Sources- Dipoles: Multiple sources

The amount of power radiated by a source depends on the surrounding fields. Therefore, when there are multiple sources in a simulations, or when radiation from the source can re-interfere with itself, the amount of power radiated by the source will change. An example of a source interfering with itself is provided on the previous page. On this page, we consider how interference between two dipole sources affects the total radiated power.

Solvers: FDTD, varFDTD
See also
Sources
FDTD and coherence
Incoherent dipole

This example has two dipole spaced half a wavelength apart. The script will calculate the power radiated by the two dipole system and compare it to the power each dipole would radiate by itself. The script uses a few techniques to measure the radiated power. To reproduce these results, open the simulation file and then run the script.

The script runs three simulations:

  • source s1 and s2
  • source s1 only
  • source s2 only

For each simulation, we calculate the radiated power in three ways:

  • Net power flow through a box of monitors surrounding the dipoles
  • Dipolepower function
  • Sourcepower function

The results of the script are shown below.

s1 and s2 in single simulation (coherent)

  • Power box method: 1.38 fW
  • Dipolepower method: 1.39 fW
  • Sourcepower method: 2 fW

s1 only simulation

  • Power box method: 0.98 fW
  • Dipolepower method: 0.99 fW
  • Sourcepower method: 1 fW

s2 only simulation

  • Power box method: 0.98 fW
  • Dipolepower method: 0.99 fW
  • Sourcepower method: 1 fW

There are a couple of important points to notice. First, all three techniques agree that a single dipole radiates 1fW of power.

For the simulation with two sources, the three techniques do not agree. The Power box and Dipolepower methods report a total radiated power of 1.4 fW while the Sourcepower reports 2 fW. The correct answer is 1.4 fW. Interference between the two sources mean the total radiated power is not simply the sum of what each dipole would radiate by itself. The Power box and Dipolepower methods correctly take this interference into account. The Sourcepower method is not correct because it simply reports the sum of what each source would radiated by itself.

Therefore, when calculating the total power radiated by sources in simulations with multiple sources, you should use the Power box or Dipolepower methods.

Note: Physical interpretation of interference changing the amount of radiated power
It is interesting to consider why the power radiated by a dipole is different when a field is incident upon the dipole. In FDTD solutions/Propagator, the dipole moment is a pre-defined function of time (p(t)) and therefore frequency (p(ω)). If we consider the dipole as an infinitely small antenna, the current is proportional the dipole moment. The power required to drive the dipole, which is equal to the power radiated by the dipole, is given by the product of the current, I, and the voltage, V. The incident electric field modifies the voltage across the dipole and therefore the power required to drive the dipole.

Note: Beam sources
As described above, the amount of power radiated by a source can change due to interference with another source, or when it interferes with itself. This is usually only relevant for dipole sources, but in principle it can occur with all types of sources in a simulation. It is not very important for beam sources because these simulations are usually setup so this interference does not occur.

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