epilot said:
but if we could find how we can amplify these small signals
There's no such thing as an 'amplifier', they don't actually 'amplify' anything - all they do is make a larger copy by modulating the power supply.
Think of it as a photo-copier! - you can 'amplify' your small picture, but you have to ptovide the larger paper, the toner, and the electricity to run the copier.
You can certainly charge batteries via RF, but the inverse square law applies - to do it over 100m you could blast high power out of a highly directional arial, and use a similar highly directional aerial at the receiver to feed a rectifier and charge the batteries. However, it's not very efficient, and you're likely to fry anyone walking inbetween :lol: