Wireless Power transmission. Is it possible to achieve 100-200w (load side) power using off-the shelf components?
Here's an answer that takes you some distance in understanding some of the physics and the problems. What you want sounds a lot like how a transformer works but without the magnetic core shared by the primary and secondary windings. For a regular transformer you can easily get power transfer efficiencies greater than 95% but without a core you start to hit problems.
The main problem is that the alternating magnetic flux produced by the driven coil only loosely couples with the receiving coil. At best, given the scenario described, this might be 30%. With only 30% of the flux received, the receiver has to have 3 times as many turns to get a 1:1 voltage transfer. That's a voltage transfer and not a power transfer.
When you have a load connected that takes significant current, that field starts to reduce - the current in the receive coil produces a counteracting field. This then reduces the net field and voltage drops. More load current means more voltage reductions.
To counter this, designers use resonance. Resonating the primary transmit winding with a capacitor means that the nature of the current flowing in the primary is massively increased (maybe ten or twenty fold). Because there is more current there is more magnetic flux proportionately.
To get 100 watts across a gap probably means a current in the several tens of amps RMS and this starts to mean you need to use Litz wire (easy to use and very neat but rather expensive).
It also means you need a fairly stable high frequency power oscillator that is capable of shoving out 100 watts plus all the power lost. This might be in the realm of 200 to 300 watts. Without a load on the receiver that's not a big deal but you have to be wary of producing emissions that can effect other local pieces of electronics.
All in all it's a problematic job for someone experienced in electronics and magnetics. I could probably crack it after a few months (and I have patents in this sort of AC magnetic technology) but it might take you a year or so or even longer.