Applying directed energy to photons

[Xilor]

What would happen if energy would be applied to a photon in some direction? Since photons always travel at c, it shouldn't change their velocity no matter from what direction the energy would come, but what does applying energy do?
I could imagine that if you applied energy from the front that the photon would lose some of its energy, and that if energy is applied to the back that some energy is given to the photon. But what happens if you apply energy from the sides, does the path of the photon change?

Or is just impossible to apply energy making this a stupid question?

 

[russ_watters]

It is impossible to "apply energy", but that doesn't make it a stupid question. We can ask what can be done to a photon to modify its energy. The answer that will probably be closest to your question is to discuss how a photon acts in a gravitational field:

In General Relativity, gravity is not a force, but a curvature of space. A photon traveling in a straight line in curved space appears to our eyes to take a curved path around massive objects. And if traveling toward or away from a massive object, the photon's energy will increase (toward) or decrease (away) due to what is called gravitational redshift (can also be blueshift, but we don't see that often). And this happens without a change in speed.

So to our eyes, a photon can be accelerated by curving its path, changing its velocity, but it can't have its speed changed (remember, speed and velocity are not the same).

 

[Xilor]

Could this bending possibly be done by energy as well then? Or is this just photons traveling in straight lines, lines which just happen to not appear like straight from our point of view.
Imagine gravity to be applying energy to particles including photons instead of gravity bending, would we still have gravitational lensing?