In fact, electrical current can be transferred via electromagnetic radiation. See for instance here: Article Design of an efficient ambient WiFi energy harvesting system
Difficulties lie in rectifying the small induced voltages with high frequencies, but definitely possible. There are even works to rectify voltages from tiny visible-light antennae.
Perhaps the issue is the way you phrased the question. Energy can be transmitted by all forms of electromagnetic radiation, of which visible light is one example.
Electricity is usually taken to be the flow of electrons (AC currents make this a little counter-intuitive, but still true). But electromagnetic radiation does not involve the movement of electrons from its source outward. The generation of electromagnetic radiation involves charged particles, as does it reception.
Moving charges can produce an electromagnetic wave (say in your WiFi transmitter) the wave travels and stimulates the movement of charges (say in your wifi receiver). However the electrons are not moving from the transmitting antenna to the receiving antenna. Energy however is transmitted.
Alexander Dräbenstedt : The visible light antennae you mentioned seem very interesting to me. Could you please, if possible, give a link to a publication on these? Thanks in advance!
One comment I can make is that 5 watts of energy between 300 MHz and 3 Ghz is enough to blind you, and you wouldn't put your head in a 800W microwave oven. Therfore, be very careful in considering power transmission my electro-magnetic means. Also consider transformer and antenna effects and losses. The gaop you transmit over needs to be small, otherwise you lose a lot of power due to absorption in the atmosphere, from geometrical divergence, and losses by eddy currents and hysteresis in magnetic fields. The reason we are not already doing this is that its difficult and dangerous. Be extra vigilent, and keep the power down to a minimum.
The electrical energy could be transmitted in form of electric current in conductors and in form of electromagnetic waves. It is so, the electrical energy can be converted into electromagnetic radiation by antennas or by light emitting diodes. The most suitable form for transmission is to concentrate the radiation into narrow beams such that one can transfer them from point to point less dispersion in the space. May be the most suitable radiation frequency is the micorwave frequencies where one can use prabolic antennas.
So, as one has to use micorwave frequencies, one has to convert the electrical power in sinusoidal waves at such frequency range using microwave oscillators.
In the receiver one has to convert the power received at microwave frequency into the the suitable electricity form either DC or AC, 50Hz.
So, AS one sees it is an indirect way to transmit electrical power which cost some losses and set up costs. The other problem is the confinement of the electromagnetic wave in a specific path since radiation is diverging in space.
Since the waves are transmitted in open space, they may be dangerous to the creatures when intercepting them.
The most staight forward method to transmit electricity is by means of conducting wires. In this way the paths of the electricity is confined to the conductors and thereby very controlled and safe where one cover these wires by insulating sheath.
In case of transmitting electricity via EM radiation one transmit them in air and space and thereby there no transmission medium cost.
In fact in electrical communication one uses the metallic conductors and the EM radiation to convey the electrical communication signals.