Raman Scattering Models

Raman scattering introduces a delayed, frequency-dependent nonlinear response that is important for pulses shorter than ~1 ps. GNLSE.jl provides three validated models for fused-silica fibers.

Choosing a Raman Model

Pass a Raman model to SimParams:

params = SimParams(;
    medium      = medium,
    raman_model = BlowWood(),      # or LinAgrawal() or Hollenbeck()
)

To disable Raman scattering (pure Kerr):

params = SimParams(;
    medium      = medium,
    raman_model = nothing,
)

Available Models

`BlowWood()`

The Blow & Wood (1989) two-exponential model. Simple and widely used:

\[h_R(t) = \frac{\tau_1^2 + \tau_2^2}{\tau_1 \tau_2^2} e^{-t/\tau_2} \sin(t/\tau_1)\]

Default parameters: $\tau_1 = 12.2$ fs, $\tau_2 = 32$ fs, $f_R = 0.18$.

raman = BlowWood()

`LinAgrawal()`

The Lin & Agrawal (2006) model, fits measured Raman gain spectrum of silica more accurately over a wider bandwidth:

raman = LinAgrawal()

`Hollenbeck()`

The Hollenbeck & Cantrell (2002) model — the most accurate for fused silica, incorporating both isotropic and anisotropic contributions:

raman = Hollenbeck()

Tip

For broadband supercontinuum simulations (>1 octave), Hollenbeck() is recommended as it fits the silica Raman gain spectrum most accurately.

Inspecting the Raman Response

The time-domain Raman response can be inspected directly:

fr, h_R = raman_response(grid, BlowWood())

println("Fractional Raman contribution: ", fr)
# plot(grid.t * 1e15, h_R, xlabel="t [fs]", label="hR(t)")

Effect on Pulse Evolution

Raman scattering produces several physically important effects:

Phenomenon	Description
Soliton self-frequency shift	Red-shift of fundamental solitons due to Raman amplification
Raman gain	Amplification of red-shifted spectral components
Supercontinuum generation	Combined Raman + soliton fission extends the spectrum

Example: Observing the Soliton Self-Frequency Shift

using GNLSE

grid = create_grid(2^12, 20e-12, 1550e-9)

medium = Medium(;
    length   = 5.0,
    gamma    = 0.01,
    betas    = [-21.5e-27],
    lambda0  = 1550e-9,
)

# Fundamental soliton input (T₀=50 fs → ~12 nm SSFS visible over 10 soliton periods)
# Note: SSFS ∝ T₀⁻⁴; using T₀=200 fs gives only ~0.05 nm (invisible!)
T0 = 50e-15  # 50 fs soliton half-width
P0 = abs(medium.dispersion.betas[1]) / (medium.gamma * T0^2)
pulse = sech_pulse(grid, P0, T0 * 2 * log(1 + sqrt(2)))

# With Raman: expect red-shift
params_raman = SimParams(; medium=medium, raman_model=Hollenbeck(), z_saves=100)
sol_raman = solve(pulse, params_raman)

# Without Raman: soliton stays centered
params_kerr = SimParams(; medium=medium, raman_model=nothing, z_saves=100)
sol_kerr = solve(pulse, params_kerr)