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?