it is known that starting from the Maxwell equations it is possible to get the following Helmholtz equations:
In time domain it corresponds to a sinusoidal EM field, according to the wave equation:
Now my question is: is the time - behaviour of E/H always sinusoidal? It seems quite strange to me: I did not see any assumption of sinusoidal behaviour of current/charge sources. From this result it seems to me that sources can have any time - behaviour (also constant) and there will be a sine EM wave in time. I think I have missed some part of the reasoning.