I am not sure if I understand your question. By doping rate, I think you mean the concentration of impurities. I think one way to think of your problem is to consider that the real part and the imaginary parts of the dielectric function are connected through the Krammer-Kronig relation.  So if you know the real part of the refractive index over a wide spectral range you in a sense should also know the absorption and vice versa. In your case if you are applying fields and can control the free carriers in the material you can be modulating the refractive index. In addition, to the absorptive losses you may also be changing the scattering within the waveguide due to variations in the refractive index due to variations in the concentrations of dopant, or have scattering from geometric considerations like side wall roughness.

Different material - different properties - it is as simple as that.

The more your optical mode overlaps your higher doped regions, the more optical loss you will get (drude scattering), however, higher doping can also soften the voltage of an active device, and hence increase efficiency, so there is a balance there.  Best if the doping profile (shape of doping across waveguide) is designed to be opposite the optical mode, so that at high points in the optical mode, the doping is low and at low points the doping is high, best of both worlds.  Reactors can produce these profiles.

Dear John, I guess you just met the point. Currently I am not sure that my BPM solver (BeamPROP) includes the Drude scattering loss, as all it requires as input is n and k of the materials involved within the waveguide. So, I can consider refraction and attenuation loss, but maybe BeamPROP does not consider the scattering effect of different doped Silicon on the travelling optical wave, besides to the changes it induces on n and k. I just saw that Lumerical can do it, so it is worthy of being tried.

You do not need BPM to figure out the waveguide loss. Just a mode-solver is enough. Since the doping profile is probably not uniform (you'll have p and n doping on the two sides, I assume?), you should divide the waveguide cross-section into areas that represent the different doping levels. Then you can calculate the overlap of the optical mode with these respective areas. Loss as a function of doping levels (p and n are different) is well known, and you can look it up in tables or you can find a more analytical expression, with parameters fitted for silicon.

If you want to be really correct, you can also add the index change as a function of doping, but for high-contrast waveguides like silicon, that shouldn't matter too much. For shallowly etched or buried laser diodes this might be significant, though.

Dear Martijn I really thank you. The doping profile in my slot waveguide is uniform both in the arms and in the strip-loads. I read in similar publications that they use uniform doping, as well, and just say loss to be negligible. Nevertheless, I should demonstrate it. So if I understand, given the profile to be uniform, I just need to consider the impact of the Silicon doping concentration in the values of n and k into the material profile settings, before simulating. I usually use the Rsoft FemSIM, that is a quite generalized Mode Solver.

Thanks again for you precious help.