Generalized nonlinear Schrödinger equation¶

Full GNLSE solver: dispersion, Kerr, Raman, self-steepening, TPA, adaptive steps. Docstrings are the source of truth, rendered with mkdocstrings (numpydoc style).

photonics_helper.gnlse ¶

Generalized nonlinear Schrödinger equation (GNLSE) solver.

Split-step Fourier solver for pulse propagation through nonlinear media, supporting Kerr, Raman, self-steepening, and two-photon absorption effects.

BetasUnit `module-attribute` ¶

BetasUnit = Literal['ps^k/m', 's^k/m', 'SI']

FigureLike `module-attribute` ¶

FigureLike: TypeAlias = MplFigure | PlotlyFigure

HBAR_J_S `module-attribute` ¶

HBAR_J_S = 1.0545718e-34

FiberProfile `dataclass` ¶

FiberProfile(n2: float, alpha: float, A_eff: Area, length: Length, confinement_factor: float = 1.0, sigma_tpa: float = 0.0, carrier_lifetime: Time | None = None, raman_response: object | None = None, beta_tpa: float = 0.0, sigma_fca: float = 0.0, group_velocity: float | None = None)

Optical fiber/waveguide parameters for GNLSE propagation.

Attributes: n2: Nonlinear refractive index n₂ (m²/W). alpha: Fiber loss coefficient α (1/m). A_eff: Effective mode area (m²). confinement_factor: Waveguide confinement factor Γ (1.0 for fibers, <1.0 for waveguides). sigma_tpa: Two-photon absorption cross-section (m²·W⁻¹). Default 0. carrier_lifetime: Carrier recombination lifetime (s). Default None. length: Fiber length (m). raman_response: Raman response function. Default None. beta_tpa: Two-photon absorption coefficient β_TPA (m/W) for the time-resolved free-carrier model. Default 0. sigma_fca: Free-carrier absorption cross-section σ_FCA (m²) for the time-resolved free-carrier model. Default 0. group_velocity: Envelope group velocity v (m/s) converting the carrier lifetime to a propagation length. Default None → C_MS.

n2 `instance-attribute` ¶

n2: float

alpha `instance-attribute` ¶

alpha: float

A_eff `instance-attribute` ¶

A_eff: Area

length `instance-attribute` ¶

length: Length

confinement_factor `class-attribute` `instance-attribute` ¶

confinement_factor: float = 1.0

sigma_tpa `class-attribute` `instance-attribute` ¶

sigma_tpa: float = 0.0

carrier_lifetime `class-attribute` `instance-attribute` ¶

carrier_lifetime: Time | None = None

raman_response `class-attribute` `instance-attribute` ¶

raman_response: object | None = None

beta_tpa `class-attribute` `instance-attribute` ¶

beta_tpa: float = 0.0

sigma_fca `class-attribute` `instance-attribute` ¶

sigma_fca: float = 0.0

group_velocity `class-attribute` `instance-attribute` ¶

group_velocity: float | None = None

from_gamma `classmethod` ¶

from_gamma(gamma: float, n2: float, omega0: float, alpha: float = 0.0, length: Length = Length(1.0, 'm'), confinement_factor: float = 1.0, sigma_tpa: float = 0.0, carrier_lifetime: Time | None = None, raman_response: object | None = None, beta_tpa: float = 0.0, sigma_fca: float = 0.0, group_velocity: float | None = None) -> FiberProfile

Create a FiberProfile from a target nonlinear coefficient γ.

Convenience constructor that mirrors laserfun's API where γ is specified directly (e.g. gamma_W_m) rather than deriving it from n₂ and A_eff.

Parameters:

Name	Type	Description	Default
`gamma`	`float — target nonlinear coefficient γ in 1/(W·m).`		required
`n2`	`float — nonlinear refractive index n₂ in m²/W.`		required
`omega0`	`float — carrier angular frequency in rad/s.`		required
`alpha`	`float — fiber loss coefficient α in 1/m. Default 0.`		`0.0`
`length`	`Length — fiber length. Default 1 m.`		`Length(1.0, 'm')`
`confinement_factor`	`float — waveguide confinement factor Γ. Default 1.0.`		`1.0`
`sigma_tpa`	`float — two-photon absorption cross-section. Default 0.`		`0.0`
`carrier_lifetime`	`Time — carrier recombination lifetime. Default None.`		`None`
`raman_response`	`object — Raman response function. Default None.`		`None`
`beta_tpa`	`float — two-photon absorption coefficient β_TPA in m/W.`	Used by the time-resolved free-carrier model (`SplitStepEngine(include_free_carriers=True)`). Default 0.	`0.0`
`sigma_fca`	`float — free-carrier absorption cross-section σ_FCA in m².`	Used by the time-resolved free-carrier model. Default 0.	`0.0`
`group_velocity`	`float \| None — envelope group velocity v in m/s used`	to convert the retarded-time carrier lifetime into a propagation length. Default `None` → the vacuum-light-speed constant.	`None`

Returns:

Type	Description
`FiberProfile — configured with the computed A_eff.`

Notes

Computes A_eff = n₂·ω₀·Γ / (c·γ) from the relation γ = n₂·ω₀·Γ / (c·A_eff).

SplitStepEngine ¶

SplitStepEngine(pulse: Wave, fiber: FiberProfile, betas: NDArray, include_raman: bool = False, include_self_steepening: bool = False, include_tpa: bool = False, include_free_carriers: bool = False, conserving_shock: bool = False, tau_shock: float | None = None, step_size: Length | None = None, dispersion_profile: ZDependentDispersion | Callable[[NDArray, float], NDArray] | None = None, a_eff_fn: Callable[[float], float] | None = None, alpha_fn: Callable[[float], float] | None = None, gamma_fn: Callable[[float], float] | None = None, min_shrink_factor: float = 0.1, betas_unit: BetasUnit = 'ps^k/m')

Split-step Fourier engine for GNLSE propagation.

Alternates linear (dispersion) and nonlinear (Kerr/Raman/steepening/TPA) steps in Fourier space with adaptive step sizing.

Parameters:

Name	Type	Description	Default
`pulse`	`Wave`	Input pulse.	required
`fiber`	`FiberProfile`	Fiber parameters.	required
`betas`	`array_like`	Dispersion coefficients [beta2, beta3, ...] in `ps^k/m` (with `Ω` in `rad/ps`), as returned by `Dispersion.get_betas()`. Pass `betas_unit="s^k/m"` (or `"SI"`) to supply SI coefficients instead; they are converted to `ps^k/m` internally.	required
`betas_unit`	`('ps^k/m', 's^k/m', 'SI')`	Unit of betas. Default `"ps^k/m"` (native internal form).	`"ps^k/m"`
`include_raman`	`bool`	Include Raman. Default False.	`False`
`include_self_steepening`	`bool`	Include self-steepening (shock term). Default `False`. When enabled, the shock operator `(1 + (i/ω₀)∂t)` of Blow & Wood (1989) and Dudley–Genty–Coen RMP 78, 1135 (2006), Eq. (3), is integrated with an interaction-picture scheme (`τ_shock` settable, default `1/ω₀`): the exactly-integrable Kerr/Raman phase `exp(iγP_NL Δz)` is factored out and only the shock correction `iγτ_shock ∂_t(A·P_NL)` is advanced with frequency-domain RK4 (the RK4IP idea of Hult 2007 / Hochbruck & Ostermann 2010). The shock factor is never clamped (see :meth:`_validate_shock_grid`). Enable explicitly for cross-library comparisons; laserfun defaults to shock on (but its shock term has the opposite linear-in-Ω asymmetry). Sign audit (2026): the multiplier `1 + Ω·τ_shock` is the correct physical factor `ω/ω₀` under this codebase's FFT convention. The grid FFT uses the numpy `e^{−iΩt}` kernel while the linear dispersion step, all spectral plots, and the DW/MI utilities map bin `W` to optical frequency `ω₀ + W`; that fixes the carrier convention to `e^{+iω₀t}` and makes `W > 0` the blue side. The convention set was verified numerically to be self-consistent: (i) Raman-only soliton propagation red-shifts under the same mapping (Gordon SSFS), (ii) a fundamental soliton with shock and β₂ only develops a blue-shifted centroid and positive spectral skew with `1 + Ω·τ` and the mirror-image red shift with `1 − Ω·τ`, and (iii) energy is conserved. laserfun's opposite raw-bin asymmetry follows from its own (unshifted-FFT) convention, not from different physics.	`False`
`include_tpa`	`bool`	Include TPA (legacy spatially-averaged carrier model). Default False.	`False`
`include_free_carriers`	`bool`	Include the opt-in time-resolved TPA / free-carrier model: the carrier population `N(t)` is resolved over the retarded-time grid instead of spatially averaged, driven by `β_TPA \|A\|⁴/(2ħω₀)` generation and `N/(τ_c v)` recombination, with the field attenuated by the TPA term `−(β_TPA/2)\|A\|²A` and free-carrier absorption `−(σ_FCA/2)N·A` (Soref & Bennett 1987; Cowan et al. 2003; Yin & Agrawal 2007). Requires `fiber.beta_tpa` / `fiber.sigma_fca`; free-carrier refraction (μ), diffusion and drift are out of scope. Default False.	`False`
`tau_shock`	`float \| None`	Shock (self-steepening) timescale in seconds (SI). `None` (default) uses `1/ω₀` at the pulse carrier frequency, matching Agrawal and the uncorrected Dudley Eq. (3) value (0.443 fs at 835 nm). Pass an explicit value for the effective-area-corrected timescale (Dudley–Genty–Coen RMP 78, 1135 (2006), Sec. V.B: `tau_shock = 0.56e-15` for the Fig. 3 PCF config). Must be > 0.	`None`
`conserving_shock`	`bool`	Enable the photon-conserving (pcGNLSE) shock operator. Default `False`. The modification substitutes `\|γ\|` for `γ` on the delayed (Raman) arm only; the instantaneous SPM/SS arm keeps the signed `γ`. Note: for any fiber with `γ > 0` (every ordinary dielectric), `abs(gamma) == gamma` and the two paths are identical — the flag is a no-op. It only has an effect when `γ < 0` (the sign bench used in `reproductions/huang_202x_pcgnlse_attractors/`). Requires `include_raman=True` and a Raman response.	`False`
`step_size`	`Length \| None`	Fixed step size (m). If None, adaptive stepping is used.	`None`
`min_shrink_factor`	`float`	Floor for the gradient-based step shrink factor in z-dependent mode. Must be in (0, 1]. Default 0.1.	`0.1`

pulse `instance-attribute` ¶

pulse = pulse

fiber `instance-attribute` ¶

fiber = fiber

betas `instance-attribute` ¶

betas = _normalize_betas(betas, betas_unit)

include_raman `instance-attribute` ¶

include_raman = include_raman

include_self_steepening `instance-attribute` ¶

include_self_steepening = include_self_steepening

include_tpa `instance-attribute` ¶

include_tpa = include_tpa

include_free_carriers `instance-attribute` ¶

include_free_carriers = include_free_carriers

conserving_shock `instance-attribute` ¶

conserving_shock = bool(conserving_shock)

step_size `instance-attribute` ¶

step_size = step_size

gamma_fn `instance-attribute` ¶

gamma_fn = gamma_fn

grid `instance-attribute` ¶

grid: TemporalGrid = pulse.grid

omega0 `instance-attribute` ¶

omega0 = pulse.central_frequency

A `instance-attribute` ¶

A = np.array(pulse.envelope_field, dtype=complex)

evolution `instance-attribute` ¶

evolution: list[Wave] = []

tau_shock `property` ¶

tau_shock: float

Shock timescale in seconds (SI): explicit override or 1/ω₀.

z_array `property` ¶

z_array: NDArray

Array of propagation distances (m) for each evolution entry.

spectra_vs_z `property` ¶

spectra_vs_z: tuple[NDArray, NDArray]

Tuple of (frequency array, spectra at each step).

energy_vs_z `property` ¶

energy_vs_z: NDArray

Pulse energy Σ|A|²·dt at each saved step (same length as z_array).

propagate ¶

propagate(num_steps: int, *, nsaves: int | None = None, show_progress: bool = False, raman_noise: bool = False, noise_seed: int | None = None) -> None

Run split-step simulation for num_steps steps.

Parameters:

Name	Type	Description	Default
`num_steps`	`int`	Target number of split-steps along the fiber (actual integration steps may be higher if adaptive stepping shrinks `dz` below `length/num_steps`).	required
`nsaves`	`int`	Number of evenly spaced snapshots to retain along `z` (including `z=0` and `z=L`). If None, every integration step is stored (can use many GB for long runs). Use ~200 for contour plots, as in laserfun's `NLSE(..., nsaves=200)`.	`None`
`show_progress`	`bool`	If True, show a `tqdm` progress bar over propagation distance. Requires `tqdm` (`pip install tqdm`).	`False`
`raman_noise`	`bool`	If True, inject spontaneous-Raman noise (Dudley Eq. 5 `Γ_R`) once per step. Default False (bit-identical to legacy runs). Requires `include_raman=True` with a Raman response on the fiber.	`False`
`noise_seed`	`int`	Seed for the per-step noise generator; same seed gives bit-identical output. `None` draws nondeterministically.	`None`

GNLSESolver ¶

GNLSESolver(pulse: Wave, fiber: FiberProfile, betas: NDArray, include_raman: bool = True, include_self_steepening: bool = False, include_tpa: bool = False, include_free_carriers: bool = False, check_phase_matching: bool = False, step_size: Length | None = None, betas_unit: BetasUnit = 'ps^k/m', tau_shock: float | None = None, conserving_shock: bool = False)

High-level GNLSE solver using split-step Fourier method.

Parameters:

Name	Type	Description	Default
`pulse`	`Wave`	Input pulse envelope.	required
`fiber`	`FiberProfile`	Fiber parameters.	required
`betas`	`array_like`	Dispersion coefficients [beta2, beta3, ...] in `ps^k/m` (with `Ω` in `rad/ps`), as returned by `Dispersion.get_betas()`. Pass `betas_unit="s^k/m"` (or `"SI"`) to supply SI coefficients instead; they are converted to `ps^k/m` internally.	required
`betas_unit`	`('ps^k/m', 's^k/m', 'SI')`	Unit of betas. Default `"ps^k/m"`.	`"ps^k/m"`
`include_raman`	`bool`	Include Raman scattering. Default True.	`True`
`include_self_steepening`	`bool`	Include self-steepening (shock term). Default `False`. Models intensity-dependent group velocity with the shock operator `(1 + (i/ω₀)∂t)` (see :class:`SplitStepEngine`; `τ_shock` settable, default `1/ω₀`). `False` by default; laserfun's `NLSE` uses `shock=True` by default — set `True` when comparing against laserfun or reproducing Dudley-style supercontinuum demos.	`False`
`include_tpa`	`bool`	Include two-photon absorption (legacy spatially-averaged model). Default False.	`False`
`include_free_carriers`	`bool`	Include the opt-in time-resolved TPA/free-carrier model (see :class:`SplitStepEngine`). Requires `fiber.beta_tpa` / `fiber.sigma_fca`. Default False.	`False`
`check_phase_matching`	`bool`	Run the phase-matching preflight and emit warnings before propagating.	`False`
`step_size`	`Length \| None`	Fixed split-step size (m). If `None` (default), the engine uses its adaptive step heuristic. Supply an explicit value for deterministic, reproducible step counts, or when the adaptive heuristic is inappropriate (e.g. CW/finite-background fields where the pulse-width based dispersion limit is not meaningful).	`None`

pulse `instance-attribute` ¶

pulse = pulse

fiber `instance-attribute` ¶

fiber = fiber

betas `instance-attribute` ¶

betas = _normalize_betas(betas, betas_unit)

betas_unit `instance-attribute` ¶

betas_unit = _validate_betas_unit(betas_unit)

include_raman `instance-attribute` ¶

include_raman = include_raman

include_self_steepening `instance-attribute` ¶

include_self_steepening = include_self_steepening

include_tpa `instance-attribute` ¶

include_tpa = include_tpa

include_free_carriers `instance-attribute` ¶

include_free_carriers = include_free_carriers

check_phase_matching `instance-attribute` ¶

check_phase_matching = check_phase_matching

step_size `instance-attribute` ¶

step_size = step_size

conserving_shock `instance-attribute` ¶

conserving_shock = bool(conserving_shock)

tau_shock `instance-attribute` ¶

tau_shock = float(tau_shock) if tau_shock is not None else None

evolution `property` ¶

evolution: list[Wave]

List of Wave objects at each propagation step.

z_array `property` ¶

z_array: NDArray

Array of propagation distances (m) for each evolution entry.

omega0 `property` ¶

omega0: float

Carrier angular frequency (rad/s).

spectra_vs_z `property` ¶

spectra_vs_z: tuple[NDArray, NDArray]

Tuple of (frequency array, spectra at each step).

energy_vs_z `property` ¶

energy_vs_z: NDArray

Pulse energy Σ|A|²·dt at each saved step (same length as z_array).

preflight_report `property` ¶

preflight_report: SimulationReadinessReport | None

Lazy preflight report from phase-matching assessment.

Builds and caches the report on first access when check_phase_matching=True. Returns None when disabled.

propagate ¶

propagate(num_steps: int = 100, *, nsaves: int | None = None, show_progress: bool = False, raman_noise: bool = False, noise_seed: int | None = None) -> None

Run split-step simulation for num_steps steps.

estimate_num_steps `classmethod` ¶

estimate_num_steps(pulse: Wave, fiber: FiberProfile, betas: NDArray, *, include_self_steepening: bool = False, include_raman: bool = False, safety_factor: float = 2.0) -> int

Estimate split-step count from dispersion and nonlinear length scales.

Uses the same limits as :meth:SplitStepEngine._adaptive_step_size, divided by safety_factor (larger → more steps). Useful for supercontinuum / soliton regimes where coarse stepping gives wrong physics.

interpolated_spectrum_db ¶

interpolated_spectrum_db(wl_min: float, wl_max: float, n_wl: int, *, step_index: int = -1) -> tuple[NDArray, NDArray]

Return spectrum (dB) on a uniform wavelength grid (nm).

Uses absolute angular frequency omega0 + grid.w before converting to wavelength, matching :func:plot_spectrum_vs_distance.

Parameters:

Name	Type	Description	Default
`wl_min`	`float`	Wavelength range in nm.	required
`wl_max`	`float`	Wavelength range in nm.	required
`n_wl`	`int`	Number of wavelength samples.	required
`step_index`	`int`	Evolution index (default -1 = final step).	`-1`

Returns:

Type	Description
`wavelength_nm, spectrum_db : 1-D arrays`

TaperedGNLSESolver ¶

TaperedGNLSESolver(pulse: Wave, fiber: FiberProfile, dispersion_profile: ZDependentDispersion | Callable[[NDArray, float], NDArray], a_eff_fn: Callable[[float], float] | None = None, alpha_fn: Callable[[float], float] | None = None, gamma_fn: Callable[[float], float] | None = None, include_raman: bool = True, include_self_steepening: bool = False, include_tpa: bool = False, include_free_carriers: bool = False, check_phase_matching: bool = False, min_shrink_factor: float = 0.1, step_size: Length | None = None, betas_unit: BetasUnit = 'ps^k/m', tau_shock: float | None = None)

High-level GNLSE solver for z-dependent (tapered/dispersion-managed) waveguides.

Wraps a SplitStepEngine configured with z-dependent dispersion, nonlinearity, and loss. Exposes the same API as GNLSESolver.

Parameters:

Name	Type	Description	Default
`pulse`	`Wave`	Input pulse envelope.	required
`fiber`	`FiberProfile`	Fiber parameters (n2, alpha, etc.).	required
`dispersion_profile`	`ZDependentDispersion or callable`	β(ω, z) profile. Either a ZDependentDispersion table or a callable beta(omega: NDArray, z: float) -> NDArray.	required
`a_eff_fn`	`callable`	A_eff(z) in m². Falls back to fiber.A_eff if None.	`None`
`alpha_fn`	`callable`	α(z) in 1/m. Falls back to fiber.alpha if None.	`None`
`include_raman`	`bool`	Include Raman scattering. Default True.	`True`
`include_self_steepening`	`bool`	Include self-steepening (shock term). Default `False` (laserfun `NLSE` defaults to `shock=True`).	`False`
`include_tpa`	`bool`	Include two-photon absorption (legacy spatially-averaged model). Default False.	`False`
`include_free_carriers`	`bool`	Include the opt-in time-resolved TPA/free-carrier model (see :class:`SplitStepEngine`). Requires `fiber.beta_tpa` / `fiber.sigma_fca`. Default False.	`False`
`min_shrink_factor`	`float`	Floor for the gradient-based step shrink factor in z-dependent mode. Must be in (0, 1]. Default 0.1. Raise it (e.g. 0.3) to trade a small amount of accuracy for speed on tapers with mild dispersion gradients.	`0.1`
`betas_unit`	`('ps^k/m', 's^k/m', 'SI')`	Unit contract for dispersion coefficients. The tapered solver takes its dispersion from dispersion_profile (β(ω, z), SI), so this flag is validated for consistency with the other solvers but does not rescale a coefficient array. Default `"ps^k/m"`.	`"ps^k/m"`

pulse `instance-attribute` ¶

pulse = pulse

fiber `instance-attribute` ¶

fiber = fiber

betas_unit `instance-attribute` ¶

betas_unit = _validate_betas_unit(betas_unit)

step_size `instance-attribute` ¶

step_size = step_size

dispersion_profile `instance-attribute` ¶

dispersion_profile = dispersion_profile

a_eff_fn `instance-attribute` ¶

a_eff_fn = a_eff_fn

alpha_fn `instance-attribute` ¶

alpha_fn = alpha_fn

gamma_fn `instance-attribute` ¶

gamma_fn = gamma_fn

include_raman `instance-attribute` ¶

include_raman = include_raman

include_self_steepening `instance-attribute` ¶

include_self_steepening = include_self_steepening

include_tpa `instance-attribute` ¶

include_tpa = include_tpa

include_free_carriers `instance-attribute` ¶

include_free_carriers = include_free_carriers

check_phase_matching `instance-attribute` ¶

check_phase_matching = check_phase_matching

min_shrink_factor `instance-attribute` ¶

min_shrink_factor = min_shrink_factor

tau_shock `instance-attribute` ¶

tau_shock = float(tau_shock) if tau_shock is not None else None

evolution `property` ¶

evolution: list[Wave]

List of Wave objects at each propagation step.

z_array `property` ¶

z_array: NDArray

Array of propagation distances (m) for each evolution entry.

omega0 `property` ¶

omega0: float

Carrier angular frequency (rad/s).

spectra_vs_z `property` ¶

spectra_vs_z: tuple[NDArray, NDArray]

Tuple of (frequency array, spectra at each step).

energy_vs_z `property` ¶

energy_vs_z: NDArray

Pulse energy Σ|A|²·dt at each saved step (same length as z_array).

preflight_report `property` ¶

preflight_report: SimulationReadinessReport | None

Lazy preflight report from phase-matching assessment.

Builds and caches the report on first access when check_phase_matching=True. Returns None when disabled.

propagate ¶

propagate(num_steps: int = 100, strict: bool = False, *, nsaves: int | None = None, show_progress: bool = False, raman_noise: bool = False, noise_seed: int | None = None) -> None

Run split-step simulation for num_steps steps.

Parameters:

Name	Type	Default
`num_steps`	`int — number of split-step steps.`	`100`
`strict`	`bool — if True, raise ValueError on excessive β clipping (>5%).`	`False`
`nsaves`	`int, optional — evenly spaced snapshots along z (see SplitStepEngine).`	`None`
`show_progress`	bool — if True, show ``tqdm`` progress bars (requires tqdm).	`False`

kerr_step ¶

kerr_step(A: NDArray, fiber: FiberProfile, grid: TemporalGrid, dz: float, omega0: float) -> NDArray

Apply instantaneous Kerr effect: A ← A · exp(i·γ·|A|²·Δz).

Parameters:

Name	Type	Default
`A`	`complex array — pulse envelope.`	required
`fiber`	`FiberProfile — fiber parameters.`	required
`grid`	`TemporalGrid — time grid.`	required
`dz`	`float — step size (m).`	required
`omega0`	`float — carrier frequency (rad/s).`	required

Returns:

Name	Type	Description
`A`	`updated complex array.`

raman_step ¶

raman_step(A: NDArray, fiber: FiberProfile, grid: TemporalGrid, dz: float, include_raman: bool, omega0: float = 0.0) -> NDArray

Apply Raman convolution: P_NL = (1-fR)|A|² + fR·(h_R ⊗ |A|²).

Uses FFT-based circular convolution on the centered grid.t axis with the same grid.fft / grid.ifft convention as the split-step engine.

Parameters:

Name	Type	Default
`A`	`complex array — pulse envelope.`	required
`fiber`	`FiberProfile — fiber parameters.`	required
`grid`	`TemporalGrid — time grid.`	required
`dz`	`float — step size (m).`	required
`include_raman`	`bool — whether to include Raman.`	required
`omega0`	`float — carrier angular frequency (rad/s).`	`0.0`

Returns:

Name	Type	Description
`A`	`updated complex array (with Raman nonlinear polarization added).`

Raises:

Type	Description
`ValueError : if include_raman is True but fiber.raman_response is None.`

free_carrier_step ¶

free_carrier_step(A: NDArray, fiber: FiberProfile, grid: TemporalGrid, dz: float, N: NDArray | None, omega0: float) -> tuple[NDArray, NDArray | None]

Time-resolved TPA / free-carrier absorption step (opt-in).

Models the per-sample carrier population over the retarded-time grid (Soref & Bennett 1987; Cowan, Rieger & Young, Appl. Phys. Lett. 82, 1745 (2003); Yin & Agrawal, Opt. Lett. 32, 2951 (2007)):

∂A/∂z|_TPA = −(β_TPA/2) |A|² A — the standard TPA attenuation; in intensity form d|A|²/dz = −β_TPA |A|⁴, solved exactly per sample for a constant intensity within the step: |A|²(z+dz) = |A|² / (1 + β_TPA |A|² dz).

∂N/∂z = β_TPA |A|⁴/(2ħω₀) − N/(τ_c v) — carrier generation by TPA and recombination (v the envelope group velocity converts the retarded-time lifetime into a propagation length); integrated exactly per sample: N = N e^{−dz/L} + S·L·(1 − e^{−dz/L}) with L = τ_c v.

∂A/∂z|_FCA = −(σ_FCA/2) N A — free-carrier absorption, applied with the mid-step carrier density.

Out of scope (documented, not implemented): free-carrier refraction (the μ index term), carrier diffusion and drift.

Parameters:

Name	Type	Description	Default
`A`	`complex array — pulse envelope.`		required
`fiber`	FiberProfile — carries ``beta_tpa``, ``sigma_fca``,	`carrier_lifetime` and `group_velocity`.	required
`grid`	TemporalGrid — time grid (defines the sample axis of ``N``).		required
`dz`	`float — step size (m).`		required
`N`	`NDArray \| None — per-sample carrier density state from the previous`	steps, on the same grid. `None` (start of propagation init).	required
`omega0`	`float — carrier angular frequency (rad/s).`		required

Returns:

Type	Description
`(A, N) — updated field and carrier states.`

tpa_step ¶

tpa_step(A: NDArray, fiber: FiberProfile, grid: TemporalGrid, dz: float, include_tpa: bool, U: float = 0.0, omega0: float = 0.0) -> tuple[NDArray, float]

Apply two-photon absorption with carrier dynamics.

dA/dz = -σ·U·A dU/dz = σ·|A|²/(2ħω) - U/τ_c

Parameters:

Name	Type	Default
`A`	`complex array — pulse envelope.`	required
`fiber`	`FiberProfile — fiber parameters.`	required
`grid`	`TemporalGrid — time grid.`	required
`dz`	`float — step size (m).`	required
`include_tpa`	`bool — whether to include TPA.`	required
`U`	`float — current carrier density (W⁻¹·m⁻³). Default 0.`	`0.0`
`omega0`	`float — carrier angular frequency (rad/s). Required when include_tpa=True.`	`0.0`

Returns:

Name	Type	Description
`A`	`updated complex array.`
`U_new`	`updated carrier density.`

Raises:

Type	Description
`ValueError : if include_tpa=True and omega0 <= 0.`

spectral_evolution_on_wavelength_grid ¶

spectral_evolution_on_wavelength_grid(solver: GNLSESolver, wl_min: float, wl_max: float, n_wl: int) -> tuple[NDArray, NDArray, NDArray]

Interpolate stored spectra onto a uniform wavelength grid (nm).

Uses absolute angular frequency omega0 + grid.w before converting to wavelength. Returns spectra in dB normalized to the global peak.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with propagated results.	required
`wl_min`	`float`	Wavelength range (nm).	required
`wl_max`	`float`	Wavelength range (nm).	required
`n_wl`	`int`	Number of wavelength samples.	required

Returns:

Type	Description
`(z_m, wavelength_nm, spectra_dB)`	`z_m` has shape (n_z,), `wavelength_nm` (n_wl,), `spectra_dB` (n_z, n_wl).

spectral_evolution_on_frequency_grid ¶

spectral_evolution_on_frequency_grid(solver: GNLSESolver, f_min_THz: float, f_max_THz: float, n_f: int) -> tuple[NDArray, NDArray, NDArray]

Interpolate stored spectra onto a uniform absolute-frequency grid (THz).

Returns:

Type	Description
`(z_m, f_THz, spectra_dB)`	`spectra_dB` has shape (n_z, n_f), normalized to global peak = 0 dB.

temporal_evolution_intensity ¶

temporal_evolution_intensity(solver: GNLSESolver) -> tuple[NDArray, NDArray, NDArray]

Build |A(t)|² at each stored propagation step.

Returns:

Type	Description
`(z_m, t_ps, intensity)`	`intensity` has shape (n_z, N_time).

plot_waterfall ¶

plot_waterfall(solver: GNLSESolver, ax=None, dB: bool = True, offset_scale: float = 1.0) -> plt.Figure

Pulse envelope waterfall plot (envelope vs propagation distance).

Each saved trace i is drawn as y_norm + i * offset_scale where y_norm is the trace normalized to unit range (0..1 linear, or -1..0 for dB scaled by 90 dB). Y-tick labels show the propagation distance of each trace, so offsets are documented and interpretable.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with propagated results.	required
`ax`	`matplotlib Axes`	Axis to plot on. Creates new figure if None.	`None`
`dB`	`bool`	Plot in dB scale. Default True.	`True`
`offset_scale`	`float`	Vertical spacing between consecutive traces in normalized units. Must be > 0. Default 1.0.	`1.0`

Returns:

Name	Type	Description
`fig`	`matplotlib Figure`

plot_spectrum_vs_distance ¶

plot_spectrum_vs_distance(solver: GNLSESolver, ax=None, dB: bool = True) -> plt.Figure

Spectrum vs propagation distance contour (legacy wrapper).

See :func:plot_spectral_evolution for wavelength range and dynamic-range control. Uses millimetres on the distance axis and the hot colormap for backward compatibility.

plot_spectral_evolution ¶

plot_spectral_evolution(solver: GNLSESolver, ax=None, *, wl_min: float | None = None, wl_max: float | None = None, f_min_THz: float | None = None, f_max_THz: float | None = None, n_points: int = 400, dynamic_range_db: float = 40.0, dB: bool = True, cmap: str = 'viridis', z_scale: str = 'm', use_imshow: bool = True) -> plt.Figure

Spectral evolution contour: wavelength or frequency vs propagation distance.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with propagated results.	required
`ax`	`matplotlib Axes`	Axis to plot on. Creates new figure if None.	`None`
`wl_min`	`float`	Wavelength limits (nm) when plotting vs wavelength.	`None`
`wl_max`	`float`	Wavelength limits (nm) when plotting vs wavelength.	`None`
`f_min_THz`	`float`	Absolute frequency limits (THz) when plotting vs frequency. If both frequency limits are set they take precedence over wavelength.	`None`
`f_max_THz`	`float`	Absolute frequency limits (THz) when plotting vs frequency. If both frequency limits are set they take precedence over wavelength.	`None`
`n_points`	`int`	Number of samples along the spectral axis.	`400`
`dynamic_range_db`	`float`	Color scale spans [global_max - dynamic_range_db, global_max] in dB.	`40.0`
`dB`	`bool`	Plot log-scale intensity (recommended). If False, plots linear power.	`True`
`cmap`	`str`	Matplotlib colormap name.	`'viridis'`
`z_scale`	`str`	`"m"` for metres on the distance axis, `"mm"` for millimetres.	`'m'`
`use_imshow`	`bool`	If True, use `imshow` with `origin='lower'` (laserfun style).	`True`

Returns:

Name	Type	Description
`fig`	`matplotlib Figure`

plot_temporal_evolution ¶

plot_temporal_evolution(solver: GNLSESolver, ax=None, *, t_min: float | None = None, t_max: float | None = None, dynamic_range_db: float = 40.0, cmap: str = 'viridis', z_scale: str = 'm', use_imshow: bool = True, time_reversal: bool = False) -> plt.Figure

Temporal evolution contour: time vs propagation distance.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with propagated results.	required
`ax`	`matplotlib Axes`	Axis to plot on. Creates new figure if None.	`None`
`t_min`	`float`	Time window in ps (in the plotted convention). Default: full grid.	`None`
`t_max`	`float`	Time window in ps (in the plotted convention). Default: full grid.	`None`
`dynamic_range_db`	`float`	Color scale spans [global_max - dynamic_range_db, global_max] in dB.	`40.0`
`cmap`	`str`	Matplotlib colormap name.	`'viridis'`
`z_scale`	`str`	`"m"` or `"mm"` for the distance axis.	`'m'`
`time_reversal`	`bool`	Kept for back-compatibility with pre-#0 notebooks; default False. Post-ISSUES.md #0 the internal time grid ALREADY uses the standard literature (Agrawal) comoving direction -- Raman-shifted solitons appear at positive delay without any flip (chirp and spectra are unaffected). Set True only to reproduce the historical (pre-#0) mirrored axis.	`False`

Returns:

Name	Type	Description
`fig`	`matplotlib Figure`

plot_scg_dashboard ¶

plot_scg_dashboard(*, z_axis: NDArray, wl_nm: NDArray, spec_db: NDArray, t_ps: NDArray, int_db: NDArray, out_wl_nm: NDArray, out_spec_db: NDArray, out_t_ps: NDArray, out_int_db: NDArray, spec_labels: NDArray, t_labels: NDArray, title: str = '', z_label: str = 'Distance (m)', wl_bounds: tuple[float, float] | None = None, t_bounds: tuple[float, float] | None = None, dynamic_range_db: float = 40.0, colorscale: str = 'Jet', annotate_features: bool = True, height: int = 850) -> FigureLike

Interactive four-panel Plotly SCG dashboard with feature hover labels.

Layout: output line profiles (a) intensity (dB) vs wavelength and (b) intensity (dB) vs time on top, with the taller (c) spectral and (d) temporal evolution heatmaps below. Hovering a heatmap cell reports wavelength/time, distance, power and the local feature class.

This is the low-level array consumer used by :func:plot_spectral_temporal_summary with plotly=True and by the Dudley Fig. 3 reproduction (which stores an Evolution rather than a solver). Requires the optional plotly dependency.

Parameters:

Name	Type	Description	Default
`z_axis`	`NDArray`	Propagation-distance values for the heatmap y axis.	required
`wl_nm`	`NDArray`	Uniform wavelength grid (nm) for the spectral heatmap columns.	required
`spec_db`	`(NDArray, shape(n_z, n_wl))`	Spectral density in dB (peak 0, clipped to the dynamic range).	required
`t_ps`	`NDArray`	Time grid (ps, plotted convention) for the temporal heatmap columns.	required
`int_db`	`(NDArray, shape(n_z, n_time))`	Temporal intensity in dB (peak 0, clipped to the dynamic range).	required
`out_wl_nm`	`NDArray`	Output spectrum line for panel (a).	required
`out_spec_db`	`NDArray`	Output spectrum line for panel (a).	required
`out_t_ps`	`NDArray`	Output intensity line for panel (b).	required
`out_int_db`	`NDArray`	Output intensity line for panel (b).	required
`spec_labels`	`NDArray`	Per-wavelength feature labels, shape `(n_wl,)` or `(n_z, n_wl)`.	required
`t_labels`	`NDArray`	Per-time feature labels, shape `(n_time,)` or `(n_z, n_time)`.	required
`title`	`str`	Figure title.	`''`
`z_label`	`str`	Label for the heatmap distance axis.	`'Distance (m)'`
`wl_bounds`	`(float, float)`	Axis ranges; default to the extent of the supplied grids.	`None`
`t_bounds`	`(float, float)`	Axis ranges; default to the extent of the supplied grids.	`None`
`dynamic_range_db`	`float`	Colour-axis floor (dB).	`40.0`
`colorscale`	`str`	Plotly colorscale name (e.g. `"Jet"`, `"Viridis"`).	`'Jet'`
`annotate_features`	`bool`	Mark the strongest cell of each feature class.	`True`
`height`	`int`	Figure height in pixels.	`850`

Returns:

Type	Description
`Figure`

plot_spectral_temporal_summary ¶

plot_spectral_temporal_summary(solver: GNLSESolver, *, wl_bounds: tuple[float, float] | None = None, wl_min: float | None = None, wl_max: float | None = None, t_bounds: tuple[float, float] | None = None, t_min: float | None = None, t_max: float | None = None, dynamic_range_db: float = 40.0, cmap: str = 'jet', z_scale: str = 'm', time_reversal: bool = False, height_ratios: tuple[float, float] = (1.0, 1.7), figsize: tuple[float, float] = (11.0, 9.0), n_points: int = 500, plotly: bool = False) -> FigureLike

Four-panel GNLSE summary with line profiles on top and dense plots below.

Layout

(a) output intensity (dB) vs wavelength — line (b) output intensity (dB) vs time — line (c) spectral evolution — density plot (taller) (d) temporal evolution — density plot (taller)

The two contour panels occupy a larger fraction of the figure (height_ratios) because their dynamic range carries the SC dynamics; the line profiles give a quantitative, easily read complement.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with stored fields (call :meth:`propagate` first).	required
`wl_bounds`	`(float, float)`	Wavelength window in nm. Defaults to the carrier ± 50 %.	`None`
`wl_min`	`float`	Individual overrides used only when wl_bounds is None.	`None`
`wl_max`	`float`	Individual overrides used only when wl_bounds is None.	`None`
`t_bounds`	`(float, float)`	Time window in ps (plotted convention). Defaults to the full grid.	`None`
`t_min`	`float`	Individual overrides used only when t_bounds is None.	`None`
`t_max`	`float`	Individual overrides used only when t_bounds is None.	`None`
`dynamic_range_db`	`float`	Colour/floor range below the peak for the density plots and the line profiles.	`40.0`
`cmap`	`str`	Matplotlib colormap for the density plots.	`'jet'`
`z_scale`	`('m', 'cm', 'mm')`	Propagation-distance unit on the density-plot y axes.	`"m"`
`time_reversal`	`bool`	Use the standard literature (Agrawal/Dudley) comoving time (default).	`False`
`height_ratios`	`(float, float)`	Relative heights of the line row and the (taller) contour row.	`(1.0, 1.7)`
`figsize`	`(float, float)`	Figure size in inches.	`(11.0, 9.0)`
`n_points`	`int`	Spectral samples used by the Plotly path.	`500`
`plotly`	`bool`	If True, return an interactive `plotly.graph_objects.Figure` whose heatmap hover labels each cell as DW / SPM / Raman soliton (see :func:`plot_scg_dashboard`). `write_html` it for a standalone page, or use :func:`save_summary_html`.	`False`

Returns:

Name	Type	Description
`fig`	`matplotlib Figure or plotly Figure`	The assembled figure (not closed), so the caller can adjust it.

save_summary_html ¶

save_summary_html(solver: GNLSESolver, path, **kwargs) -> Path

Render the interactive summary and write a standalone HTML file.

Builds :func:plot_spectral_temporal_summary with plotly=True and writes a self-contained .html document (Plotly.js loaded from the CDN). This is the automated path that turns a propagated solver into the interactive Fig. 3-style dashboard described in the reproduction docs.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with stored fields.	required
`path`	`str or Path`	Output HTML path; parent directories are created.	required
`**kwargs`		Forwarded to :func:`plot_spectral_temporal_summary` (for example `wl_bounds`, `t_bounds`, `dynamic_range_db`).	`{}`

Returns:

Type	Description
`Path`	The written path.

gnlse_spectrogram ¶

gnlse_spectrogram(solver: GNLSESolver, *, gate: NDArray | None = None, n_delays: int = 161, delay_span_ps: float | None = None, snapshot: int = -1, wl_bounds: tuple[float, float] | None = None, n_wavelength: int = 500, time_reversal: bool = False) -> tuple[NDArray, NDArray, NDArray]

Cross-correlation spectrogram of a propagated field (GNLSE Eq. 4).

Computes

Σ(Ω, τ) = |∫ E(t) g(t − τ) e^{−iΩt} dt|²

with the complex envelope E(t) taken from the last stored field (or snapshot) and a real gate g (by default the input pulse envelope, as in Dudley et al., Rev. Mod. Phys. 78, 1135 (2006), Fig. 10). This is the cross-correlation FROG trace, not a conventional STFT: the gate is the actual pulse rather than a fixed window, and the trace preserves the relative phase information of the pulse.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with stored fields (call :meth:`propagate` first).	required
`gate`	`NDArray`	Real gate sampled on `solver.pulse.grid.t`. Defaults to the input pulse envelope `real(E_in(t))`.	`None`
`n_delays`	`int`	Number of delay samples.	`161`
`delay_span_ps`	`float`	Half-range of the delay axis in ps. Defaults to 40 % of the full temporal window.	`None`
`snapshot`	`int`	Index into `solver.evolution` of the field to analyse (default last).	`-1`
`wl_bounds`	`(float, float)`	Wavelength window `(wl_min, wl_max)` in nm. Defaults to the carrier wavelength ± 50 %, i.e. `(0.5·λ0, 1.5·λ0)`; pass an explicit tuple to zoom or widen.	`None`
`n_wavelength`	`int`	Number of samples on the uniform wavelength grid.	`500`
`time_reversal`	`bool`	Kept for back-compatibility with pre-#0 notebooks; default False. Post-ISSUES.md #0 the internal time grid already uses the standard literature (Agrawal) comoving time `T` (Raman red-shift -> positive delay); spectra and the Raman red-shift are unaffected either way. Set True only to reproduce the historical (pre-#0) mirrored axis.	`False`

Returns:

Name	Type	Description
`delay_ps`	`(NDArray, shape(n_delays))`
`wavelength_nm`	`(NDArray, shape(n_wavelength))`
`spectrogram`	`(NDArray, shape(n_delays, n_wavelength))`	Power spectrogram (arb. units; normalise with its maximum).

plot_spectrogram ¶

plot_spectrogram(solver: GNLSESolver, ax=None, *, gate: NDArray | None = None, n_delays: int = 161, delay_span_ps: float | None = None, snapshot: int = -1, wl_bounds: tuple[float, float] | None = None, dynamic_range_db: float = 40.0, cmap: str = 'jet', with_projections: bool = False, t_min: float | None = None, t_max: float | None = None, time_reversal: bool = False, plotly: bool = False, annotate_features: bool = True) -> FigureLike

Plot the supercontinuum spectrogram (Dudley et al. Fig. 10 style).

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with stored fields.	required
`ax`	`matplotlib Axes`	Axis for the spectrogram when `with_projections=False` and `plotly=False`.	`None`
`wl_bounds`	`(float, float)`	Wavelength window `(wl_min, wl_max)` in nm. Defaults to the carrier ± 50 %.	`None`
`with_projections`	`bool`	If True, build a matplotlib figure with the spectrogram plus its temporal (bottom) and spectral (right) projections (ignores `ax`).	`False`
`t_min`	`float`	Delay limits in ps (defaults to the full delay span).	`None`
`t_max`	`float`	Delay limits in ps (defaults to the full delay span).	`None`
`time_reversal`	`bool`	Use the standard literature (Agrawal) comoving time (default True).	`False`
`plotly`	`bool`	If True, return an interactive `plotly.graph_objects.Figure` instead of a matplotlib figure. The hover text labels each `(delay, λ)` cell as a dispersive wave, SPM/pump, or Raman soliton, and (with `annotate_features=True`) the strongest cell of each class is marked.	`False`
`annotate_features`	`bool`	Add feature labels in the Plotly path. Ignored for matplotlib.	`True`

Returns:

Name	Type	Description
`fig`	`matplotlib Figure or plotly Figure`	The figure, so the caller can adjust axes/labels afterwards.

plot_intensity_metrics ¶

plot_intensity_metrics(solver: GNLSESolver, ax=None) -> plt.Figure

Peak power and pulse width vs propagation distance.

Parameters:

Name	Type	Description	Default
`solver`	`GNLSESolver`	Solver with propagated results.	required
`ax`	`matplotlib Axes`	Axis to plot on. Creates new figure with two subplots if None.	`None`

Returns:

Name	Type	Description
`fig`	`matplotlib Figure`

Generalized nonlinear Schrödinger equation¶

photonics_helper.gnlse ¶

BetasUnit module-attribute ¶

FigureLike module-attribute ¶

HBAR_J_S module-attribute ¶

FiberProfile dataclass ¶

n2 instance-attribute ¶

alpha instance-attribute ¶

A_eff instance-attribute ¶

length instance-attribute ¶

confinement_factor class-attribute instance-attribute ¶

sigma_tpa class-attribute instance-attribute ¶

carrier_lifetime class-attribute instance-attribute ¶

raman_response class-attribute instance-attribute ¶

beta_tpa class-attribute instance-attribute ¶

sigma_fca class-attribute instance-attribute ¶

group_velocity class-attribute instance-attribute ¶

from_gamma classmethod ¶

SplitStepEngine ¶

pulse instance-attribute ¶

fiber instance-attribute ¶

betas instance-attribute ¶

include_raman instance-attribute ¶

include_self_steepening instance-attribute ¶

include_tpa instance-attribute ¶

include_free_carriers instance-attribute ¶

conserving_shock instance-attribute ¶

step_size instance-attribute ¶

gamma_fn instance-attribute ¶

grid instance-attribute ¶

omega0 instance-attribute ¶

A instance-attribute ¶

evolution instance-attribute ¶

tau_shock property ¶

z_array property ¶

spectra_vs_z property ¶

energy_vs_z property ¶

propagate ¶

GNLSESolver ¶

pulse instance-attribute ¶

fiber instance-attribute ¶

betas instance-attribute ¶

betas_unit instance-attribute ¶

include_raman instance-attribute ¶

include_self_steepening instance-attribute ¶

include_tpa instance-attribute ¶

include_free_carriers instance-attribute ¶

check_phase_matching instance-attribute ¶

step_size instance-attribute ¶

conserving_shock instance-attribute ¶

tau_shock instance-attribute ¶

evolution property ¶

z_array property ¶

omega0 property ¶

spectra_vs_z property ¶

energy_vs_z property ¶

preflight_report property ¶

propagate ¶

estimate_num_steps classmethod ¶

interpolated_spectrum_db ¶

TaperedGNLSESolver ¶

pulse instance-attribute ¶

fiber instance-attribute ¶

betas_unit instance-attribute ¶

step_size instance-attribute ¶

dispersion_profile instance-attribute ¶

a_eff_fn instance-attribute ¶

alpha_fn instance-attribute ¶

gamma_fn instance-attribute ¶

include_raman instance-attribute ¶

include_self_steepening instance-attribute ¶

include_tpa instance-attribute ¶

include_free_carriers instance-attribute ¶

check_phase_matching instance-attribute ¶

min_shrink_factor instance-attribute ¶

tau_shock instance-attribute ¶

evolution property ¶

z_array property ¶

omega0 property ¶

spectra_vs_z property ¶

BetasUnit `module-attribute` ¶

FigureLike `module-attribute` ¶

HBAR_J_S `module-attribute` ¶

FiberProfile `dataclass` ¶

n2 `instance-attribute` ¶

alpha `instance-attribute` ¶

A_eff `instance-attribute` ¶

length `instance-attribute` ¶

confinement_factor `class-attribute` `instance-attribute` ¶

sigma_tpa `class-attribute` `instance-attribute` ¶

carrier_lifetime `class-attribute` `instance-attribute` ¶

raman_response `class-attribute` `instance-attribute` ¶

beta_tpa `class-attribute` `instance-attribute` ¶

sigma_fca `class-attribute` `instance-attribute` ¶

group_velocity `class-attribute` `instance-attribute` ¶

from_gamma `classmethod` ¶

pulse `instance-attribute` ¶

fiber `instance-attribute` ¶

betas `instance-attribute` ¶

include_raman `instance-attribute` ¶

include_self_steepening `instance-attribute` ¶

include_tpa `instance-attribute` ¶

include_free_carriers `instance-attribute` ¶

conserving_shock `instance-attribute` ¶

step_size `instance-attribute` ¶

gamma_fn `instance-attribute` ¶

grid `instance-attribute` ¶

omega0 `instance-attribute` ¶

A `instance-attribute` ¶

evolution `instance-attribute` ¶

tau_shock `property` ¶

z_array `property` ¶

spectra_vs_z `property` ¶

energy_vs_z `property` ¶

pulse `instance-attribute` ¶

fiber `instance-attribute` ¶

betas `instance-attribute` ¶

betas_unit `instance-attribute` ¶

include_raman `instance-attribute` ¶

include_self_steepening `instance-attribute` ¶

include_tpa `instance-attribute` ¶

include_free_carriers `instance-attribute` ¶

check_phase_matching `instance-attribute` ¶

step_size `instance-attribute` ¶

conserving_shock `instance-attribute` ¶

tau_shock `instance-attribute` ¶

evolution `property` ¶

z_array `property` ¶

omega0 `property` ¶

spectra_vs_z `property` ¶

energy_vs_z `property` ¶

preflight_report `property` ¶

estimate_num_steps `classmethod` ¶

pulse `instance-attribute` ¶

fiber `instance-attribute` ¶

betas_unit `instance-attribute` ¶

step_size `instance-attribute` ¶

dispersion_profile `instance-attribute` ¶

a_eff_fn `instance-attribute` ¶

alpha_fn `instance-attribute` ¶

gamma_fn `instance-attribute` ¶

include_raman `instance-attribute` ¶

include_self_steepening `instance-attribute` ¶

include_tpa `instance-attribute` ¶

include_free_carriers `instance-attribute` ¶

check_phase_matching `instance-attribute` ¶

min_shrink_factor `instance-attribute` ¶

tau_shock `instance-attribute` ¶

evolution `property` ¶

z_array `property` ¶

omega0 `property` ¶

spectra_vs_z `property` ¶

energy_vs_z `property` ¶

preflight_report `property` ¶