Dispersion Models

GNLSE.jl provides three ways to specify the chromatic dispersion of your waveguide.

Taylor Expansion

The most common approach: provide dispersion coefficients $\beta_n$ at the center wavelength.

# betas[1] = β₂, betas[2] = β₃, ... (β₀ and β₁ excluded)
disp = TaylorDispersion([-21.5e-27, 1.4e-40, -1.8e-55])
medium = Medium(0.5, 0.002, 0.0, disp, 1550e-9)

Alternatively, pass betas directly to the Medium keyword constructor:

medium = Medium(;
    length  = 0.5,
    gamma   = 0.002,
    betas   = [-21.5e-27, 1.4e-40],  # β₂, β₃
    lambda0 = 1550e-9,
)

For birefringent fibers, a group-velocity mismatch $\beta_1$ (walk-off) can also be specified:

disp_slow = TaylorDispersion([-21.5e-27], 0.0)       # x axis: no walk-off
disp_fast = TaylorDispersion([-21.5e-27], 1.0e-10)   # y axis: 100 fs/mm walk-off

Tabulated Dispersion

When you have measured $\beta(\omega)$ data from your waveguide characterization:

using GNLSE

# Relative frequencies [rad/s] and corresponding β(ω) [1/m]
detuning = range(-5e13, 5e13; length=201)
beta     = 0.5 .* (-21.5e-27) .* detuning.^2  # example: parabolic

disp = TabulatedDispersion(collect(detuning), collect(beta))
medium = Medium(1.0, 0.002, 0.0, disp, 1550e-9)

The tabulated dispersion is linearly interpolated onto the simulation grid. Outside the provided range, the nearest endpoint value is held (flat extrapolation).

Sellmeier Dispersion

For standard glass materials where the refractive index is described by Sellmeier coefficients:

# Fused silica Sellmeier coefficients (Malitson 1965)
B = [0.6961663, 0.4079426, 0.8974794]
C = [0.0684043^2, 0.1162414^2, 9.896161^2]  # [μm²]

disp = SellmeierDispersion(B, C; microns=true)  # microns=true (default)
medium = Medium(1.0, 0.002, 0.0, disp, 1550e-9)

Checking Your Dispersion

Use dispersion_operator to inspect the computed $D(\omega)$ operator on your grid:

grid = create_grid(2^12, 10e-12, 1550e-9)
D = dispersion_operator(grid, medium)
# D is a complex vector in monotonic-frequency order

The imaginary part of D is the propagation-constant deviation $B(\omega)$; the real part is $(g - \alpha)/2$ — the net gain/loss contribution (zero for a plain Medium with loss=0, negative for lossy fibers via loss, positive for active fibers via AmplifyingMedium's g0/g0_db).