  # Soft sources

“Soft” sources create radiation that is added to the existing electromagnetic fields without causing scattering of any radiation that is incident upon the source. “Hard” sources force the electromagnetic fields to have a pre-defined value at certain points in the simulation, and therefore have the potential to scatter incident radiation.

All sources in FDTD Solutions/MODE Solutions’ propagator, including dipole sources, are “soft” sources

#### Solvers

FDTD
VarFDTD The total electromagnetic fields in a simulation with multiple sources is given by the coherent sum of the field due to each individual source. Therefore, it is equivalent to calculate the total field by:

• directly simulating the entire system by including all sources in a single simulation

• run one simulation per source, then coherently sum the fields from each simulation
$$\mathbf{E_{total}} =\mathbf{E_{s_1+s_2}=\mathbf{E_{s1}}+\mathbf{E_{s2}}}$$

To see an example that shows these two techniques are equivalent, see the FDTD and coherence - Incoherent dipole page. This examples calculates the interference pattern between two dipoles. A screenshot of the coherent interference pattern of the two dipoles from this example is shown above. This field profile can be obtained from a single simulation with two sources, or the coherent sum of two simulations that had one source each.

For the purposes of showing that the above techniques are equivalent, we are only interested in the coherent interference patterns from this example. The incoherent sum of the fields is not relevant to understanding this point.

##### Note: Radiated power and coherence

The amount of power radiated by a set of coherent dipoles will be different that a set of incoherent dipoles. For more information, see this link:
Radiated power from multiple dipoles

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