[Paper Review] The mechanism of high harmonic generation in liquid alcohol

Oliver Alexander, Jonathan C. T. Barnard+11 more|arXiv (Cornell University)|Feb 25, 2022

Spectroscopy and Quantum Chemical Studies4 citations

TL;DR

This study demonstrates high harmonic generation (HHG) in liquid isopropanol using few-cycle, carrier-envelope-phase-controlled laser pulses below the breakdown threshold, achieving XUV emission up to 50 eV. The mechanism is identified as strong-field recombination, with electron scattering in the liquid environment encoded in the harmonic spectra, enabling in situ measurement of reduced scattering cross sections compared to the gas phase.

ABSTRACT

The observation of non-perturbative harmonic emission in solids from ultrashort laser pulses [1] sparked a wave of studies [2,3] as a probe of charge carrier dynamics in solids under strong fields and a route to extreme ultraviolet (XUV) attosecond photonic devices [4]. High harmonic generation (HHG) in liquids [5,6] is far less explored, despite their relevance to biological media, and the mechanism is hotly debated. Using few-cycle pulses below the breakdown threshold, we demonstrate HHG in alcohol with data showing carrier-envelope-phase-dependent XUV spectra extending to 50 eV from isopropanol. We study the mechanism of the harmonic emission through its dependence on the driving field and find it to be consistent with a strong-field recombination mechanism. This maps emitted photon energy to the electron trajectories. We explore the role of the liquid environment in scattering the trajectories and find evidence that information on electron scattering from neighbouring molecules is encoded in the harmonic spectra. Using simulations we exploit this to estimate the scattering cross section and we confirm that the cross-section in liquid isopropanol is significantly reduced compared to vapour. Our findings suggest an extit{in situ} measurement strategy for retrieving accurate values of scattering cross sections in liquids, and also a pathway to liquid-based attosecond XUV devices.

Motivation & Objective

• To investigate the mechanism of high harmonic generation (HHG) in liquid alcohol, particularly in the non-perturbative regime.
• To determine whether HHG in liquids follows a strong-field recombination mechanism similar to gases and solids.
• To explore how the dense liquid environment affects electron dynamics and harmonic emission.
• To extract accurate scattering cross sections in liquids by comparing experimental HHG spectra with simulations.
• To establish a pathway for in situ measurement of electron-molecule scattering in condensed phases using HHG as a probe.

Proposed method

• Few-cycle, CEP-controlled, 1.8 µm laser pulses with energies from 100–350 µJ are focused into a <2 µm thick liquid sheet of isopropanol in vacuum.
• Harmonic emission is detected using a flat-field XUV spectrometer with calibration via metallic absorption edges (Al, Zr, Sn) at 15, 25, 55, and 72 eV.
• A billiard-ball model is used to calculate the probability of electron non-scattering along classical trajectories: $ p_{ ext{n.s.}} = e^{- ho_N k au ar{v}} $, where $ ho_N $ is number density, $ k $ scales empirical cross sections for liquid effects, and $ ar{v} $ is average velocity.
• The scattering probability per unit time is modeled as $ p_{ ext{scat}}(t) = ho_N k au v(t) $, with $ au $ as effective cross-sectional area and $ v(t) $ as trajectory velocity.
• Numerical simulations use a 3D split-step method solving the forward Maxwell equation with cylindrical symmetry, including dispersion, diffraction, nonlinearity, and plasma dephasing.
• Single-atom HHG dipoles are computed using the strong field approximation with stationary phase integration over momentum and birth time, followed by spatial integration accounting for density, absorption, and diffraction.

Experimental results

Research questions

• RQ1 Does high harmonic generation in liquid alcohol follow a strong-field recombination mechanism, as seen in gases and solids?
• RQ2 How does the dense liquid environment—characterized by high molecular density and short intermolecular distances—affect electron trajectories and harmonic emission?
• RQ3 Can the harmonic spectrum encode information about electron-molecule scattering in liquids, particularly regarding scattering cross sections?
• RQ4 To what extent are scattering cross sections in liquids reduced compared to the gas phase due to screening, correlation, and exchange effects?
• RQ5 Can experimental HHG spectra be used to infer accurate scattering cross sections in liquids through comparison with simulations?

Key findings

• High harmonic generation in liquid isopropanol is observed up to 50 eV in photon energy using few-cycle pulses below the breakdown threshold.
• The harmonic spectra exhibit carrier-envelope-phase dependence, confirming a non-perturbative, recombination-driven mechanism.
• Electron scattering in the liquid phase reduces the effective scattering cross section by a factor of ~2.5 compared to the gas phase, as inferred from simulation-experiment comparison.
• The simulation-derived scattering cross section in liquid isopropanol is significantly lower than empirical gas-phase values, indicating strong screening and correlation effects.
• The harmonic cutoff energy scales linearly with laser intensity, consistent with the classical cutoff law $ ilde{ ext{E}}_{ ext{max}} = I_{ ext{pot}} + 3.17U_{ ext{ponder}} $, supporting recombination dynamics.
• Temporal apodization is effective in suppressing long trajectories, reducing computational cost while preserving accuracy in macroscopic harmonic field calculation.