How the laser beam size conditions the temporal contrast in pulse stretchers of chirped-pulse amplification lasers

Simon Roeder; Yannik Zobus; Christian Brabetz; Vincent Bagnoud

doi:10.1017/hpl.2022.18

Journals >High Power Laser Science and Engineering >Volume 10 >Issue 6 >Page 06000e34 > Article

High Power Laser Science and Engineering
Vol. 10, Issue 6, 06000e34 (2022)

How the laser beam size conditions the temporal contrast in pulse stretchers of chirped-pulse amplification lasers

Simon Roeder^1、2、*, Yannik Zobus^1、2, Christian Brabetz¹, and Vincent Bagnoud^1、2、3

Author Affiliations

¹GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

²Technische Universität Darmstadt, Darmstadt, Germany

³Helmholtz-Institut Jena, Jena, Germany

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DOI: 10.1017/hpl.2022.18 Cite this Article Set citation alerts

Simon Roeder, Yannik Zobus, Christian Brabetz, Vincent Bagnoud. How the laser beam size conditions the temporal contrast in pulse stretchers of chirped-pulse amplification lasers[J]. High Power Laser Science and Engineering, 2022, 10(6): 06000e34 Copy Citation Text

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Abstract

In this work, we propose and verify experimentally a model that describes the concomitant influence of the beam size and optical roughness on the temporal contrast of optical pulses passing through a pulse stretcher in chirped-pulse amplification laser systems. We develop an analytical model that is capable of predicting the rising edge caused by the reflection from an optical element in a pulse stretcher, based on the power spectral density of the surface and the spatial beam profile on the surface. In an experimental campaign, we characterize the temporal contrast of a laser pulse that passed through either a folded or an unfolded stretcher design and compare these results with the analytical model. By varying the beam size for both setups, we verify that optical elements in the near- and the far-field act opposed to each with respect to the temporal contrast and that the rising edge caused by a surface benefits from a larger spatial beam size on that surface.

Keywords

chirped-pulse amplification laser stretcher temporal contrast

$$\begin{align}E\left(\omega \right)={E}_0\left(\omega \right){e}^{i\delta \phi \left(\omega \right)},\end{align}$$

((1))

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$$\begin{align}\delta \phi \left(\omega \right)=\left(4\pi /{\lambda}_0\right)\cdot H\left(\omega \right),\end{align}$$

((2))

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$$\begin{align}E\left(\omega \right)=\int f\left[x-{a}_{\omega}\omega \right]{e}^{{i}\delta \phi ({x})}{\textrm{d}xE}_0\left(\omega \right).\end{align}$$

((3))

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$$\begin{align}\hspace{-12pt}E\left(\omega \right)=\int f\left(x-{a}_{\omega}\omega \right)\left[1+ i\delta \phi (x)\right]{\textrm{d}xE}_0\left(\omega \right),\end{align}$$

((4))

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$$\begin{align}\hspace{40pt}={E}_0\left(\omega \right)+i\int f\left(x-{a}_{\omega}\omega \right)\delta \phi (x){\textrm{d}xE}_0\left(\omega \right),\end{align}$$

((5))

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$$\begin{align}&\tilde{E}(t)=\notag\\&{\tilde{E}}_0(t)+ i\left[\int \int {e}^{{i}\omega {t}}f\left(x-{a}_{\omega}\omega \right)\delta \phi (x) \textrm{d}\omega \textrm{d}x\right]\circledast {\tilde{E}}_0(t),\end{align}$$

((6))

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$$\begin{align}&\hspace{-10pt}\tilde{E}(t)=\notag\\&\hspace{-10pt}{\tilde{E}}_0(t)+ \left[\int {e}^{-{i}\frac{x^{\prime }}{{a}_{\omega }}{t}}f\left({{x}}^{\prime}\right)\frac{\textrm{d}{x}^{\prime }}{-{a}_{\omega }}\int {e}^{{i}\frac{{x}}{{a}_{\omega }}t}\delta \phi (x) \textrm{d}x\right]\circledast {\tilde{E}}_0(t).\end{align}$$

((7))

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$$\begin{align}E(t)={\tilde{E}}_0(t)-\frac{i}{a_{\omega }}\left[\tilde{f}\left(t/{a}_{\omega}\right)\tilde{\delta}\phi \left(t/{a}_{\omega}\right)\right]\circledast {\tilde{E}}_0(t).\end{align}$$

((8))

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$$\begin{align*}I(t)={I}_0(t)+\frac{1}{a_{\omega}^2}{\left|\left[\tilde{f}\left(t/{a}_{\omega}\right)\tilde{\delta}\phi \left(t/{a}_{\omega}\right)\right]\circledast {\tilde{E}}_0(t)\right|}^2\end{align*}$$

()

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$$\begin{align}-\frac{2}{a_{\omega }}\mathbf{\operatorname{Im}}\left\{{\tilde{E}}_0(t)\left\{\left[ {\tilde{f}}^{\ast}\left(t/{a}_{\omega}\right)\tilde{\delta}{\phi}^{\ast}\left(t/{a}_{\omega}\right)\right]\circledast {\tilde{E}}_0^{\ast }(t)\right\}\right\}.\end{align}$$

((9))