# Spectral and Divergence Characteristics of Plateau High-Order Harmonics Generated by Femtosecond Chirped Laser Pulses in a Semi-Infinite Gas Cell

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## Abstract

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## 1. Introduction

## 2. The Experimental Setup

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic layout of the HHG experimental setup. Femtosecond IR Ti:Sa laser pulses, chirped by varying the spacing between the compressor gratings (CG), are focused on a semi-infinite Ar gas cell generating coherent XUV harmonic radiation. The XUV beam propagates collinearly with the IR laser beam to the third stage of the setup, where the IR is filtered by two silicon wafers (Si-W). The XUV beam is then dispersed by a flat-field XUV concave grating (FFG) and the plateau XUV harmonics spectra and divergence are imaged by an XUV CCD camera. D: Adjustable grating distance; M: low dispersion fs mirror; L: low dispersion thin-focusing lens. The plasma formation inside the semi-infinite gas cell is imaged by a CCD camera.

**Figure 2.**XUV harmonic spectral images (

**left**) and corresponding plasma formation images (

**right**) measured for various laser pulse durations and Ar gas pressures in the semi-infinite cell. The focus of the laser beam is at the exit pinhole of the semi-infinite cell. The negative/positive signs of the laser pulse durations correspond to the imposed negative/positive chirp, respectively. The nominal spectral locations of the harmonics order, estimated according to the optical geometry of the experimental setup, are noted at the bottom of the XUV spectral images for each gas pressure. The colour intensity of the XUV spectral images corresponding to the pressures of 40 and 50 Torr was multiplied by a factor of two, as indicated at the top of the images, for better visibility.

**Figure 3.**Same as in Figure 2, except that the focus of the laser beam is 3 mm before the exit pinhole of the semi-infinite cell.

**Figure 4.**Relative enhancement of the measured XUV band emission for the spectral areas between the harmonics as a function of the generating gas pressure. The data correspond to those of Figure 3 for the pulse duration of $\tau $ = $-43$ fs. Relative XUV band emission error bars are estimated lower than 1% and are within the data symbols.

**Figure 5.**Experimentally determined divergence of the 21st harmonic short (black solid circle) and long (red solid square) trajectories as a function of the chirped laser pulse duration for the case of 90 Torr Ar gas pressure of Figure 2. Indicative error bars for the short and long trajectories are shown.

**Figure 6.**Experimentally determined spectral shift of the 17th (black solid square), 19th (red solid cirlce), and 21st (green solid triangle) high-order harmonics as a function of the chirped laser pulse duration for the pressure of 80 Torr of Figure 3. Dashed horizontal lines correspond to the unshifted harmonic peak positions. Estimated error bars are within the data symbols.

**Figure 7.**Qualitative comparison between measured XUV harmonic spectral images for chirped laser pulse durations of −150 fs, −43 fs, and +150 fs, corresponding to those presented in Figure 3, and XUV harmonic spectra obtained with our model calculations, corresponding to the experimental conditions of their counterpart XUV harmonic spectral images. Long and short trajectory contributions are included separately.

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**MDPI and ACS Style**

Petrakis, S.; Bakarezos, M.; Tatarakis, M.; Benis, E.P.; Papadogiannis, N.A.
Spectral and Divergence Characteristics of Plateau High-Order Harmonics Generated by Femtosecond Chirped Laser Pulses in a Semi-Infinite Gas Cell. *Atoms* **2022**, *10*, 53.
https://doi.org/10.3390/atoms10020053

**AMA Style**

Petrakis S, Bakarezos M, Tatarakis M, Benis EP, Papadogiannis NA.
Spectral and Divergence Characteristics of Plateau High-Order Harmonics Generated by Femtosecond Chirped Laser Pulses in a Semi-Infinite Gas Cell. *Atoms*. 2022; 10(2):53.
https://doi.org/10.3390/atoms10020053

**Chicago/Turabian Style**

Petrakis, Stylianos, Makis Bakarezos, Michael Tatarakis, Emmanouil P. Benis, and Nektarios A. Papadogiannis.
2022. "Spectral and Divergence Characteristics of Plateau High-Order Harmonics Generated by Femtosecond Chirped Laser Pulses in a Semi-Infinite Gas Cell" *Atoms* 10, no. 2: 53.
https://doi.org/10.3390/atoms10020053