Examples Overview & Literature Benchmarks

Each example in GNLSE.jl reproduces a key result from the nonlinear optics literature, providing exact parameters to match published figures and experimental data. All quantities are specified in natural SI units.

📚 Benchmark Summary Table

#	Title	Reference Paper	Key Physical Phenomena	Primary Modules
1	Supercontinuum in PCF	Dudley et al., Rev. Mod. Phys. 78, 1135 (2006)	Soliton fission, Cherenkov dispersive waves	`Medium`, `Hollenbeck`, `sech_pulse`
2	Soliton Self-Frequency Shift	Mitschke & Mollenauer (1986); Gordon (1986)	Raman red-shift ($\propto T_0^{-4}$)	`BlowWood`, `track_solitons`
3	Supercontinuum Coherence	Dudley & Coen, Opt. Lett. 27, 1180 (2002)	MI noise seeding, ensemble coherence	`add_noise`, `spectral_coherence`
4	Soliton Trapping in Birefringent Fiber	Menyuk, J. Opt. Soc. Am. B 5, 392 (1988)	XPM polarization locking, vector GNLSE	`BirefringentMedium`, `VectorialPulse`
5	Higher-Order Soliton Compression	Mollenauer et al., Phys. Rev. Lett. 45, 1095 (1980)	Periodic temporal compression ($N=3$)	`soliton_number`, `Medium`
6	Stable N=3 Soliton Recurrence	Zakharov & Shabat (1972); Akhmediev (1987)	FPUT recurrence & perturbation stability	`solve`, `ERK4IP`
7	Gas-Filled Hollow-Core PCF	Russell et al., Nat. Photonics 8, 278 (2014)	Pressure-tuned dispersion ($\beta_n(P)$) & gas Raman	`HollowCoreFiber`, `MolecularRamanGas`
8	Silicon Photonics (TPA)	Yin & Agrawal, Opt. Lett. 32, 2031 (2007)	Two-photon absorption & free-carrier blue-shift	`SemiconductorMedium`
9	Femtosecond EDFA Amplifier	Agrawal, Nonlinear Fiber Optics, Ch. 11	Gain saturation & quantum ASE noise	`AmplifyingMedium`
10	Multithreaded Parameter Sweep	ZDW Boundary & Dispersive Wave Trapping	2D Spectral Heatmap across ZDW	`solve_sweep`, `Threads`

🛠️ Common Workflow Patterns

1. Standard Scalar GNLSE (Photonic Crystal Fiber)

using GNLSE, Plots

medium = commercial_fiber("NKT_NL_PM_750", length=0.15) # 15 cm fiber
grid   = create_grid(2^13, 12.5e-12, medium.lambda0)
pulse  = sech_pulse(grid, 10_000.0, 50e-15)
sol    = solve(pulse, SimParams(; medium=medium, raman_model=Hollenbeck(), self_steepening=true))
plot(sol) # Dashboard visualization

2. Birefringent Coupled Vectorial GNLSE

using GNLSE

grid   = create_grid(2^12, 50e-12, 1550e-9)
disp_x = TaylorDispersion([-21.5e-27], 0.0)
disp_y = TaylorDispersion([-21.5e-27], 1e-12) # group-velocity mismatch
medium = BirefringentMedium(5.0, 0.0011, 0.0, disp_x, disp_y, 0.0, 1550e-9)

Ax     = sech_pulse(grid, 100.0, 1e-12).At
vpulse = VectorialPulse(Ax, Ax, grid) # 45° launch
vsol   = solve(vpulse, SimParams(; medium=medium, solver=SSFM(1e-3), raman_model=nothing))

3. Active EDFA Fiber Amplifier

using GNLSE

grid   = create_grid(2^13, 10e-12, 1550e-9)
pulse  = gaussian_pulse(grid, 50.0, 100e-15)
edfa   = AmplifyingMedium(; length=2.0, gamma=0.0012, g0_db=12.0, Esat=2.0e-6, noise_figure_db=4.5, betas=[-22.0e-27], lambda0=1550e-9)
sol    = solve(pulse, SimParams(; medium=edfa, raman_model=nothing))

4. Gas-Filled Hollow-Core PCF

using GNLSE

grid   = create_grid(2^13, 15e-12, 800e-9)
pulse  = sech_pulse(grid, 50e3, 30e-15)
hcf    = HollowCoreFiber(; radius=15e-6, gas=:Ar, pressure=3.0, length=0.5, lambda0=800e-9)
sol    = solve(pulse, SimParams(; medium=hcf, raman_model=nothing))

5. Silicon Nanowire (TPA & Free Carriers)

using GNLSE

grid   = create_grid(2^12, 40e-12, 1550e-9)
pulse  = gaussian_pulse(grid, 30.0, 2.0e-12)
soi    = SemiconductorMedium(; length=0.01, gamma=300.0, alpha2=5.0e-12, Aeff=0.1e-12, tau_c=1.0e-9, betas=[-1000e-27], lambda0=1550e-9)
sol    = solve(pulse, SimParams(; medium=soi, raman_model=nothing))

📏 Key Characteristic Quantities

Before running simulations, compute these parameters to understand the dominant regime:

# 1. Soliton Order N
N = soliton_number(beta2, gamma, T0, P0)

# 2. Dispersion & Nonlinear Lengths
LD  = dispersion_length(beta2, T0)   # L >> LD -> dispersion dominant
LNL = nonlinear_length(gamma, P0)    # L >> LNL -> nonlinearity dominant

# 3. Soliton Fission Length
L_fiss = LD / N

# 4. Soliton Self-Frequency Shift Rate (Gordon 1986)
dΩdz = -8 * 3e-15 * abs(beta2) / (15 * T0^4)