Wavelength-Dependent Nonlinearity

GNLSE.jl supports three levels of nonlinearity specification:

1. Constant Nonlinearity

The simplest model: a scalar $\gamma$ [1/(W·m)].

# As a scalar in Medium
medium = Medium(0.1, 0.11, 0.0, [-1.2e-26], 835e-9)

# Or explicitly as ConstantNonlinearity
γ_model = ConstantNonlinearity(0.11)
medium = Medium(0.1, γ_model, 0.0, TaylorDispersion([-1.2e-26]), 835e-9)

2. Z-Dependent (Tapered Fiber)

For tapered or graded-index fibers where $\gamma$ varies along the propagation distance:

# Exponential taper: γ(z) = γ₀ exp(-α_taper * z)
gamma_0 = 0.11
alpha_taper = 10.0   # 1/m
gamma_func = z -> gamma_0 * exp(-alpha_taper * z)

medium = Medium(0.01, gamma_func, 0.0, TaylorDispersion([-1.2e-26]), 835e-9)

The function signature must be gamma_func(z::Float64) -> Float64, returning $\gamma(z)$ in [1/(W·m)].

3. Frequency-Dependent Nonlinearity

When the nonlinear coefficient varies with frequency (e.g., due to the frequency-dependent effective mode area):

# Direct frequency-domain function
γ_of_ω = ω -> 0.11 * (ω / (2π * 3e14))^0.5   # hypothetical dispersion

γ_model = FrequencyDependentNonlinearity(γ_of_ω)
medium = Medium(0.1, γ_model, 0.0, TaylorDispersion([-1.2e-26]), 835e-9)

4. Effective Mode Area Model

The most physically rigorous model: compute $\gamma(\omega)$ from the material nonlinear index $n_2$ and the frequency-dependent effective mode area $A_{\rm eff}(\omega)$:

\[\gamma(\omega) = \frac{n_2 \omega}{c \, A_{\rm eff}(\omega)}\]

n2 = 2.6e-20               # Nonlinear index [m²/W] (fused silica)
Aeff_func = ω -> 80e-12    # Constant Aeff = 80 µm² (standard SMF-28)

γ_model = NonlinearityFromEffectiveArea(n2, Aeff_func)
medium = Medium(1.0, γ_model, 0.0, TaylorDispersion([-21.5e-27]), 1550e-9)

A more realistic $A_{\rm eff}(\omega)$ would be obtained from a mode solver:

# Hypothetical frequency-dependent Aeff from numerical mode solver data
using Interpolations
aeff_data  = [90e-12, 85e-12, 82e-12, 80e-12, 79e-12]   # [m²]
omega_data = range(1.1e15, 1.4e15; length=5)
Aeff_itp   = LinearInterpolation(omega_data, aeff_data; extrapolation_bc=Flat())

γ_model = NonlinearityFromEffectiveArea(n2, ω -> Aeff_itp(ω))

Summary Table