Compact Model for our Waveguide
Given the prior information we can come up with a Taylor expansion expression for \(n_{eff}\)
\(n_{eff}(\lambda) = n_1+n_2(\lambda-\lambda_0)+n_3(\lambda-\lambda_0)^2\)
Leveraging \cite{Chrostowski_2015} matlab code to match our Lumerical Mode generated data to the above expression we calculate the values for \(n_1,n_2,\) and \(n_3\) for \(\lambda = 1.55\) to be
\(n_{eff}(\lambda) = 2.44365-1.13171(\lambda-1.55)-0.0424756(\lambda-1.55)^2\)
Waveguide Properties to Concider
While performing analysis some other relationships to note for an ideal waveguide 500nm x 220 nm at wavelength of 1550 nm include:
* n_eff = 2.445 : effective index decreases as lambda increases.
* waveguide loss = 4.39 db/cm : decreases as wavelength increases
* n_g = 4.198 : Group index increases with wavelenth
* v_g = 7.141 m/s : Group velocity decreases with wavelength
* g_delay = 1.4 ps/km : Group delay increases with wavelength
* Dispersion = 446 ps/nm/km and isn't linearly related
* Beta = .99 1/m : decreases with wavelength