Wireless Powering Products
It is possible to recharge wirelessly. There are two basic choices available.

1) Incorporate a solar cell into your product. This can provide a small amount of power, as converted from light, to recharge of maintain a battery. This approach would work for distances well over 50cm. Keep in mind that the current available from a small solar cell will be tiny so this method would be best for use when the device itself operates on very low power and has a small battery. One commercial product that you may have seen that uses this approach are LED yard or driveway edge lights that require no wiring.

2) The other method is to use electromagnetic coupling between the charger and the device. This method is not feasible at 50cm and actually requires the device to be brought into contact with the charger source. An example commercial product that uses this approach is an electric tooth brush. The charging stand on these actually has a part that physically pokes into the device as part of the electromagnetic coupling system. This system can be used for devices with a bit larger batteries.

RF coupled systems that attempt to harvest power from the RF field being transmitted are possible to make if your device operates on the most minuscule amount of power. But you need to have the capabilities to design circuits that work with a few nanoamps of current at very low voltages. For 99.999% of applications and designers capabilities this option is just not feasible.