Abstract

We proposed a new phase-locking technique for multibeam coherent beam combination. By near-field angle modulation and angular spectrum measurement, we obtained the relative phase between each pair of beams with one camera. This method is appropriate for multibeam schemes and possesses the advantages of high accuracy, resistance to energy fluctuation, and simplicity, as shown by the analysis in this study. In a proof-of-principle experiment, we realized the phase-locking of three beams, achieving a Strehl ratio of 89.5%. Our method may supply a scheme for multibeam coherent combining of ultra-intense bulk laser systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

2016 (4)

J. Mu, Z. Li, F. Jing, Q. Zhu, K. Zhou, S. Wang, S. Zhou, N. Xie, J. Su, J. Zhang, X. Zeng, Y. Zuo, L. Cao, and X. Wang, “Coherent combination of femtosecond pulses via non-collinear cross-correlation and far-field distribution,” Opt. Lett. 41(2), 234–237 (2016).
[Crossref] [PubMed]

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

B. King and T. Heinzl, “Measuring vacuum polarization with high-power lasers,” High Power Laser Sci. Eng. 4, e5 (2016).
[Crossref]

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

2015 (2)

V. E. Leshchenko, V. A. Vasiliev, N. L. Kvashnin, and E. V. Pestryakov, “Coherent combinig of relativistic-intensity femtosecond laser pulses,” Appl. Phys. B 118(4), 511–516 (2015).
[Crossref]

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).
[Crossref]

2013 (2)

2011 (2)

2009 (1)

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

2008 (1)

2007 (1)

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[Crossref]

2006 (2)

2005 (1)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

2004 (1)

1986 (1)

T. Kreis, “Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method,” J. Opt. Soc. Am. 3(6), 847 (1986).
[Crossref]

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

An, N.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Augst, S. J.

Baker, J. T.

Benham, V.

Beresnev, L. A.

Breitkopf, S.

Bulanov, S. V.

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
[Crossref]

Cao, L.

Carhart, G. W.

Cheriaux, G.

Chosrowjan, H.

Chvykov, V.

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[Crossref]

Cui, Y.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Culpepper, M. A.

Dai, Y.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Danson, C.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).
[Crossref]

Dong, Q.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Dong, X.

Du, W.

Eidam, T.

Eliezer, S.

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

Fan, T. Y.

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004).
[Crossref] [PubMed]

Fujioka, S.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Fujita, M.

Fujiwara, T.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Furuse, H.

Gao, Y.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Gottschall, T.

Hädrich, S.

Hamamoto, K.

Han, J. M.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Heinzl, T.

B. King and T. Heinzl, “Measuring vacuum polarization with high-power lasers,” High Power Laser Sci. Eng. 4, e5 (2016).
[Crossref]

Henis, Z.

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

Hillier, D.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).
[Crossref]

Hopps, N.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).
[Crossref]

Izawa, Y.

Jing, F.

Kalinchenko, G.

Kawanaka, J.

Kienel, M.

King, B.

B. King and T. Heinzl, “Measuring vacuum polarization with high-power lasers,” High Power Laser Sci. Eng. 4, e5 (2016).
[Crossref]

Klenke, A.

Krausz, F.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[Crossref]

Kreis, T.

T. Kreis, “Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method,” J. Opt. Soc. Am. 3(6), 847 (1986).
[Crossref]

Krushelnick, K.

Kvashnin, N. L.

V. E. Leshchenko, V. A. Vasiliev, N. L. Kvashnin, and E. V. Pestryakov, “Coherent combinig of relativistic-intensity femtosecond laser pulses,” Appl. Phys. B 118(4), 511–516 (2015).
[Crossref]

Lee, Y. W.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Leng, J.

Leshchenko, V. E.

V. E. Leshchenko, V. A. Vasiliev, N. L. Kvashnin, and E. V. Pestryakov, “Coherent combinig of relativistic-intensity femtosecond laser pulses,” Appl. Phys. B 118(4), 511–516 (2015).
[Crossref]

Li, D.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Li, R.

Li, W.

Li, Y.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Li, Z.

Liang, X.

Limpert, J.

Liu, J. J.

Liu, R.

Liu, Z.

Lu, C. A.

Ma, W.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Ma, Y.

Maksimchuk, A.

Martinez-val, J. M.

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

Matsuoka, T.

Mima, K.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Miyanaga, N.

Mourou, G.

Mourou, G. A.

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
[Crossref]

Mu, J.

Nakabayashi, Y.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Neely, D.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).
[Crossref]

Nees, J.

Nelson, D. J.

Nishimura, H.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Nissim, N.

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

Peng, C.

Pestryakov, E. V.

V. E. Leshchenko, V. A. Vasiliev, N. L. Kvashnin, and E. V. Pestryakov, “Coherent combinig of relativistic-intensity femtosecond laser pulses,” Appl. Phys. B 118(4), 511–516 (2015).
[Crossref]

Pilkington, D.

Pinhasi, S. V.

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

Planchon, T.

Polnau, E. E.

Raicher, E.

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

Rao, D.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Ravid, A.

S. Eliezer, J. M. Martinez-val, Z. Henis, N. Nissim, S. V. Pinhasi, A. Ravid, M. Werdiger, and E. Raicher, “Physics and applications with laser-induced relativistic shock waves,” High Power Laser Sci. Eng. 4, e25 (2016).
[Crossref]

Rhee, Y. J.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Rostov, A. P.

Rothhardt, J.

Rousseau, P.

Salzmann, D.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Sanchez, A.

Sanchez, A. D.

Shan, J.

Y. Cui, Y. Gao, Z. Zhao, D. Rao, Z. Xu, N. An, J. Shan, D. Li, J. Yu, T. Wang, G. Xu, W. Ma, and Y. Dai, “High precision and large range timing jitter measurement and control of ultrashort laser pulses,” IEEE Photonics Technol. Lett. 28(20), 2215–2217 (2016).
[Crossref]

Shay, T. M.

Si, L.

Spring, J.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

Su, J.

Tajima, T.

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
[Crossref]

Takabe, H.

S. Fujioka, H. Takabe, N. Yamamoto, D. Salzmann, F. Wang, H. Nishimura, Y. Li, Q. Dong, S. Wang, Y. Zhang, Y. J. Rhee, Y. W. Lee, J. M. Han, M. Tanabe, T. Fujiwara, Y. Nakabayashi, G. Zhao, J. Zhang, and K. Mima, “X-ray astronomy in the laboratory with a miniature compact object produced by laser-driven implosion,” Nat. Phys. 5(11), 821–825 (2009).
[Crossref]

Tanabe, M.

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Figures (7)

Fig. 1
Fig. 1 CBC of two beams: (a) near-field fringe pattern in one dimension (x is the position on the x axis), (b) angular spectrum (u is the spatial frequency).
Fig. 2
Fig. 2 Relationship between measured phase and actual phase (a) without other conditions (inset shows a scaled-down view in a small range) and (b) with a 50%–150% laser energy fluctuation (inset shows the artificial energy fluctuation).
Fig. 3
Fig. 3 CBC of three beams: (a) near-field fringe pattern in one dimension, (b) angular spectrum (the corresponding angles are marked).
Fig. 4
Fig. 4 Experimental setup design used for phase locking of CBC of three beams.
Fig. 5
Fig. 5 Near-field measurement results: (a) fringe pattern recorded by camera 2 (red line represents the chosen data on the x axis), (b) intensity distribution on the x axis, (c) angular spectrum.
Fig. 6
Fig. 6 Relative phase between each pair of beams when feedback loop is off (blue line) and on (red line): (a) B1 and B2, (b) B1 and B3, (c) B2 and B3.
Fig. 7
Fig. 7 (a)–(c) Focal spot when feedback loop is off, (d) focal spot when feedback loop is on, (e) peak intensity of the focal spot when the feedback loop is off and on.

Tables (1)

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Table 1 Factors affecting measurement accuracy

Equations (14)

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i(x,t)=| E n (x,t) | 2 ,
E n (x,t)= A n (x)exp[j( k n x ω n t)+j ϕ n ].
i(x,t)= A n (x) 2 +2 n m,mn A n (x) A m (x) cos[( k n k m )x( ω n ω m )t+( ϕ n ϕ m )].
i(x)= A n (x) 2 +2 n m,mn A n (x) A m (x) cos[2π( α n α m )x/λ+( ϕ n ϕ m )].
i(x)=b(x)+ n m,mn c(x) exp[2jπ( α n α m )x/λ]+ n m,mn c * (x) exp[2jπ( α n α m )x/λ] ,
I(u)=B(u)+ n m,mn C [u2π( α n α m )/λ]+ n m,mn C * [u+2π( α n α m )/λ],
A n (x)=Aexp[ (x x 0 ) 2 / r 2 ],
p l ~ (l1)d ld i(x)dx ,
p l ~ (l1)d ld A 2 exp[2 (x x 0 ) 2 / r 2 ] {N+2 n m,mn cos[2π( α n α m )x/λ+( ϕ n ϕ m )] }dx .
p l ~2 A 2 d+2 A 2 n m,mn sin(π( α n α m )d/λ) π( α n α m ) *cos[π( α n α m )(2l1)d/λ+( ϕ n ϕ m )] .
P(q/L)= l=1 L p l exp(j2πql/N)
P(q/L)= l=1 L 2 A 2 dexp(j2πql/L)+ l=1 L n m,mn Dexp{j2πl[( α n α m )d/λq/L ]} + l=1 L n m,mn D * exp{j2πl[( α n α m )d/λ+q/L]} ,
ϕ n ϕ m =arctan[Im(D)/Re(D)]+π( α n α m )d/λ .
SR= I combined ( I 1 + I 2 + I 3 ) 2 ,

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