# Grating Configurations for the Spectral Selection of Coherent Ultrashort Pulses in the Extreme-Ultraviolet

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Single-Grating Monochromators for Ultrashort Pulses

_{G}= mλN/c, where N is the number of the illuminated grooves.

**Figure 1.**(

**a**) The OPM grating geometry. (

**b**) The OPM monochromator: the polychromatic light at the input is dispersed in the vertical direction and the spectral selection is performed through the horizontal slit. The blue beam is the radiation at the wavelength λ that has been selected to be transmitted through the slit by choosing the proper grating rotation, the red beam is the radiation at another generic wavelength that is stopped by the slit.

_{FWHM}= ΔS (σ q)

^{−1}, where ΔS is the width of the slit. The values for a 50-μm-wide slit are reported in Table 1.

Spectral region | 30-100 eV (41–12 nm) | |
---|---|---|

Gratings | Altitude | 3.5° |

G1 | Energy region | 80-100 eV (15.5–12 nm) |

Groove density | 600 gr/mm | |

Bandwidth (100-um slit) | Δλ = 0.26 nm, ΔE = 1.7 eV@90 eV | |

G2 | Energy region | 80-100 eV (15.5–12 nm) |

Groove density | 1200 gr/mm | |

Bandwidth (100-um slit) | Δλ = 0.13 nm, ΔE = 0.85 eV @90 eV | |

G3 | Energy region | 80-100 eV (15.5–12 nm) |

Groove density | 2400 gr/mm | |

Bandwidth (50-um slit) | Δλ = 0.06 nm, ΔE = 0.42 eV @90 eV | |

G4 | Energy region | 30-40 eV (41–31 nm) |

Groove density | 200 gr/mm | |

Bandwidth (50-um slit) | Δλ = 0.77 nm, ΔE = 0.8 eV @35 eV | |

G5 | Energy region | 30-40 eV (41–31 nm) |

Groove density | 900 gr/mm | |

Bandwidth (50-um slit) | Δλ = 0.17 nm, ΔE = 0.17 eV @35 eV |

**Table 2.**Time response of the OPM monochromator for a beam aperture of 4 mrad × 4 mrad and 4 mrad × 2 mrad, calculated as the half-width spread of the optical paths at the output slit.

4 mrad × 4 mrad Full Aperture | 4 mrad × 2 mrad Full Aperture | |
---|---|---|

G1, 600 gr/mm | 35 fs at 90 eV | 18 fs at 90 eV |

G2, 1200 gr/mm | 70 fs at 90 eV | 35 fs at 90 eV |

G3, 2400 gr/mm | 140 fs at 90 eV | 70 fs at 90 eV |

G4, 200 gr/mm | 30 fs at 35 eV | 15 fs at 35 eV |

G5, 900 gr/mm | 140 fs at 35 eV | 70 fs at 35 eV |

^{11}photons/s for H23 (35.6 eV) in argon and 5 × 10

^{8}photons/s in the H33-H49 region (35.6−80 eV) in neon has been measured at the output. Only odd harmonics are generated, therefore, the radiation diffracted by the grating at second order is not overlapped to any of the harmonics. No evidence of second orders contribution is visible in the spectra. Note that the monochromator, although designed to operate in two relatively narrow spectral regions that are tailored to the experimental requirements, may be tuned-in a much broader region.

## 3. Double-Grating Monochromators for Ultrashort Pulses

^{−1}and 200 mm

^{−1}central groove density, are used to cover the 6−60 nm spectral region. G1 is operated in the internal spectrum, i.e., β

_{G1}< α

_{G1}, resulting in α

_{G1}> 85°, that is safe under the intense FEL beam. G2 is operated in the external spectrum to compensate for the pulse-front tilt, i.e., β

_{G2}= α

_{G1}> α

_{G2}= β

_{G1}.

^{3/4}(see Reference [32]). The resolution, as calculated from ray-tracing simulations, is shown in Figure 5a for a 50-um slit. The pulse-front tilt is shown in Figure 5b both at the slit plane and at the output. The double-grating configuration is really effective, being able to compensate for the front-tilt from the picosecond time scale down to few femtoseconds. Indeed, the temporal resolution of the beamline is increased by almost three orders of magnitudes by using the double-grating design. Finally, the spot size at the output has been simulated to be in the 10–15 um FWHM range in the whole interval of operation.

Distances | |
---|---|

S–M1 | 60 m |

M1–G1 | 1 m |

G1–Slit | 2 m |

Slit-M2 | 0.5 m |

M2–G2 | 1.5 m |

G2–M3 | 2.5 m |

M3–M4 | 0.5 m |

M4–focus | 1.5 m |

Mirror M1 | Plane / Elliptical |

Entrance arm | 60 m |

Exit arm | 3 m |

Incidence angle | 87° |

Mirror M2 | Plane |

Incidence angle | 88.5° |

Mirror M3 | Plane / Elliptical |

Entrance arm | 67.5 m |

Exit arm | 2 m |

Incidence angle | 87° |

Mirror M4 | Plane / Elliptical |

Entrance arm | 5 m |

Exit arm | 1.5 m |

Incidence angle | 85.5° |

Gratings | |

Type | VLS plane |

Deviation Angle | 168° |

Grating set 1 | 6–20 nm, 600 mm^{−1} |

Grating set 2 | 18–60 nm, 200 mm^{−1} |

**Figure 5.**Resolution on a 50-μm slit (

**a**) and pulse front-tilt (

**b**) of the double-grating monochromator for FLASH II. The two scales on the x-axis refer to the two grating sets. The values in the y-axis are the same for both sets of gratings.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflict of Interest

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**MDPI and ACS Style**

Frassetto, F.; Miotti, P.; Poletto, L.
Grating Configurations for the Spectral Selection of Coherent Ultrashort Pulses in the Extreme-Ultraviolet. *Photonics* **2014**, *1*, 442-454.
https://doi.org/10.3390/photonics1040442

**AMA Style**

Frassetto F, Miotti P, Poletto L.
Grating Configurations for the Spectral Selection of Coherent Ultrashort Pulses in the Extreme-Ultraviolet. *Photonics*. 2014; 1(4):442-454.
https://doi.org/10.3390/photonics1040442

**Chicago/Turabian Style**

Frassetto, Fabio, Paolo Miotti, and Luca Poletto.
2014. "Grating Configurations for the Spectral Selection of Coherent Ultrashort Pulses in the Extreme-Ultraviolet" *Photonics* 1, no. 4: 442-454.
https://doi.org/10.3390/photonics1040442