I have this quite basic question regarding photonic crystals.

As I understand, a periodic dielectric structure (photonic crystal) has modes (spatial profiles) at discrete frequencies from:

[tex] \nabla \times \Big( \frac{1}{\epsilon(r)}\nabla \times H(r) \Big) = \frac{\omega^2}{c^2} H(r)[/tex]

However, dispersion diagrams ([tex]\omega[/tex] vs. [tex]k[/tex]) are continuous plots.

**Doesn't each [tex]k[/tex] characterize a different mode?**

I'm refering "Photonic Crystals Molding the Flow of Light" and believe it's the best book to learn about photonic crystals.

Really appreciate some guidance.

Thanks