Significance of same frequency at different K values within photonic band gap

Using dispersion plot (ω Vs K), we can understand the nature of guided modes, present within the photonic band-gap. The photonic band-gap (PBG) appears since different discrete values of ω present at same K value.

How can I understand the phenomena, if at different K values there exist same value of ω, within PBG? for example, if the dispersion plot becomes parallel to the K axis at ω=ω0, a single frequency exist for all K values. How the frequency response should look like? Will there be single narrow spike at ω=ω0?

This doens't necessarily mean there's a band gap. A band gap is given by the absence of any (real) K values in a certain range of ω. Different values of ω present at same K value just means there are multiple modes supported by the structure (or you're observing multiple Brillouin zones).

Resonance. It means that the frequency of the mode is the same, regardless of K, as you'd expect from for example a LC resonator. Subsequently, yes -- the frequency response will generally have a narrow spike in this region (depending on the quality factor).

Thank you. It helps me lot.



[QUOTE=Different values of ω present at same K value just means there are multiple modes supported by the structure (or you're observing multiple Brillouin zones).[/QUOTE]

We know wavelength and frequency are related with each other through c (velocity), By multiple modes, do you mean that the light with a single wavelength may propagate with different velocity? The change in velocity is reflected by the change in frequency since the wavelength is constant?

The point of k-ω diagrams is to examine a medium's dispersion. Only in a vacuum is light truly non-dispersive, in which k = ω/c.

Yes. The medium will support multiple propagating modes at any given frequency, where each mode will have its own phase and group velocity profile.