Difference between Material dispersion and waveguide dispersion?

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

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