Nonlinear Photonic Band Gap Simulation

[Malik Javaid]

Hello,

I am creating a nonlinear 3rd order photonic crystal out of silicon, with n2 value of 3*10^-18 through which I calculated the susceptibility using the equation n(2)=3Chi(3)/(4n^2). The dielectric constant I used was 15.813. The crystal has air holes with n=1. However, when I ran the PWE band solver simulation, there were no band gaps found, even though the contrast between the two refractive indices is great. Can you assist me with what might possibly yield band gaps?

I attached the file to this post.

[Scott Newman]

Hello Malik,

Run your PWEM calculation using the TM polarization and you will find that there is 2 bandgaps. The one I believe you are looking for is the one from [w/2pic] 0.517826 to 0.547916.

I realize that the reference you are likely using probably says you should be looking at the TE polarization. It is important to note that there are different conventions for TE and TM. For a 2D simulation with infinite Y, OptiFDTD uses TE (Ey, Hx, Hz) and TM (Hy, Ex, Ez). While this may differ from some references it is inline with many waveguide based reference.

On another note, the PWEM calculation in OptiFDTD does not take into consideration the power of the source so the bandgap you are calculating is based on the linear permitivity of 15.813 that you entered.

Scott

[Malik Javaid]

Is there any way to find the bandgap taking into consideration the power other than the PWEM calculation?

[Scott Newman]

You can run straight FDTD simulations where you inject a plane wave into the photonic crystal and monitor the transmitted power. However, unless multiple simulations are done this will only give you the result for a single direction or the equivalent of one vertical slice from band diagram obtained from PWEM.

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