How do transmitters convert electrical signals into photon energy?
Moving charged particles back and forth produces electromagnetic waves, just as you can produce waves in water by moving an object back and forth in the water.
A radio transmitter works by applying a changing voltage to the antenna, causing electrical charges in the antenna to move back and forth. These in turn create electromagnetic waves which travel outwards, carrying energy with them.
How can a voltage be applied if it is not a complete circuit?
You need a complete circuit to get current to flow when your circuit is in equilibrium but you don't need a complete circuit to apply a voltage or to get current to flow for a very short time.
Google for "LC oscillator" for a simple example.
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