Abstract

Propagation properties of high-power fiber laser with high-order-mode (HOM) content are studied numerically for the first time to the best of our knowledge. The effect of HOM on the propagation property is evaluated by the power in the bucket (PIB) metric. It is shown that PIB is mainly dependent on HOM content rather than the relative phase between the fundamental mode and HOM. The PIB in vacuum is more than 80% when the power fraction of the HOM is controlled to be less than 50% at 5 km. The relative phase has an impact on the peak intensity position and concentration of the far-field intensity distribution. If an adaptive optics system is used to correct the peak intensity deviation, the results indicate that there exists a maximal value of PIB as relative phase increases. Such effect is weakened when propagating in turbulence. Compared to the laser beams without HOM, laser beams with HOM content are less influenced by the turbulence and can reduce average intensity fluctuation. The results may be useful in the design of a high-power fiber laser system.

© 2015 Chinese Laser Press

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References

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2014 (3)

2013 (3)

H.-J. Otto, C. Jauregui, and F. Stutzki, “Controlling mode instabilities by dynamic mode excitation with an acousto-optic deflector,” Opt. Express 21, 17285–17298 (2013).
[Crossref]

M. He, Z. Chen, and J. Pu, “Propagation properties and self-reconstruction of azimuthally polarized non-diffracting beams,” Opt. Commun. 30, 916–922 (2013).
[Crossref]

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjoldb, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).
[Crossref]

2012 (3)

2011 (5)

2010 (3)

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere,” Chin. Phys. B 19, 024205 (2010).
[Crossref]

G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. 35, 715–717 (2010).
[Crossref]

X. Li, X. Ji, H. T. Eyyuboglu, and Y. Baykal, “Turbulence distance of radial Gaussian Schell-model array beams,” Appl. Phys. B 98, 557–565 (2010).
[Crossref]

2009 (2)

W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express 17, 17829–17836 (2009).
[Crossref]

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

2007 (1)

2006 (4)

2002 (1)

1998 (1)

1997 (1)

B. Lü and B. Zhang, “Propagation and focusing of laser beams with amplitude modulations and phase fluctuations,” Opt. Commun. 135, 361–368 (1997).
[Crossref]

1977 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beam through the atmosphere,” Appl. Phys. 11, 329–335 (1977).

Alkeskjoldb, T. T.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjoldb, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).
[Crossref]

Aschenbach, K.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

Baykal, Y.

X. Li, X. Ji, H. T. Eyyuboglu, and Y. Baykal, “Turbulence distance of radial Gaussian Schell-model array beams,” Appl. Phys. B 98, 557–565 (2010).
[Crossref]

Beresnev, L. A.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

Cai, Y.

Cang, J.

Carhart, G. W.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

Chen, Z.

M. He, Z. Chen, and J. Pu, “Propagation properties and self-reconstruction of azimuthally polarized non-diffracting beams,” Opt. Commun. 30, 916–922 (2013).
[Crossref]

Cheng, W.

Chu, X.

X. Chu and W. Wen, “Quantitative description of the self-healing ability of a beam,” Opt. Express 22, 6899–6904 (2014).
[Crossref]

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere,” Chin. Phys. B 19, 024205 (2010).
[Crossref]

Dajani, I.

Dang, A.

Dietrich, S.

R. Protz, J. Zoz, F. Geidek, S. Dietrich, and M. Fall, “High-power beam combining–a step to a future laser weapon system,” Proc. SPIE 8547, 854708 (2012).
[Crossref]

Dimarcello, F. V.

Eidam, T.

Eyyuboglu, H. T.

X. Li, X. Ji, H. T. Eyyuboglu, and Y. Baykal, “Turbulence distance of radial Gaussian Schell-model array beams,” Appl. Phys. B 98, 557–565 (2010).
[Crossref]

Fall, M.

R. Protz, J. Zoz, F. Geidek, S. Dietrich, and M. Fall, “High-power beam combining–a step to a future laser weapon system,” Proc. SPIE 8547, 854708 (2012).
[Crossref]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beam through the atmosphere,” Appl. Phys. 11, 329–335 (1977).

Ferman, M.

Fini, J. M.

Flatte, S. M.

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beam through the atmosphere,” Appl. Phys. 11, 329–335 (1977).

Gaida, C.

Geidek, F.

R. Protz, J. Zoz, F. Geidek, S. Dietrich, and M. Fall, “High-power beam combining–a step to a future laser weapon system,” Proc. SPIE 8547, 854708 (2012).
[Crossref]

Ghalmi, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Guo, H.

Haus, J. W.

He, M.

M. He, Z. Chen, and J. Pu, “Propagation properties and self-reconstruction of azimuthally polarized non-diffracting beams,” Opt. Commun. 30, 916–922 (2013).
[Crossref]

Jansen, F.

Jauregui, C.

Ji, X.

X. Li, X. Ji, H. T. Eyyuboglu, and Y. Baykal, “Turbulence distance of radial Gaussian Schell-model array beams,” Appl. Phys. B 98, 557–565 (2010).
[Crossref]

Jørgensen, M. M.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjoldb, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).
[Crossref]

Lægsgaard, J.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjoldb, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).
[Crossref]

Laurila, M.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjoldb, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).
[Crossref]

Li, X.

X. Li, X. Ji, H. T. Eyyuboglu, and Y. Baykal, “Turbulence distance of radial Gaussian Schell-model array beams,” Appl. Phys. B 98, 557–565 (2010).
[Crossref]

Liang, C.

Limpert, J.

Liu, L.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

Liu, X.

Liu, Z.

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere,” Chin. Phys. B 19, 024205 (2010).
[Crossref]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Lü, B.

B. Lü and B. Zhang, “Propagation and focusing of laser beams with amplitude modulations and phase fluctuations,” Opt. Commun. 135, 361–368 (1997).
[Crossref]

Luo, B.

Ma, H.

Ma, Y.

Mansuripur, M.

Monberg, E.

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beam through the atmosphere,” Appl. Phys. 11, 329–335 (1977).

Nicholson, J. W.

Noordegraaf, D.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjoldb, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).
[Crossref]

Otto, H.-J.

Ou, B.

Polynkin, P.

Protz, R.

R. Protz, J. Zoz, F. Geidek, S. Dietrich, and M. Fall, “High-power beam combining–a step to a future laser weapon system,” Proc. SPIE 8547, 854708 (2012).
[Crossref]

Pu, J.

M. He, Z. Chen, and J. Pu, “Propagation properties and self-reconstruction of azimuthally polarized non-diffracting beams,” Opt. Commun. 30, 916–922 (2013).
[Crossref]

Ramachandran, S.

Robin, C.

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).

Schmidt, O.

Schreiber, T.

Smith, A. V.

Smith, J. J.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Stiles, E.

E. Stiles, “New developments in IPG fiber laser technology,” in Proceedings of the 5th International Workshop on Fiber Lasers, Dresden, Germany, 2009.

Stutzki, F.

Tang, H.

Tang, M.

J. Xu, M. Tang, and D. Zhao, “Propagation of electromagnetic non-uniformly correlated beams in the oceanic turbulence,” Opt. Commun. 331, 1–5 (2014).
[Crossref]

Tünnermann, A.

Voelz, D.

Vorontsov, M. A.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

Wang, K.

Wang, X.

Ward, B.

Wen, W.

Weyrauch, T.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

Wielandy, S.

Wirth, C.

Wisk, P.

Wu, G.

Xiao, X.

Xu, J.

J. Xu, M. Tang, and D. Zhao, “Propagation of electromagnetic non-uniformly correlated beams in the oceanic turbulence,” Opt. Commun. 331, 1–5 (2014).
[Crossref]

Xu, X.

H. Zhao, X. Wang, H. Ma, P. Zhou, Y. Ma, X. Xu, and Y. Zhao, “Adaptive conversion of a high-order mode beam into a near-diffraction-limited beam,” Appl. Opt. 50, 4389–4392 (2011).
[Crossref]

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere,” Chin. Phys. B 19, 024205 (2010).
[Crossref]

Yan, M. F.

Yoda, H.

Yu, S.

Zhan, Q.

Zhang, B.

B. Lü and B. Zhang, “Propagation and focusing of laser beams with amplitude modulations and phase fluctuations,” Opt. Commun. 135, 361–368 (1997).
[Crossref]

Zhao, C.

Zhao, D.

J. Xu, M. Tang, and D. Zhao, “Propagation of electromagnetic non-uniformly correlated beams in the oceanic turbulence,” Opt. Commun. 331, 1–5 (2014).
[Crossref]

Zhao, H.

Zhao, Y.

Zhou, P.

H. Zhao, X. Wang, H. Ma, P. Zhou, Y. Ma, X. Xu, and Y. Zhao, “Adaptive conversion of a high-order mode beam into a near-diffraction-limited beam,” Appl. Opt. 50, 4389–4392 (2011).
[Crossref]

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere,” Chin. Phys. B 19, 024205 (2010).
[Crossref]

Zoz, J.

R. Protz, J. Zoz, F. Geidek, S. Dietrich, and M. Fall, “High-power beam combining–a step to a future laser weapon system,” Proc. SPIE 8547, 854708 (2012).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beam through the atmosphere,” Appl. Phys. 11, 329–335 (1977).

Appl. Phys. B (1)

X. Li, X. Ji, H. T. Eyyuboglu, and Y. Baykal, “Turbulence distance of radial Gaussian Schell-model array beams,” Appl. Phys. B 98, 557–565 (2010).
[Crossref]

Chin. Phys. B (1)

P. Zhou, Z. Liu, X. Xu, and X. Chu, “Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere,” Chin. Phys. B 19, 024205 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15, 269–280 (2009).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

B. Lü and B. Zhang, “Propagation and focusing of laser beams with amplitude modulations and phase fluctuations,” Opt. Commun. 135, 361–368 (1997).
[Crossref]

J. Xu, M. Tang, and D. Zhao, “Propagation of electromagnetic non-uniformly correlated beams in the oceanic turbulence,” Opt. Commun. 331, 1–5 (2014).
[Crossref]

M. He, Z. Chen, and J. Pu, “Propagation properties and self-reconstruction of azimuthally polarized non-diffracting beams,” Opt. Commun. 30, 916–922 (2013).
[Crossref]

Opt. Express (10)

S. M. Flatte, “Calculations of wave propagation through statistical random media, with and without a waveguide,” Opt. Express 10, 777–804 (2002).
[Crossref]

J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14, 69–81 (2006).
[Crossref]

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20, 11407–11422 (2012).
[Crossref]

A. V. Smith and J. J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express 20, 24545–24558 (2012).
[Crossref]

H.-J. Otto, C. Jauregui, and F. Stutzki, “Controlling mode instabilities by dynamic mode excitation with an acousto-optic deflector,” Opt. Express 21, 17285–17298 (2013).
[Crossref]

X. Chu and W. Wen, “Quantitative description of the self-healing ability of a beam,” Opt. Express 22, 6899–6904 (2014).
[Crossref]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19, 13218–13224 (2011).
[Crossref]

X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 14, 6986–6992 (2006).
[Crossref]

S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Express 15, 15402–15409 (2007).
[Crossref]

W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express 17, 17829–17836 (2009).
[Crossref]

Opt. Lett. (5)

Proc. SPIE (2)

R. Protz, J. Zoz, F. Geidek, S. Dietrich, and M. Fall, “High-power beam combining–a step to a future laser weapon system,” Proc. SPIE 8547, 854708 (2012).
[Crossref]

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjoldb, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).
[Crossref]

Other (4)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

E. Stiles, “New developments in IPG fiber laser technology,” in Proceedings of the 5th International Workshop on Fiber Lasers, Dresden, Germany, 2009.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).

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Figures (14)

Fig. 1.
Fig. 1. Scheme of the launch of LMA fiber laser.
Fig. 2.
Fig. 2. Comparison between the analytic and simulated results when z=1km and Cn2=1×1015m2/3.
Fig. 3.
Fig. 3. Irradiance distribution of fiber modes. (a) LP01; (b) LP11.
Fig. 4.
Fig. 4. Irradiance distribution at z=5km. (a) Near-field intensity with ALP11=0. (b) Near-field intensity with ALP11=0.3, Δϕ=π/4. (c) Far-field intensity with ALP11=0. (d) Far-field intensity with ALP11=0.3, Δϕ=π/4.
Fig. 5.
Fig. 5. Normalized intensity distribution.(a) ALP11=0.1, z=5km. (b) ALP11=0.1, Δϕ=π/4. (c) ALP11=0.2, z=5km. (d) ALP11=0.2, Δϕ=π/4. (e) ALP11=0.3, z=5km. (f) ALP11=0.3, Δϕ=π/4. (g) Δϕ=π/4, z=5km.
Fig. 6.
Fig. 6. PIB as a function of relative phase and HOM content ALP11. (a) z=5km. (b) Δϕ=0.
Fig. 7.
Fig. 7. PIB as a function of Δϕ.
Fig. 8.
Fig. 8. Example of phase screen used in numerical simulation. (a) Cn2=5×1016m2/3. (b) Cn2=1×1015m2/3.
Fig. 9.
Fig. 9. Irradiance distribution at z=5km. (a) Without HOM content. (b) ALP11=0.3, Δϕ=π/4.
Fig. 10.
Fig. 10. Normalized intensity distribution. (a) ALP11=0.2, Δϕ=π/2. (b) ALP11=0.2.
Fig. 11.
Fig. 11. PIB as a function of HOM content ALP11.
Fig. 12.
Fig. 12. PIB as a function of turbulence strength.
Fig. 13.
Fig. 13. SI as a function of turbulence strength.
Fig. 14.
Fig. 14. PIB as a function of Δϕ. (a) Cn2=1×1016m2/3. (b) Cn2=5×1016m2/3. (c) Cn2=1×1015m2/3.

Equations (19)

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ΨLPmn=fmn(r)Nmncos(mϕ),
fmn(r)=Jm(Umnr/a)Jm(Umn)ar>0,
fmn(r)=Km(Wmnr/a)Km(Wmn)r>a,
Umn2+Vmn2=V2,
V=2πaλNA,
N0n=2π0f0n2(r)rdrform=0,
Nmn=π0fmn2(r)rdrform>0,
Enear field=ALP11eiΔϕΨLP11+1ALP11ΨLP01,
Enear field=(ALP11eiΔϕΨLP11+1ALP11ΨLP01)eik2Fr2,
E(x,y,zi+1)=F1{exp[jΔzi2k(Kx2+Ky2)]×F{exp[jϕ(x,y,zi)E(x,y,zi)]}},
IG(r⃗,z)=E02w02τ2exp(2w02τ2r2),
τ2=τ12+τ22+τ32,
PIB=P×hhhhIdxdyIdxdy,
σI2=I2I21,
I(p,q,z)=k2(2πz)2E(x,y,z=0)E*(ξ,η,z=0)×exp{ik2z[(px)2+(qy)2(pξ)2(qη)2]}×exp[ψ(p,q,x,y)+ψ*(p,q,ξ,η)]dxdydξdη,
I(p,q,z)=I11+I01+I01×11,
I11=k2ALP11(2πz)2exp{ik2f[(x2+y2)(ξ2+η2)]}×ΨLP11(x,y)ΨLP11(ξ,η)exp{ik2z[(px)2+(qy)2(pξ)2(qη)2]}×exp[ψ(p,q,x,y)+ψ*(p,q,ξ,η)]dxdydξdη,
I01=k2(1ALP11)(2πz)2exp{ik2f[(x2+y2)(ξ2+η2)]}×ΨLP01(x,y)ΨLP01(ξ,η)exp{ik2z[(px)2+(qy)2(pξ)2(qη)2]}×exp[ψ(p,q,x,y)+ψ*(p,q,ξ,η)]dxdydξdη,
I01×11=k2ALP11(1ALP11)(2πz)2exp{ik2f[(x2+y2)(ξ2+η2)]}×[eiΔϕΨLP11(x,y)ΨLP01(ξ,η)+eiΔϕΨLP11(ξ,η)ΨLP01(x,y)]×exp{ik2z[(px)2+(qy)2(pξ)2(qη)2]}×exp[ψ(p,q,x,y)+ψ*(p,q,ξ,η)]dxdydξdη.

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