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 Tg is given by the product of the propagation distance z by the first
frequency-derivative of the propagation constant:

Optical Fiber - equation 10

where n is the refractive index, λ = 2πc / ω,k= 2π/λ

We have:

Optical Fiber - equation 11

The dispersion coefficient D is defined as:

Optical Fiber - equation 12

In bulk materials, we have:

Optical Fiber - equation 13

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:

Optical Fiber - equation 14

where the confinement factor of each layer is Γi. 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 Neff of the fiber mode. First, the mode solver calculates the relation
between Neff and wavelength λ, then the waveguide dispersion is calculated by:

Optical Fiber - equation 15

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 Neff . The total dispersion of a fiber is:

Optical Fiber - equation 16