Does self-phase modulation generate new frequency components?

Question

Not a physicist. Hope to clarify some conceptual issues I have with non-linear propagation of light through a medium, since I seem to be mixing up some very fundamental concepts. Specifically, I am having some doubts regarding the chirping that occurs during, for example, self phase modulation of a wave propagating through a non-linear medium (or even chromatic dispersion).

Here is my current understanding: since only the index of the material is changing during SPM, I guess there isn't any generation of photons at different frequencies. A linear change in index across a propagating pulse, however, introduces an additional linear phase component such that the frequency is effectively increased/decreased. By the same argument, an added quadratic phase component across the pulse yields a chirp across the pulse.

I am having trouble reconciling these two things. Intuitively, I think it's just a mix-up between frequency and wavelength, but I'd like to make it clear. However, then, if I measure a pulse after propagating through a medium (assuming only SPM) via e.g. heterodyne detection, should I observe new frequency components? Or alternatively, if probed with an optical spectrum analyzer, will the bandwidth increase?

Thanks

Answer 1

Self-phase modulation very much does generate new frequency components. In fact, SPM is one of the leading ways to produce spectral broadening, all the way through to supercontinuum generation.

To be concrete:

Or alternatively, if probed with an optical spectrum analyzer, will the bandwidth increase?

very much so. This is an everyday tool, and an everyday way to benchmark that the tool is working correctly.

So, where's the problem?

since only the index of the material is changing during SPM, I guess there isn't any generation of photons at different frequencies.

This line of argument doesn't really work. If you want to work on a photon picture, then the core process is that two photons at the original frequency $\omega_0$ are "absorbed", and immediately re-emitted as two photons of frequency $\omega_0 \pm \delta\omega$, with $\delta\omega$ covering a small continuum. (This process is then repeated over and over as the pulse propagates through the material.)

However, that said, this photon picture is tricky to work with and to pin down correctly -- not least because SPM only works for a pulse with a nonzero original bandwidth. It's generally much better to stick to the time-domain view, where the dynamics are much clearer.