I want to optimize the different parameters to limit the dispersion in the optical fiber, which objective function to use according to these parameters, and the initial dispersion in order to estimate the error, thank you in advance
Broadly speaking, there are two types (or origins) of dispersion in a waveguide such as an optical fibre. First, that due to the properties of the material (e.g. silica); and second that due to the geometry of the waveguide itself. Often it is the geometric (spatial structure) part that we can fine tune the most, and can even try to balance or counteract the material dispersion.
If you are hoping for a more detailed answer from anyone here, you need to better specify the problem you are trying to solve.
Thank you very much for your conclusive answer; in reality I designate the materialchromatic dispersion D=f(lynda) , How to optimse the main parameters of the optical fiber in ordre to minise entierly the dispersion, thank you for your kind attention.
The principle of minimising the dispersion is basic textbook stuff. I recall that I saw it in "Fiber optics essentials" by Thyagarajan & Ghatak (Wiley, 2007), but I would think any text with similar coverage would do.
The idea is that if (e.g.) at the frequency (or wavelength) of interest, the material dispersion is positive; then you engineer the structure to have a negative dispersion of the same magnitude at that same frequency (wavelength); and so the two contributions to the dispersion basically cancel out.