# SPDX-FileCopyrightText: 2026 John C. Travers and contributors
#
# SPDX-License-Identifier: GPL-3.0-or-later

r"""
Cross-phase modulation in the deep ultraviolet
==============================================

A strong pulse modulates the refractive index seen by any other pulse that overlaps
it. In the co-polarised, constant-susceptibility approximation used here,
the Kerr index change seen by a weak probe is :math:`2 n_2 I_\text{pump}(t)`, twice
the self-phase modulation coefficient, and a weak probe acquires a time-dependent
phase that broadens its spectrum -- **cross-phase modulation** (XPM). Because the
two pulses travel at different group velocities they slide through each other, and
the broadening a probe acquires depends on where it starts relative to the pump: a
probe that is overtaken by the pump sees the whole of the pump's intensity profile
sweep across it, and its spectrum is broadened, and shifted, most.

This makes XPM a way to broaden and compress pulses at wavelengths where direct
self-phase modulation is impractical. Here a weak deep-ultraviolet seed at 267 nm
(40 fs, 200 uJ) is spectrally broadened by a strong near-infrared pump at 800 nm (42 fs,
1 mJ) in a 1 m capillary of 125 um core radius filled with neon at 1.5 bar. The pump is
launched 60 fs *after* the seed (``t0=60e-15``); the ultraviolet seed is slower, so
the pump catches it up and passes through it along the fibre.

**What to look for.** In time, the pump overtakes the seed within the first part of
the fibre. The seed's spectrum around 267 nm broadens far more than it would alone,
with a pronounced asymmetry set by the direction of the walk-off; the pump itself is
modified much less.

**What is approximate.** Only the fundamental mode is carried; photoionisation of
neon is included but small at these intensities.

This is panel (d) of the survey of nonlinear processes in the review by Travers et
al.; the scheme is described by Jiang et al., Optica 11, 291 (2024).

See :doc:`pulses and relative timing </guide/setup/pulses>` for the two-pulse
launch and :doc:`/guide/media/dispersive-kerr` for the limitations of using one
electronic coefficient across widely separated colours.
"""

# %%
# The run
# -------

import time

import matplotlib.pyplot as plt
import numpy as np

from solprop.driver import prop_capillary
from solprop.plotting import prop_2d, spec_1d, time_1d
from solprop.processing import get_spectral_density
from solprop.pulses import GaussianPulse

pump = GaussianPulse(wavelength=800e-9, fwhm=42e-15, energy=1e-3, t0=60e-15)
seed = GaussianPulse(wavelength=267e-9, fwhm=40e-15, energy=200e-6)

started = time.perf_counter()
run = prop_capillary(
    125e-6,
    1.0,
    "Ne",
    1.5,
    lambda0=800e-9,
    pulses=[pump, seed],
    trange=800e-15,
    wavelength_limits=(200e-9, 3e-6),
    n_save=301,
    progress="none",
)

# %%
# Spectral and temporal evolution
# -------------------------------

figures = prop_2d(
    run,
    "wavelength",
    wavelength_range=(200e-9, 1.2e-6),
    trange=(-100e-15, 200e-15),
    db_min=-40,
)
figures[-1].set_size_inches(9.5, 3.6)
figures[-1].tight_layout()

# %%
# The seed's spectrum
# -------------------
# The ultraviolet part of the spectrum at the entrance and the exit, and the pulses in
# time at both ends.

fig, (left, right) = plt.subplots(1, 2, figsize=(10.0, 3.6))
time_1d(run, z=[0.0, 1.0], trange=(-100e-15, 200e-15), ax=left)
spec_1d(run, z=[0.0, 1.0], ax=right, wavelength_range=(200e-9, 350e-9), log=False)
fig.tight_layout()


def rms_width(wavelength, density, band):
    """Return the rms spectral width of the density inside a wavelength band, m."""
    inside = (wavelength > band[0]) & (wavelength < band[1])
    weights = density[inside] / np.sum(density[inside])
    mean = np.sum(weights * wavelength[inside])
    return float(np.sqrt(np.sum(weights * (wavelength[inside] - mean) ** 2)))


band = (200e-9, 350e-9)
before = rms_width(*get_spectral_density(run, "wavelength", plane=0), band)
after = rms_width(*get_spectral_density(run, "wavelength", plane=-1), band)
print(
    f"rms width of the ultraviolet seed: {before * 1e9:.2f} nm at the entrance, "
    f"{after * 1e9:.2f} nm at the exit ({after / before:.1f} times)"
)

# %%
# Runtime and reproducibility
# ----------------------------

print(f"{time.perf_counter() - started:.0f} s; backend {run.metadata.backend.name}")