Turbulence-induced beam wandering during femtosecond laser filamentation

Tao Zeng; Hui Gao; Xiaodong Sun; Weiwei Liu

doi:10.3788/COL201513.070008

Journals >Chinese Optics Letters >Volume 13 >Issue 7 >Page 070008 > Article

Chinese Optics Letters
Vol. 13, Issue 7, 070008 (2015)

Turbulence-induced beam wandering during femtosecond laser filamentation

Tao Zeng¹, Hui Gao², Xiaodong Sun³, and Weiwei Liu^1、4、*

Author Affiliations

¹Key Laboratory of Optical Information Science and Technology, Institute of Modern Optics, Nankai University, Ministry of Education, Tianjin 300071, China

²School of Science, Tianjin Polytechnic University, Tianjin 300387, China

³School of Electronics Information Engineering, Tianjin Polytechnic University, Tianjin 300387, China

⁴Cooperative Innovation Center of Terahertz Science, University of Electronic Science and Technology, Chengdu 611731, China

show less

DOI: 10.3788/COL201513.070008 Cite this Article Set citation alerts

Tao Zeng, Hui Gao, Xiaodong Sun, Weiwei Liu. Turbulence-induced beam wandering during femtosecond laser filamentation[J]. Chinese Optics Letters, 2015, 13(7): 070008 Copy Citation Text

EndNote(RIS)

BibTex

Plain Text

show less

Abstract

The influence of air turbulence on the transverse wandering of a single femtosecond laser filament is studied by numerical simulation. The results show that the average transverse displacement of the single filament

δ r

is proportional to the square root of turbulent structure constant and the relations between

δ r

and the propagation distance can be fit by a power function. In addition, by using an axicon as a focusing optics, the wandering of a single filament is suggested to be stronger than the free-propagation case.

2 i k_{0} \frac{\partial A}{\partial z} + (\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}}) A + 2 k_{0}^{2} Δ n A + 2 k_{0}^{2} \tilde{n} (x, y, z) A = 0,

(1)

View in Article

F_{n} (κ_{x}, κ_{y}, κ_{z}) = 0.033 C_{n}^{2} {(κ^{2} + κ_{0}^{2})}^{- \frac{11}{6}} \exp [- {(κ / κ_{m})}^{2}],

(2)

View in Article

F_{ϕ} (κ_{x}, κ_{y}) = 2 π k_{0}^{2} Δ z F_{n} (κ_{x}, κ_{y}, 0) .

(3)

View in Article

ϕ_{n m} = \frac{1}{\sqrt{N M}} \sum_{p = - \frac{N}{2}}^{\frac{N}{2} - 1} \sum_{q = - \frac{M}{2}}^{\frac{M}{2} - 1} a_{p q} (ε_{p q} + i η_{p q}) \exp [i \frac{2 π}{N} (p n + q m)],

(4)

View in Article

a_{p q}^{2} = F_{ϕ} (p Δ k_{x}, q Δ k_{y}) Δ k_{x} Δ k_{y},

(5)

View in Article

Δ k_{x} = \frac{2 π}{L_{x}}, Δ k_{y} = \frac{2 π}{L_{y}} .

(6)

View in Article

ϕ_{n m}^{LF} = \sum_{k = 1}^{N_{k}} 3^{- k} \frac{1}{\sqrt{N M}} \sum_{p = - 3}^{2} \sum_{q = - 3}^{2} a_{p q} (ε_{p q} + i η_{p q}) \times \exp {i \frac{2 π}{N} 3^{- k} [(p + 0.5) n + (q + 0.5) m]},

(7)

View in Article

\tilde{n} (x, y, z) = \frac{ϕ (x, y)}{k_{0} Δ z} .

(8)

View in Article

D (r) = 〈 {[φ (r^{'}) - φ (r^{'} + r)]}^{2} 〉 = 6.88 {(r / r_{0})}^{5 / 3},

(9)

View in Article

〈 δ r 〉 = a z^{b},

(10)

View in Article

Tao Zeng, Hui Gao, Xiaodong Sun, Weiwei Liu. Turbulence-induced beam wandering during femtosecond laser filamentation[J]. Chinese Optics Letters, 2015, 13(7): 070008

Download Citation

EndNote(RIS)

BibTex

Plain Text

Set citation alerts for the article

Tools

Set citation alerts for the article

Save the article for my favorites

Paper Information