Chromatic dispersion a linear or a non linear impairment ?

Let us understand under what scenarios can CD become non linear impairment .Let us take an example of Intensity modulation direction detection receiver wherein as we know intensity(amplitude) is being modulation which follows square law detection .The effect on the electric field is linear in the frequency domain because the phase shift applied to each frequency component is proportional to the frequency's deviation from the center frequency, which means that signal distortions now depend on the square of the field. This results in nonlinear interference between different frequency components.

Chromatic dispersion is a linear impairment in coherent detection so does that mean the square law detection doesnt hold true here no the photodetector sees both the signal and LO fields. The output is proportional to the total field's intensity, which contains the interference term . This interference allows the photodetector to produce a current that is linearly proportional to the received signal field amplitude, rather than its square. Just remember the following :-

Photocurrent(t)∝E(Signal)+E(Local oscillator)

Whereas in IM-DD

Photocurrent(t)∝|E(Signal)|^2

So to conclude if we are using IM-DD CD becomes a non linear component while in coherent detection its a linear component