light line equation in EBG

hi

I am searching for the light line equations to plot the EBG dispersion diagram in MATLAB.

Can anyone help me?

Thanks

The light line is non-dispersive, so you know that

Since the dispersion diagram plots Beta*d, you want to plot

Specifically, I plot my light line vs a Beta*d step of 5 degrees, for which I use the equation

LightLine(Angle5) = (1/sqrt(eps*mu))*Angle5*(pi/180)/(2*pi*(d))

Which is a simple re-arrangement of the above equation to give the frequency of the light line at an angle Beta*d

hi
Thank you for guidance