Difference between Material dispersion and waveguide dispersion?

[Cerkit]

Can someone please explain the difference between Material dispersion and waveguide dispersion?

 

[Meir Achuz]

"Dispersion" is determined by the relation between wave number
k(=2\pi/\lambda) and frequency \omega(=2\pi f).
In a medium, the relation is k=\sqrt{\epsilon\mu}\omega/c.
In a wave guide, it is k=[\sqrt{\epsilon\mu}/c]\sqrt{\omega^2-\omega^2_c},
where \omega_c depends on the dimensions of the wave guide.