Hi,

you can find your answer in these papers.

"High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide"

Or

"Photonic crystal waveguides with semi-slow light"

Hi Ali,

you still extract the group velocity from the band structure. Youb have to simulate a supercell that includes one period of your defect waveguide. Then the modes of the defect appear within the band structure and you can calculate the group velocity.

You could also use the MIT mpb simulation code (https://github.com/stevengj/mpb) which has a command that extracts the group velocity for you.

There is an additional script here (https://github.com/sschulz365/PhC_simulations) that you can used to help with the setup of your waveguide.

I hope the Group velocity dispersion (GVD) equals to Chromatic dispersion in the single mode guidance of solid core PCF. Therefore, the reciprocal of the integration of Chromatic dispersion function over the wavelength region should be the group velocity.

Please rectify me if it is not correct.

Hi Ali,

In addition to the excellent answers, you also could consider propagation time of a Gaussian pulse along your proposed waveguide. Firstly, you can calculate the group velocity from PWE results, as Dr. Schultz explained. Then, you can confirm obtained group velocity by another FDTD simulation.

In this case, you can calculate the group velocity and GVD in one shot.

Hi Ali,

For PhCs with defects, it's similar as PhCs without defects, you can extract group velocity from band structure by including the defect in your supercell.

Considering your initial supercell (X=1, Y=1, Z=1) if your structure is consisting of a horizontal line defect (x-direction), your supercell should be (X=1, Y=1, Z=N) where N is the number of rods in the z-direction.