I am interested to calculate the effective mode index of the sub-wavelength gratings (SWG). Basically I calculated the effective index using the refractive index, i.e. the refractive index of the SWG on SOI platform on any particular wavelength is given as:
n = sqrt(n1^2*DC + (1-DC)*n2^2)
where, n1 - refractive index of silicon, n2 is the refractive index of cladding (mostly silica) and DC is the duty cycle of the SWG waveguide.
Now I am using the value of ‘n’ as the refractive index of new material and calculating the effective index. Now the effective index which I am getting by this way is basically I am assuming the true effective index of the SWG waveguide. But I am not sure about this method as this is a kind of approximation, any comments on it?
I will be very thankful if you please guide me the exact way to calculate the effective index of the SWG waveguide using Lumerical Mode/FDTD solution.