[SOLVED] how obtain dispersion curve of photonc crystal fiber by FDTD?

[ghasem_008]

Hi.
I want to simulate the Dispersion curve of a photonc crystal fiber (PCF) by FDTD.
I'm familiar with FDTD very well. Also,I can obtain Band Structure diagrams of two dimensional photonic crystals.
But I don't know how obtain Dispersion curve.
in Fact my questions are as following:
1.should I use 2D or 3D FDTD for PCF?
2. I know that propagation constant along the fiber is β,such that wave propagate as "exp(-jβz)".
But I don't know how import a correct value for β in FDTD simulation.

in finding Photonic Bandgap diagram by FDTD,we have to repeat "fdtd Time Loop" for several Bloch wave vector to obtain mode frequencies by FFT of sampled field.

But, if I want to obtain " effective refractive index n=β/k0 " for dispersion,what do I do?
how import k0=2π/λ0 in FDTD simulation?

please write a proper algorithm...
thanks

 

[ghasem_008]

is there anyone who help me?

 

[ghasem_008]

I used from silica (n=1.45) in fiber with several air holes.
my outputs are:
λ = [1.781298,1.49299 ,1.284458 ,1.127039 ,1.003993 ,0.755335,0.605274 ,0.504786];
n_effective =[1.417512 ,1.425701,1.430995 ,1.434991 ,1.438115 ,1.442584 ,1.444986 ,1.446106];

Now,I want use from following formula to obtain dispersion curve:
D = -λ/c0*(d²n_effective/dλ²)

but my dispersion curve is not good.why?