Receiving 27MHz wireless power
I don't know how to deal with the transmitter and receiver coil


At 27 MHz, the wavelength is 11 metres so, at a read-distance of 46 cm, you are clearly in the near-field of any radiating antenna. This means that you cannot rely on the far-field advantages of H and E fields reducing linearly with distance.

Apart from that, to make a simple EM radio wave antenna needs some form of dipole and you appear to be opting for a transmit coil. At this frequency, a relatively compact transmit coil won't be able to produce a fully-fledged EM wave so, that looks like a done-deal on defining the field intensity you generate might pick up at some distance.

Here's a picture and some math taken from hyperphysics that describe this: -



The upshot of this is that the magnetic flux density at a point along the centre-line, is inversely proportional distance cubed (when z becomes more significant than R). When R is more significant than z, the flux density falls with distance. This tends to mean that it is preferable to make the coil radius of the same order as the maximum gap distance in order not to suffer from the inverse cube law. 

So how much current can you drive around your transmit coil? The lower you can make the coil inductance, the more current you can pass but, if you are dealing with a 25 watt output that is intended for a 50 ohm antenna then you will likely need to use a step down transformer.

How much can a receive coil expect to generate is dependent on the surface area of the coil i.e. how much flux it "nets". The bigger the surface area the more flux that it "captures" and the bigger the voltage liberated.

So, on the receiver side you should aim for the same type of coil and then parallel or series tune it to liberate the required voltage you need. I don't think you will need to use caps and diodes acting as doublers.

If you go for significantly smaller coils then you will be facing difficulties that are high.