# Waveguide Dispersion

Greeting.
I am currently investigating the dispersion properties of waveguides.

The dispersion of an optical fiber is usually mostly contributed to by the material dispersion.
Ignoring any dopant, this is just dependent on the refractive index of silica.
It is easy to take the Sellmeier equation to get n($$\lambda$$)
Then D=-$$\frac{\lambda}{c}$$ $$\frac{d^{2}n}{d\lambda^{2}}$$

To find the total dispersion of the waveguide however, you need to include the waveguide dispersion, this is different for each of the allowed modes in the waveguide. I could past half a page of equations here, but I don't fully understand it so I wont confuse you.

Finding information on this is easy for a basic step index fiber. I'm interested in more complicated index profiles i.e. photonic crystal fibers(solid core). Finding information on this is hard, so I'm hoping that someone here might know a bit more about this.

Once I have figured this out I will be able to figure out the dispersion curves for different allowed modes in the fiber I am using. So does anyone here know about this stuff?