Divergence in radiation fields: Three paradoxes: Toward highly focused neuron stimulation for neurology and HCI

Three thought experiments demonstrate that under certain circumstances radiation fields have to be attenuated or amplified by means other than superposition in order not to violate the conservation of energy. At least one of them provides a basis for verification by real experiments. Multiplicative modulation of radiation is theoretically made possible by inserting additional terms into the source slots of the Maxwell equations. Low frequency components in modulated UWB radiation would enable the well focused stimulation of neurons for diagnostic and therapeutic purposes as well as for information transfer in human computer interfaces.