Two-dimensional phase cartography for high-harmonic spectroscopy

Antoine Camper,Nan Lin,Thierry Auguste,Vincent Gruson,Bertrand Carré,Richard Taïeb,Robert R Lucchese,Pascal Salières,Alfred Maquet,Romain Géneaux,Emmanouil Skantzakis,Zsolt Diveki,Jérémie Caillat,Elizabeth English,François Risoud,Thierry Ruchon

doi:10.1364/optica.403859

Abstract

Extremely nonlinear spectroscopy based on high-order-harmonic generation has become a powerful investigation method for attosecond dynamics in gas and solid targets. In particular, the phase of harmonic emission was shown to carry profound insight into atomic and molecular structure and dynamics. However, current techniques offer phase measurements only along specific directions, thus providing partial characterization. Here we report on a new approach combining optical and quantum interferometers measuring along two dimensions the intensity and phase of harmonic emission from aligned molecules in the exact same experimental conditions. This two-dimensional cartography technique measures the phase with no arbitrary offset and no uncertainty on its sign. Measurements along different dimensions can be combined in two ways: either a single mapping or a redundant mapping allowing high-precision phase recovery using a Shack–Hartmann-like algorithm. We demonstrate both methods in a nitrogen test case, which allows disentangling structural and dynamical effects. Two-dimensional phase cartography paves the way to high-resolution high-harmonic spectroscopy for applications such as quantum orbital tomography and attosecond charge migration in molecules.

Highlights

High-harmonic spectroscopy (HHS) has opened the perspective of studying electronic and nuclear motion in all states of matter with both attosecond and Ångström resolution
This qualitatively reproduces the experimental trends for both phases and amplitudes. This is an indication of the A-channel (HOMO-1) contribution at large angles and high orders, interfering with the X-channel (HOMO) contribution, which results in phase jumps and intensity minima in the harmonic emission
The 2D phase cartography presented and qualified here in nitrogen allowed disentangling structural and dynamical effects that had led to conflicting interpretations

Summary

INTRODUCTION

High-harmonic spectroscopy (HHS) has opened the perspective of studying electronic and nuclear motion in all states of matter with both attosecond and Ångström resolution. Only one attempt at mapping the phase of the harmonic emission in two dimensions, called linked attosecond phase interferometry (LAPIN), has been published [32] This pioneering work based on the combination of TSI and gas mixing provides the phase difference with a reference gas, which allows performing molecular orbital tomography. CHASSEUR links every pair of coordinates of the macroscopic momentum space by one path only, whereas in MAMMOTH, the multiple connections between coordinates contained in the redundant information are combined using a Shack–Hartmannlike algorithm In both cases and in contrast to techniques such as gas mixing [26] and transient grating [27], the sign of the resulting phase map defined as φ(θ, hν) − φ(θ0, hν0) is resolved. The experimental results are compared to simulations based on the quantitative rescattering (QRS) theory [33,34], and reveal the interplay between structural and dynamical effects in the 20–40 eV spectral range

PRINCIPLE OF 2D PHASE CARTOGRAPHY

RECONSTRUCTION OF BIDIMENSIONAL PHASE MAPS

DISCUSSION

CONCLUSION AND OUTLOOK