Suppressing small-scale self-focusing of high-power femtosecond pulses

Mikhail Martyanov; Vladislav Ginzburg; Alexey Balakin; Sergey Skobelev; Dmitry Silin; Anton Kochetkov; Ivan Yakovlev; Alexey Kuzmin; Sergey Mironov; Ilya Shaikin; Sergey Stukachev; Andrey Shaykin; Efim Khazanov; Alexander Litvak

doi:10.1017/hpl.2023.20

Journals >High Power Laser Science and Engineering >Volume 11 >Issue 2 >Page 02000e28 > Article

High Power Laser Science and Engineering
Vol. 11, Issue 2, 02000e28 (2023)

Suppressing small-scale self-focusing of high-power femtosecond pulses

Mikhail Martyanov^*, Vladislav Ginzburg, Alexey Balakin, Sergey Skobelev, Dmitry Silin, Anton Kochetkov, Ivan Yakovlev, Alexey Kuzmin, Sergey Mironov, Ilya Shaikin, Sergey Stukachev, Andrey Shaykin, Efim Khazanov, and Alexander Litvak

Author Affiliations

Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

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DOI: 10.1017/hpl.2023.20 Cite this Article Set citation alerts

Mikhail Martyanov, Vladislav Ginzburg, Alexey Balakin, Sergey Skobelev, Dmitry Silin, Anton Kochetkov, Ivan Yakovlev, Alexey Kuzmin, Sergey Mironov, Ilya Shaikin, Sergey Stukachev, Andrey Shaykin, Efim Khazanov, Alexander Litvak. Suppressing small-scale self-focusing of high-power femtosecond pulses[J]. High Power Laser Science and Engineering, 2023, 11(2): 02000e28 Copy Citation Text

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Abstract

It was shown experimentally that for a 65-fs 17-J pulse, the effect of filamentation instability, also known as small-scale self-focusing, is much weaker than that predicted by stationary and nonstationary theoretical models for high B-integral values. Although this discrepancy has been left unexplained at the moment, in practice no signs of filamentation may allow a breakthrough in nonlinear pulse post-compression at high laser energy.

Keywords

B-integral cubic Kerr nonlinearity filamentation instability high-power femtosecond laser nonlinear post-compression

$$\begin{align}{\theta}_{{\mathrm{cr}}}=2\sqrt{n_0{n}_2{I}_0},\end{align}$$

((1))

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$$\begin{align*}{K}_{\mathrm{p}}={\left|{E}_{{\mathrm{noise}}}\left(z=L,\overrightarrow{\kappa}\right)\right|}^2/{\left|{E}_{{\mathrm{noise}}}\Big(z=0,\overrightarrow{\kappa}\Big)\right|}^2,\end{align*}$$

()

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$$\begin{align}{K}_{\mathrm{p}}\left(\theta \right)=1+\frac{2}{x^2}{\mathrm{sh}}^2(Bx),\end{align}$$

((2))

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$$\begin{align}B={k}_0{n}_2{LI}_0,\end{align}$$

((3))

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$$\begin{align}{K}_{\mathrm{e}}\left(\theta \right)=\frac{\int {K}_{\mathrm{p}}\left(\theta, t\right)\cdot {I}_0(t) \mathrm{d}t}{\int {I}_0(t) \mathrm{d}t}=1+2\frac{\int {x}^{-2}\mathrm{sh}(Bx){I}_0(t) \mathrm{d}t}{\int {I}_0(t) \mathrm{d}t}.\end{align}$$

((4))

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$$\begin{align}\xi =\frac{z}{L},\kern-1pt\quad \eta =\frac{t-z/u}{\tau_0},\kern-1pt\quad \overrightarrow{\rho}=\overrightarrow{r}\sqrt{\frac{k_0{n}_0}{L}},\kern-1pt\quad \Psi =\frac{U}{\sqrt{I_0}},\end{align}$$

((5))

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$$\begin{align}\begin{array}{l}\left(\frac{\partial }{\partial \xi }-\frac{i}{2}D\frac{\partial^2}{\partial {\eta}^2}-\frac{i}{2}\left(1-\frac{i}{2\pi N}\frac{\partial }{\partial \eta}\right){\varDelta}_{\overrightarrow{\rho}}\right)\Psi =\\ {}\kern7em - iB\left(1+\frac{i}{2\pi N}\frac{\partial }{\partial \eta}\right){\left|\Psi \right|}^2\Psi, \end{array}\end{align}$$

((6))

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$$\begin{align}N={\tau}_0/T,\end{align}$$

((7))

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$$\begin{align}D={k}_2L/{\tau}_0^2,\end{align}$$

((8))

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$$\begin{align}\left(\frac{\partial^2}{\partial \xi \partial \eta }-\frac{D}{12\pi N}\frac{\partial^4}{\partial {\eta}^4}-\pi N{\varDelta}_{\overrightarrow{\rho}}\right)\Psi =\frac{B}{2\pi N}\frac{\partial^2}{\partial {\eta}^2}{\left|\Psi \right|}^2\Psi .\end{align}$$

((9))

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$$\begin{align}C=2{\pi}^2\frac{DN^2}{B}=\frac{k_0{c}^2{k}_2}{2{n}_2{I}_0}.\end{align}$$

((10))

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$$\begin{align}K\left(\theta \right)=\frac{\iint_0{\left|{E}_{{\mathrm{noise}}, {\mathrm{out}}}\left(t,\overrightarrow{\kappa}\right)\right|}^2 \mathrm{d}t\mathrm{d}\phi}{\iint_0{\left|{E}_{{\mathrm{noise}}, {\mathrm{in}}}\left(t,\overrightarrow{\kappa}\right)\right|}^2 \mathrm{d}t\mathrm{d}\phi},\end{align}$$

((11))