## Material dispersion of the bulk glasses

If the refractive index of the fiber material varies with wavelength, thus causing the

group velocity to vary, it is classified as material dispersion.

The group delay *T _{g}* is given by the product of the propagation distance z by the first

frequency-derivative of the propagation constant:

where n is the refractive index, λ = 2π*c / ω,k _{0 }= 2π/λ*

We have:

The dispersion coefficient D is defined as:

In bulk materials, we have:

## Material dispersion of the fiber

In a fiber, the materials of core and cladding are different. If there are L layers in the

fiber cross-section, each layer has different refractive index.

The total material dispersion of a fiber is calculated by:

where the confinement factor of each layer is Γ_{i}. The confinement factor is the

portion of total power guided in the i-th layer.

## Waveguide dispersion of the fiber

Waveguide dispersion is the result of the wavelength-dependence of the effective

refractive index *N _{eff}* of the fiber mode. First, the mode solver calculates the relation

between

*N*and wavelength λ, then the waveguide dispersion is calculated by:

_{eff }## Total dispersion of the fiber

The total dispersion is the total effect of material and waveguide dispersion. It is

calculated in a similar way as for calculating waveguide dispersion. In this case, the

fiber refractive index profile depends on the wavelength. The material dispersion

effect should be calculated first. Then the mode solver calculates the mode effective

index *N _{eff }*. The total dispersion of a fiber is: