How does optical phase modulation produce photons with different frequencies? The classical description of electro-optic modulators is an index of refraction that depends on the applied voltage. For example, for a sine modulation $\sin(\Omega t)$, a monochromatic laser of frequency $\omega$ would get an additionnal phase $\varphi\propto\sin(\Omega t)$. This results in sidebands in the spectrum at $\omega-\Omega$ and $\omega+\Omega$.
Now, what is the interpretation of this phenomenon in terms of photons? A photon with initial frequency $\omega$ will end up at $\omega-\Omega$ or $\omega+\Omega$. How can the time-variation of the refractive index create new photon frequencies? Is it a non-linear effect similar to second-harmonic generation? If yes, it could be explained by an interaction such as $\hbar\omega + \hbar\omega \rightarrow \hbar (\omega-\Omega ) + \hbar(\omega+\Omega)$?
EDIT:
A corollary to the original question.
I shake my hand very fast in front of a laser beam, what happens to the photons? Do they get chopped in shorter photons? Instead of my hands, I could use a super-fast chopper. I would see photons with new frequencies (the sidebands) because of this modulation. How come the incident photons get a different energy?
 A: A photon is an elementary particle , a building block of the Standard Model. Elementary particles follow quantum mechanics and not classical physics trajectories, once one has been able to isolate one of them and follow it course.
A light beam which optics works with, microscopically emerges from the congruence of zillions of photons, each moving at the velocity of light and with point dimensions within the Heisenberg uncertainty principle, HUP. An individual photon cannot be chopped, it is either there or it is not. Lubos Motl, who contributes here, has an article in his blog on how classical electromagnetic fields emerge out of an ensemble of photons. One could in principle use similar mathematics for any kind of light beam but it would be as stupid as digging a well with a surgical knife. Classical EM works beautifully and QM is necessary only when paradoxes and anomalies appear, to explain them.
So the photon manifestation is not useful for your observation except to explain changes in frequency on the elementary particle level. These can happen:
1) within the HUP, but due to the smallness of h would not be observable macroscopically
2) to interactions at the quantum level that again build up from the ensemble a coherent light beam.
If one is ambitious enough one should examine the collective atomic/molecular field that induces the change in the index of refraction, the generic higher order Van der Waals fields, and consider the interactions: compton scattering with the field; or excitation from a low to a higher energy level in the induced spectrum of the WdW field, and subsequent decay to a lower level than initial, etc . 
That is how interactions work at the micro elementary particle level. That a change in frequency has been seen means an interaction, that a coherent beam emerges means that there is a coherent mechanism in the medium that allows for the rebuild/emergence of a different frequency beam.

Do they get chopped in shorter photons?

Absolutely not. The photon is there and interacts in the detector, or not. It is an elementary particle. You can chop beams because no matter how fast you try to chop them they are composed of zillions of photons. Can you chop water down the stream and consider you are chopping individual molecules?
For edification of readers of this, there exist experiments where photons appear individually one by one building up the two slit experiments showing the interference slowly emerging. The smallest chop of a beam is a photon at a time. 
A: One mathematical approach (which I personally don't like because it doesn't say whats physically  going on) involves looking at the electric field of the beam.  This is the Fourier transform of the spectrum of the beam, so for a monochromatic beam with angular frequency = $\omega$
$E(x,t) = A\cos\left(kx - \omega t\right)$

After applying a sine-wave chopper at angular frequency $\gamma$:
$E(x,t) = A\cos(kx - \omega t)cos(\gamma t)$
Use the convolution theorem to transform this to a spectrum without picking up your pencil:
Two frequencies active now: $\omega \pm \gamma $

For a square-wave* chopper:
$E(x,t) = A\cos(kx - \omega t)\,\textrm{square}(\gamma t)$
Spectrum contains many components now (centered on a maximum at $\omega$), since the spectrum of a perfect* square wave has infinite terms.
* I put an asterisk on square-wave, since it must be slightly round at the corners rather than perfectly square.  The reason for this is that if the chopper could switch from transparent to opaque instantly across the whole beam, then special relativity would scream at you since information (chopper on/off) would be moving faster than light.
I had quite a discussion with a professor at Oxford about a problem similar to this, and I'm currently working with a friend on a more "real-world" explanation and understanding of fast choppers.  I'll type up some more detail another day when I'm more awake.
A: Yes, it is similar to second harmonic generation, or more generally, three-wave mixing.
The e-o modulation can be thought of as a low-frequency polariton.  The incident photon is destroyed, and a new photon is emitted with slightly more or less energy, along with the destruction or creation of a quantum of the polariton field.
A: The photons generated in a laser optical cavity have frequencies imposed by the cavity resonances. 
Thus, when changing the refractive index in the cavity the cavity resonances change and the generated
photons have different frequencies. Once generated the photons do not change frequency but the 
cavity refractive index change induces the change of the frequency of generated photons.
