image plots above. Due to the diffraction of the gaussian beam Ephi is non zero when the azimuthal angle is different than 15 degrees.
To see the effect of changing to S polarization, modify the property "polarization angle" to 90 degrees from 0, see the polarization angle definition.
After re-running the FDTD Simulation, run the script file again. A comparison of the two source polarizations is shown below. We can see the expected result that at the beam center there is only an Etheta component when the source is P polarized, but only an Ephi component when the source is S polarized.
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P-polarized source (polarization angle = 0 degree) |
S polarized source (polarization angle = 90 degree) |
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Etheta  |
Etheta  |
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Ephi  |
Ephi  |