• Photonics Research
  • Vol. 6, Issue 12, 1130 (2018)
Jia-Qi Lü1, Ping-Ping Li1, Dan Wang1, Chenghou Tu1, Yongnan Li1、4, and Hui-Tian Wang2、3、*
Author Affiliations
  • 1School of Physics and Key Laboratory of Weak-Light Nonlinear Photonics, Nankai University, Tianjin 300071, China
  • 2National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
  • 3Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
  • 4e-mail: liyongnan@nankai.edu.cn
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    DOI: 10.1364/PRJ.6.001130 Cite this Article Set citation alerts
    Jia-Qi Lü, Ping-Ping Li, Dan Wang, Chenghou Tu, Yongnan Li, Hui-Tian Wang. Extending optical filaments with phase-nested laser beams[J]. Photonics Research, 2018, 6(12): 1130 Copy Citation Text show less

    Abstract

    Extending the length of femtosecond laser filamentation has always been desired for practical applications. Here, we demonstrate that significant extending of a single filament in BK7 glass can be achieved by constructing phase-nested beams. The filamentation and the following energy replenishment are assembled in a single phase-nested beam. The central part of the phase-nested beam is an apertured Gaussian beam, which is focused into one focal spot to produce a short filament. In contrast, the rest of the annular part converges gradually towards the central axis to continuously replenish the energy for supporting the regeneration of filaments. The common-path generating system ensures the stability of generated filaments and easily optimizes the beam parameters to obtain the longest high-quality filament due to its flexibility. In addition, we discuss the significance of continuous replenishment for extending filaments and the potential for generating more extended filaments based on this method.
    t={eiπ2[1+cos(2πf0x)],(0ρρc)eiπ2[1+cos(2πf0x+ϕa)],(ρc<ρ1),(1)

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    ϕa=2πγ[(ρρ1)2(ρcρ1)2]+ϕ0.(2)

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    E(ρ)={A0eρ2w2,(0ρρc)A0eρ2w2+iϕa,(ρc<ρ1).(3)

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    E(ρ)={A0eρ2w2i2πr02ρ2λf,(0ρρc)A0eρ2w2i2πr02ρ2λf+iϕa,(ρc<ρ1).(4)

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    dΨdζ=i(2ρ2+ρρ+2ρ2ϕ2)Ψ+i(PPc|Ψ|2ϵP2Pc2|Ψ|4)Ψβ(K)|Ψ|2K2Ψ,(5)

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    Jia-Qi Lü, Ping-Ping Li, Dan Wang, Chenghou Tu, Yongnan Li, Hui-Tian Wang. Extending optical filaments with phase-nested laser beams[J]. Photonics Research, 2018, 6(12): 1130
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