Question

Dependence of attenuation on the wavelength?

Dependence of LP modes on wavelength?

Answer 1

Attenuation refers to the loss of any kind of flux through a medium. Considering that you are speaking about electromagnetic radiation, i shall proceed.
For electromagnetic radiation, attenuation is generally caused by the incident radiation. EM waves cause the electron clouds of the molecules in the medium to oscillate. Other sources may include scattering due to opaque impurities present. Therefore, all radiation faces attenuation in a medium.
However, if the frequency(thereby wavelength) of the incident light matches for the excitation energy of the electron cloud, there is stronger scaterring due to the process of absorption and emission. In this way, certain wavelengths are attenauated far more than their neighbouring wavelengths in a medium.

For Linearly Polarized modes, there is no dependence on wavelength. However, shorter the wavelength, more the LP modes that can be guided into a optical fibre.