High-order harmonic generation from the dressed autoionizing states

Abstract

In high-order harmonic generation, resonant harmonics (RH) are sources of intense, coherent extreme-ultraviolet radiation. However, intensity enhancement of RH only occurs for a single harmonic order, making it challenging to generate short attosecond pulses. Moreover, the mechanism involved behind such RH was circumstantial, because of the lack of direct experimental proofs. Here, we demonstrate the exact quantum paths that electron follows for RH generation using tin, showing that it involves not only the autoionizing state, but also a harmonic generation from dressed-AIS that appears as two coherent satellite harmonics at frequencies ±2Ω from the RH (Ω represents laser frequency). Our observations of harmonic emission from dressed states open the possibilities of generating intense and broadband attosecond pulses, thus contributing to future applications in attosecond science, as well as the perspective of studying the femtosecond and attosecond dynamics of autoionizing states.

Figure 1. High-order harmonic spectra with tunable driving laser.

The extreme-ultraviolet spectra measured at different driving laser wavelengths ranging from 1.81 μm to 1.89 μm. Maximum harmonic intensity is observed for a pulse centred at 1.84 μm, as this wavelength is exactly 39-photon resonant with the 4d¹⁰5s²5p→4d⁹5s²5p² transition of Sn⁺. The harmonic intensity then decreases rapidly as the central driving laser wavelength is detuned. The driving laser intensity for these spectra is maintained at ∼1.3 × 10¹⁴ W cm⁻².

Figure 2. Overlap of resonant harmonic and direct harmonic at resonant energy.

High-order harmonic spectrum of Sn⁺ at 1.75 μm driving laser wavelength, showing that the stronger resonant harmonic (RH) and relatively weak direct harmonic (DH) are overlapped with each other at energy∼26.3 eV. This spectrum is recorded at laser intensity of ∼1.43 × 10¹⁴ W cm⁻².

Figure 3. Separation of resonant harmonic and direct harmonic at detuned driving laser.

(a) High-order harmonic spectrum of Sn⁺ using a driving laser with 1.785 μm central wavelength. This spectrum demonstrates that the resonant harmonic (RH) and the direct harmonic (DH) can be separated by detuning the driving laser wavelength. In this spectrum, two additional coherent harmonics are observed at ±2Ω around the RH, which are generated from the dressed autoionizing state (AIS). This spectrum is recorded at a driving laser intensity of ∼1.4 × 10¹⁴ W cm⁻². (b) The harmonic spectrum calculated via 3D time-dependent Schrödinger equation for a model Sn⁺ ion in the laser field, showing good agreement with experimental observations.

Figure 4. Schematic illustrations of electron quantum paths.

Schematic diagram describing the four-step model of HHG from dressed AIS of Sn⁺. When high-intensity laser pulses (∼10¹⁴ W cm⁻²) interact with Sn⁺, an electron is detached from the ground state (Step 1). This electron is then accelerated in the continuum by the laser field (Step 2). In the third step, the continuum electron has two possible paths to follow. It can either recombine directly to the ground state (Step 3*) and generate DH, or it can be trapped so that the system finds itself in the AIS or dressed AIS (Step 3) and then relaxes to the ground state and emits the RH (Step 4). In the latter scenario, three coherent RHs are generated.