cutoff frequencies in photonic crystals

[elifelite]

Hi all,

How can I calculate the cutoff frequencies in a photonic crystal waveguide. It seems it is similar to rectangular waveguide, but it doesnt correspond to same values.

Is there any formula to calculate cutoffs for photonic crystal waveguides?

Thanks in advance,

 

[maciasas]

it depends of distance between cells, look for slow wave factor - SWF or photonic band gap - PGB and you shell find the solution

 

[elifelite]

it depends of distance between cells, look for slow wave factor - SWF or photonic band gap - PGB and you shell find the solution

Hi Maciasas,

I have obtained the dispersion curve as well as the transmission plots for my design, but at the points transmission decreases sharply, this should correspond to cutoff frequency, right?

But these point are not the same point that modes change.

or maybe I am completely lost??

Thanks anyway, I would be grateful if you can give me an idea or suggest anything.

 

[maciasas]

Photonic crystals and PBG structures are usually operated at frequencies where the lattice period p is of the order of a multiple of half a guided wavelength, p ≈ nλg/2. The waves scattered by adjacent layers of the lattice interfere constructively for some specific angles of incidence. Therefore, net rejection of the incoming energy, corresponding to zero group velocity, occurs at these angles. This phenomenon is similar to Bragg diffraction in X-ray optics and is sometimes referred to as “Bragglike” diffraction. The Bragg condition for maximum diffraction is given by
2p sin θ = mλg, m= 0, 1, 2,
where it is clearly seen that the Bragg angles are function of frequency (via λg). This condition, with
β = 2π/λg, is equivalent to
β(ω) =mπp sin θ(ω), m= 0, 1, 2,
where the function β(ω) [or, more commonly, its inverse ω(β)] is the dispersion relation, from which the dispersion diagram is computed. The points of the dispersion curves ω(β) where the Bragg condition is met have a zero slope (or tangent), since the slope of ω(β) corresponds to the group velocity, vg = dω/dβ, which is zero there. This means that Bragg points delimit the stop bands or band gaps in the dispersion diagram.