Learning Forum

[Greg Baethge]

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.nSolvers: FDTD, varFDTDnSee also:nSourcesnFDTD and coherencenIncoherent, unpolarized dipolesnWe are considering here two dipole spaced half a wavelength apart. We can calculate the power radiated by the two dipole system and compare it to the power each dipole would radiate by itself. We will need 3 simulations:nsource s1 and s2 nsource s1 only nsource s2 onlynFor each simulation, we calculate the radiated power in three ways:nNet power flow through a box of monitors surrounding the dipoles nDipolepower function nSourcepower functionnThe results are shown below.ns1 and s2 in single simulation (coherent)nPower box method: 1.38 fWnDipolepower method: 1.39 fWnSourcepower method: 2 fWns1 only simulationnPower box method: 0.98 fWnDipolepower method: 0.99 fWnSourcepower method: 1 fWns2 only simulationnPower box method: 0.98 fWnDipolepower method: 0.99 fWnSourcepower method: 1 fWnThere are a couple of important points to notice. First, all three techniques agree that a single dipole radiates 1fW of power.nFor 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.nTherefore, when calculating the total power radiated by sources in simulations with multiple sources, you should use the Power box or Dipolepower methods.nNote: Physical interpretation of interference changing the amount of radiated powernIt is interesting to consider why the power radiated by a dipole is different when a field is incident upon the dipole. In FDTD, the dipole moment is a pre-defined function of time (p(t)) and therefore frequency (p(?)). 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.nNote: Beam sourcesnAs 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.n