Plane wave source power of order 10e-14 Watts


Dear Numerical Team,

as I have written in my previous post, I am using FDTD solutions to irradiate the surface to get Electric field, that would be used for further calculations. Could you explain me, please, how can I set an input electric field and/or the source power and intensity? For example, I would like to use a cw laser, power of 200mW.
I know about the possibility to check the source power using following commands:
?"Source power (Watts): "+num2str(sp);
?"Source intensity (Watts/um^2): " + num2str(I1e-12);
?"Ensure Intensity
Area=Power: " + num2str(I*area/sp);
However I do not understand, what they mean. The result power I get is of order 10e-14 Watts . Could you explain their meaning or send a link to the explanation, please?

Thank you in advance!

Best regards,

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Hi @diana.nechepurenko,

In order to interpret the power results from a simulation, there are a couple of things we should discuss.

First, the actual power injected in the FDTD simulation by a plane wave source depends on the amplitude setting, the area of the source and the shape of the injected pulse.

  • Amplitude: For beam sources, such as plane waves, this is the peak electric field amplitude in units of V/m.
  • Area of the source: Wavefronts from plane wave sources are infinite. Therefore, the amount of power carried by a plane wave is not a well-defined quantity: it depends on the area of the plane wave source. As my colleague @bkhanaliloo mentioned in his reply to your earlier post, this is the reason why we use amplitude to define the source. The fact that the wavefronts of a plane wave extend to infinity also means that you should use Bloch/periodic boundaries and the source area will extend all the way to these boundaries. Therefore, the source area will be the same as the area of the simulation region in the plane perpendicular to the injection axis.
  • Pulse shape: In FDTD simulations, a pulse is injected in time-domain (you can see the pulse shape and spectrum in the source settings). This means that not all frequencies have the same amplitude. Therefore, in principle the power will depend on frequency as well.

The frequency dependence due to the pulse shape can be easily removed using the CW normalization. This is the normalization state used by default and it is the easiest to interpret the results for linear simulations because it allows you to find the CW (or impulse) response of the system, i.e. the response as if all frequencies were injected with the same amplitude, independent of the source pulse used to excite the system.

If you want to find out how much power was injected in the simulation (with and without CW normalization) you can use the sourcepower script function. In the CW norm state this will return the power in Watts, which will be essentially flat because of the CW normalization (for more details visit this KB page). This power will still depend on the area of the plane wave source and the amplitude. If you have a periodic structure you will normally simulate one unit cell only, so this will restrict the source area to be the same as the area of the unit cell. You can still change the amplitude setting to modify the sourcepower result; however, in linear simulations it is not necessary to do this as explained next.

You mentioned that you have a CW laser with power of 200mW. Presumably, this is the total power injected by the laser over the laser spot. To relate this power to the results from a simulation with a plane wave source, it is more meaningful to use the source intensity (power per unit area) instead of the net power. Assuming the power is uniform over the laser spot, the source intensity would be the power divided by the spot area.

The transmission results from DFT monitors are normalized to sourcepower (in both CW norm and no norm states); in other words, the transmission is a fraction of the power injected by the source. Thus, if you want to find the transmitted intensity in the experiment you simply need to multiply the normalized transmission by the laser intensity. Then you can multiply by area to get power; for example, if you multiply by the spot are you get the total transmitted power, or if you multiply by the area of the unit cell of a periodic structure you get the power transmitted per unit cell.

As you can see, you normally don’t need to tune the amplitude setting. This discussion applies to linear simulations only. In non-linear simulations the amplitude setting is usually very important.

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Thank you very much for the answer!