Do sidebands corresponds to real photons at that frequency?

Say I have a carrier laser (optical) frequency $$\omega_c$$: $$E=E_0 e^{i\omega_c t}$$.

I propagate it through an electro-optical modulator that modulates the phase by $$\beta \sin\Omega t$$: $$E = E_0 e^{i\omega_c t + i\beta \sin(\Omega t)}$$.

If $$\beta \ll 1$$, the field can be expanded into:

$$E \propto e^{i\omega_c t} + e^{i(\omega_c+\Omega) t} + e^{i(\omega_c-\Omega) t} ,$$

where the new $$\omega_c\pm\Omega$$ are the sidebands.

Question:

The laser emits photons at energy $$\hbar\omega_c$$. After the modulation, are there actually photons at energies $$\hbar(\omega_c\pm\Omega)$$?

• If you put the beam into a spectrometer what would you see? Are those not real photons? Commented Oct 18, 2019 at 4:05
• What else could they possibly be? Commented Dec 28, 2019 at 0:36
• I am puzzled by second-harmonic generation devices needing a non-linear effect to generate photons of a different frequency from the incident one. An EOM since to be able to do this too easily. Commented Dec 28, 2019 at 0:42

First of all, I believe the answer to the question in the title is yes, they are real photons. As Jon Custer mentioned, in a spectrometer there would be photons detected at the frequencies $$\omega_c \pm \Omega$$. Moreover, if you make the EOM modulation depth very strong, e.g. $$\beta = 2.405 =$$ a root of first Bessel function, you can completely extinguish the carrier: there are no photons of $$\omega_c$$ left.
The products of creating sidebands usually have very similar energies as the initial photons, essentially no energy has to be added or taken away from the initial photons. Therefore a 'small' non-linearity is enough to prepare them. The EOM does act as a non-linear element, the non-linearity given by the response of a polarising beam splitter on a turning polarisation, which is sinusoidal, that is, non-linear. (You can create sidebands with an EOM operating on the linear slope the sine and then you only get sidebands at $$\pm\Omega$$ but no higher harmonics than that.) Similarly, in an electrical circuit you can simply have the input voltage of a voltage-controlled oscillator (VCO) oscillate and you will get some sidebands at $$n\Omega$$. But the bandwidth of this input voltage is not usually enough to create multiples of the carrier frequency $$\omega_c$$.