As noted in the last section, the actual power emitted by a dipole is highly dependant on the surrounding materials, and can vary significantly from the analytic formula for a dipole in a homogeneous material. This section looks at a specific example of a dipole near a metal wall. In these cases, the CW normalization option will not work correctly because it will normalize data to the analytic formula, rather than the actual power emitted. For accurate power normalization, we must normalize results using the dipolepower function (actual radiated power) rather than the standard sourcepower function (analytic power radiated in a homogeneous material).
Normalizing a dipole near a metal wall
In LEDs and OLEDs, the dipoles typically radiate near a metal wall. It is worthwhile to consider power normalization calculations near metal walls.
Open the file usr_dipole_power_metal1.fsp. This structure we are modeling is shown in the following screenshot.
All boundaries are PML, except for the lower z boundary, which is set to metal. There is a single dipole source in the simulation volume. Run the simulation, then paste the following script commands into the script prompt to create the following figures.
power2=dipolepower(f, "real_source"); # actual power radiated by the dipole
legend("Analytic power radiated in homogeneous material",
"Actual power radiated by dipole near metal wall");
plot(c/f*1e6,power2/power1,"wavelength (um)","normalized power");
When the simulation is done, run the script the above commands. They will calculate the total power radiated by the dipole, normalized to the analytic expression for the power radiated by this dipole in a homogeneous material. You'll see the following result shown in the following figure.
You can see that the radiated power is significantly different than the same dipole in free space. To understand these results, we can consider the equivalent problem to the metal wall. Let’s look at the problem using the method of image charges. The metal wall can be replaced by a dipole with the appropriate orientation at an equal distance behind where the original metal wall was, as shown below:
To simulate this system, load the file usr_dipole_power_metal2.fsp. It is setup with an image charge in place of the metal wall. The lower z boundary has been extended, and set to use PML. The dipole source is appropriately positioned. After running the simulation, paste the same script code into the script prompt again. Notice that the figures are exactly the same as the first simulation. In the following figure, the two curves lie on top of one another.
Note: Dipole radiated power
It may seem strange that the total power radiated by the dipole changes when it is near a metal wall, despite the fact that the dipole amplitude is fixed. To understand how this can be, we should realize that a dipole is effectively a small antenna with a fixed current, I. The total radiated power is given by P = I2Rrad, where Rrad is the radiation resistance of the antenna. By placing the antenna in a different location, we can change the radiation resistance and therefore the total radiated power. Energy is conserved however, because the power needed to drive the antenna is different in each case. From the quantum mechanical point of view, which is useful for LEDs, we see that the local density of states is different in free space than it is near a metal wall. This will affect the rate of decay of electron-hole pairs into photons, and can ultimately be used to improve the quantum efficiency.
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. It is not very important for beam sources because these simulations are usually setup so this interference does not occur.
Barnes, W. L. (1998). Fluorescence near interfaces: The role of photonic mode density. Journal of Modern Optics, 45,661-669. DOI: 10.1080/09500349808230614