Spatiotemporal characterization of laser pulse amplification in double-pass active mirror geometry

Tinghao Liu; Qiang Liu; Zhan Sui; Mali Gong; Xing Fu

doi:10.1017/hpl.2020.28

Journals >High Power Laser Science and Engineering >Volume 8 >Issue 3 >Page 03000e30 > Article

High Power Laser Science and Engineering
Vol. 8, Issue 3, 03000e30 (2020)

Spatiotemporal characterization of laser pulse amplification in double-pass active mirror geometry

Tinghao Liu^1、2, Qiang Liu^1、2, Zhan Sui³, Mali Gong^1、2, and Xing Fu^1、2、*

Author Affiliations

¹Key Laboratory of Photonic Control Technology (Tsinghua University), Ministry of Education, Beijing 100084, China

²State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China

³Shanghai Institute of Laser Plasma, China Academy of Engineering Physics, Shanghai 201800, China

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DOI: 10.1017/hpl.2020.28 Cite this Article Set citation alerts

Tinghao Liu, Qiang Liu, Zhan Sui, Mali Gong, Xing Fu. Spatiotemporal characterization of laser pulse amplification in double-pass active mirror geometry[J]. High Power Laser Science and Engineering, 2020, 8(3): 03000e30 Copy Citation Text

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Abstract

We present a spatiotemporal model of pulse amplification in the double-pass active mirror (AM) geometry. Three types of overlap condition are studied, and the spatiotemporal scaling under the four-pulse overlapping (4PO) condition is fully characterized for the first time, by mapping the temporal and spatial segments of beam to the instantaneous gain windows. Furthermore, the influence of spatiotemporal overlaps on the amplified energy, pulse distortion and intensity profile is unraveled for both AM and zigzag configurations. The model, verified by excellent agreement between the predicted and measured results, can be a powerful tool for designing and optimizing high energy multi-pass solid-state laser amplifiers with AM, zigzag and other geometries.

Keywords

active mirror amplifier double-pass pulse overlap spatiotemporal characterization

\begin{align}{\eta}_{\rm op}=\left\{\kern-4pt\begin{array}{l}\dfrac{T_c-2{T}_D}{T_c+2{T}_{{G}}+2{T}_D}\quad \left({T}_c\ge 2{T}_D\right),\\ {}0\qquad\qquad\qquad\ \ \ \,\,\left({T}_c<2{T}_D\right),\end{array}\right.\end{align}

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\begin{align}{f}_g(x)=\frac{1}{\sqrt{2\pi}\sigma}\exp \left[-\frac{{\left(x-\mu \right)}^2}{2{\sigma}^2},\right],\end{align}

(2)

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\begin{align}{I}_\mathrm{in}(x,z,T)\mathrm{d}t=\sum \limits_{j=1\pm, 2\pm }I({nx}_j(x,z,T),{nt}_j(x,z,T),T)\mathrm{d}t.\end{align}

(3)

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\begin{align}&{G}_e(x,z,T)\nonumber\\[4pt]&=\frac{E_{\mathrm{sat}}\ln \{1+\exp [{E}_{\mathrm{st}}(x,z,T)\mathrm{d}l/{E}_{\mathrm{sat}}]\{\exp [{I}_\mathrm{in}(x,z,T)\mathrm{d}t]/{E}_{\mathrm{sat}}-1\}\}}{I_\mathrm{in}(x,z,T)\mathrm{d}t},\end{align}

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\begin{align}&I\left({nx}_j\left(x,z,T\right),{nt}_j\left(x,z,T\right),T+\mathrm{d}t\right)\nonumber\\&\quad={G}_e\left(x,z,t\right)I\left({nx}_j\left(x,z,T\right),{nt}_j\left(x,z,T\right),T\right),\kern0.75em j=1\pm, 2\pm,\end{align}

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\begin{align}&{E}_{\mathrm{st}}\left(x,z,T+\mathrm{d}t\right)\nonumber\\&\quad={E}_{\mathrm{st}}\left(x,z,T\right)-[{G}_e\left(x,z,T\right)-1]\cdot {I}_\mathrm{in}\left(x,z,T\right)\mathrm{d}t/\mathrm{d}l.\end{align}

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\begin{align} \Delta {E}_{\mathrm{st}}&=\dfrac{\mathrm{d}{E}_{\mathrm{st}}}{\mathrm{d}t}\nonumber\\[4pt] &=-\left\{{E}_{\mathrm{sat}}\,\ln \left\{1+\exp \left(\dfrac{E_{\mathrm{st}}}{E_{\mathrm{st}}}\mathrm{d}l\right)\left[\exp \left(\sum \dfrac{I}{E_{\mathrm{sat}}}\mathrm{d}t\right)\right]-1\right\} \Bigg/ \left(\sum I\mathrm{d}t\right)-1\right\} \nonumber\\ & \quad \cdot \sum I/\mathrm{d}l.\end{align}

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\begin{align}\tan \gamma& =\dfrac{p_2-{p}_1}{c_n\left({\tau}_2-{\tau}_1\right)}=\dfrac{2L\sin \beta \cos \beta }{c_n\left[2L/{c}_n-\left({d}_2-{d}_1\right)/c\right]}\nonumber \\[5pt]&=\dfrac{2L\sin \beta \cos \beta }{2L\left[1-\left(\sin \beta \sin \alpha \right)\right]/n}=\tan \beta,\end{align}

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\begin{align}\tan {\gamma}^{\prime }&=\frac{d/n}{d\cos \beta /\sin \alpha }=\tan \beta,\end{align}

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\begin{align}\left\{\kern-4pt\begin{array}{l}{p}_1=x\cos \beta -\left({H}_0+z\right)\sin \beta, \\ {}{p}_2=x\cos \beta -\left({H}_0-z\right)\sin \beta, \\ {}{\tau}_1=\left[x\sin \beta +\left({H}_0+z\right)\cos \beta \right]/{c}_n,\\ {}{\tau}_2=\left[x\sin \beta +\left({H}_0-z\right)\cos \beta \right]/{c}_n,\end{array}\right.\end{align}

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