Hi. I am new to chromatic dispersion related work and have read how it affects the shape of optical pulses. I want to ask how does it work for analog continous wave laser signal? why all books only mention laser pulses and pulse broadening of digital signals. what about using analog CW laser and modulating analog IF signals on it. How will CD affect it through pulse broadening . . . secondly, books mention that CD is a linear process. Is it because the pulse broadening factor equation has only L (not L square?) because the GVD equation contains lambda square (square of wavelength or frequency). how is it a linear process then? thanks a lot
Dear @Amir,
In case of analog modulation, the dispersion is caused by the variation of the refractive index with the wavelength of the LASER beam. In the analog modulation if the bandwidth of the signal is small, it can be considered that refractive index is consatnt and the variation is negligible, then the dispersion can be neglected.
Otherwise the change of the path with the frequency must be considered as phase distortion in the signal. As the range of the frequencies is small then one can approximate the refractive index around the carrier frequency by a linear piece.
Best wishes
Analog signal distortion results from the interaction of signal optical bandwidth with the non-zero slope of dispersion vs wavelength. Thus the signal distortion is a change in phase from the instantaneous frequency of your analog signal. Since your analog signal has non-zero bandwidth, the optical signal will have non-zero bandwidth (as will the laser source itself) and will experience phase distortion as it travels through fiber with dispersion. (Note that an optical fiber can have a zero cumulative dispersion because you can catenate fiber with positive- and negative-dispersion and get no net dispersion - this is possible because the process is linear and thus reversible. If you are engineering a system with sensitivity to phase distortion, consider this approach.) Your analog signal modulation should be large relative to laser phase noise, so you can pretty easily simulate the resulting signal distortion by shifting the signal phase by the instantaneous frequency times the dispersion at that frequency.
Indeed, the process is linear and reversible as long as the transmitted power stays low or constant, as the fiber index of refraction is also mildly power dependent. If you transmit high powers with wide bandwidths or multiple carriers, then the signals can interact via this nonlinearity, and things get irreversible and complicated very quickly.
As for square-law: This comes from the fact that GVD is a velocity and dispersion is a phase shift - they are two sides of the same coin, you just need to pick which you are computing. The very first paragraph of https://www.rp-photonics.com/group_velocity_dispersion.html shows the derivation.
It is a linear process, because actually it does not affect the spectral content, but only the relative phases between different frequency components. As you surely know, the width in time depends on the spectral shape only if the phase is flat (bandwidth-limited pulse). Otherwise, the pulse shape is affected by the phase and is broadened in time if the spectral phase is not constant.
If you look for "radio over fiber", you will realize that your question still represents an active research subject.
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