# Hydrated Electrons in Phase-Matching Generation of Second-Order Stokes X-Waves in Water

## TL;DR

The paper studies how hydrated electrons in water influence the generation of second-order Stokes X-waves through phase-matching and four-wave mixing processes.

## Contribution

The study reveals the role of hydrated electrons in inducing angle-dependent phase-matching for off-axis X-waves and their impact on Raman shifts.

## Key findings

- Near-axis and off-axis X-waves showed opposite emission angle evolution with increasing pump energy.
- Hydrated electrons from cascade ionization caused phase-matching for off-axis X-waves.
- Anomalous Raman shifts at second-order Stokes wavelengths were linked to electron injection into water's hydrogen bond network.

## Abstract

Two components of X-waves, near-axis and off-axis, were observed in the generation of second-order Stokes around 550 nm, excited by intense 400 nm, 100 fs pump pulses in a 50 cm water cuvette. The emission angles of these two X-waves exhibited different evolutions; when the pump energy increased, the emission angle of the near-axis X-wave increased, while that of the off-axis X-wave decreased. These abnormal features of second-order X-waves came from the four-wave mixing process, accompanied by induced intense hydrated electrons via cascade ionization. The induced wave vector from high-density hydrated electrons led to angle-dependent phase-matching for the generation of the off-axis X-wave. However, for the generation of the near-axis X-wave, the induced wave vector from hydrated electrons initially compensated for the phase mismatch at a low pump energy, but as the energy increased, the phase mismatch also increased. Moreover, anomalous Raman shifts at second-order Stokes wavelengths (3262 cm−1 and 3350 cm−1) exhibited a similar evolutionary process to the anomalous Raman peaks at the Stokes wavelengths. The shifts arose from excess electrons being injected into the hydrogen bond network of water clusters.