Abstract

Coherent beam combining (CBC) technology holds the promise of enabling laser systems with very high power and near-ideal beam quality. We propose and demonstrate a novel servo system composed of multilevel optical phase lock loops. This servo system is based on entirely electronic components and consequently can be considerably more compact and less expensive compared to servo systems made of optical phase/frequency shifters. We have also characterized the noise of a 1064nm Yb-doped fiber amplifier to determine its effect on the CBC and studied theoretically the efficiency of combining a large array of beams with the filled-aperture implementation. In a proof-of-concept experiment we have combined two 100mW 1064nm semiconductor lasers with an efficiency of 94%.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. S. Demoustier, A. Brignon, E. Lalliere, and J. P. Huignard, "Coherent combining of 1.5 μm Er-Yb doped single mode fiber amplifier," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CThAA5.
    [PubMed]
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    [CrossRef]
  9. L. H. Enloe and J. L. Rodda, "Laser phase-locked loop," Proc. Inst. Electr. Eng. 53, 165-166 (1965).
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    [CrossRef]
  11. W. Liang, N. Satyan, A. Yariv, A. Kewitsch, G. Rakuljic, F. Aflatouni, H. Hashemi, and J. Ungar, "Coherent power combination of two master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops," Opt. Express 15, 3201-3205 (2007).
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  12. S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, "Direct frequency-modulation in AlGaAs semiconductor-lasers," IEEE J. Quantum Electron. 18, 582-595 (1982).
    [CrossRef]
  13. A. Yariv, "Dynamic analysis of the semiconductor laser as a current-controlled oscillator in the optical phased-lock loop: applications," Opt. Lett. 30, 2191-2193 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. G. J. Cowle, P. R. Morkel, R. I. Laming, and D. N. Payne, "Spectral broadening due to fiber amplifier phase noise," Electron. Lett. 26, 424-425 (1990).
    [CrossRef]
  21. E. Desurvire, Erbium-Doped Fiber Amplifiers Principles and Applications (Wiley, 1994), pp. 399-404.
  22. L. Moller, "Novel aspects of spectral broadening due to fiber amplifier phase noise," IEEE J. Quantum Electron. 34, 1554-1558 (1998).
    [CrossRef]
  23. E. Rochat and R. Dandliker, "New investigations on the effect of fiber amplifier phase noise," IEEE J. Sel. Top. Quantum Electron. 7, 49-54 (2001).
    [CrossRef]
  24. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1996).
  25. C. D. Nabors, "Effects of phase errors on coherent emitter arrays," Appl. Opt. 33, 2284-2289 (1994).
    [CrossRef] [PubMed]
  26. D. S. Elliott, R. Roy, and S. J. Smith, "Extra-cavity laser band-shape and bandwidth modification," Phys. Rev. A 26, 12-18 (1982).
    [CrossRef]
  27. J. K. Lawson, D. M. Aikens, R. E. English, Jr., W. T. Whistler, W. House, and M. A. Nichols, "Surface figure and roughness tolerances for NIF optics and the interpretation of the gradient, P-V wavefront, and RMS specifications," Proc. SPIE 3782, 510-517 (1999).
    [CrossRef]

2007

2006

2005

2004

2002

2001

E. Rochat and R. Dandliker, "New investigations on the effect of fiber amplifier phase noise," IEEE J. Sel. Top. Quantum Electron. 7, 49-54 (2001).
[CrossRef]

2000

Y. Kono, M. Takeoka, K. Uto, A. Uchida, and F. Kannari, "A coherent all-solid-state laser array using the Talbot effect in a three-mirror cavity," IEEE J. Quantum Electron. 36, 607-614 (2000).
[CrossRef]

1999

L. Bartelt-Berger, U. Brauch, A. Giesen, H. Huegel, and H. Opower, "Power-scalable system of phase-locked single-mode diode lasers," Appl. Opt. 38, 5752-5760 (1999).
[CrossRef]

L. N. Langley, M. D. Elkin, C. Edge, M. J. Wale, U. Gliese, X. Huang, and A. J. Seeds, "Packaged semiconductor laser optical phase-locked loop (OPLL) for photonic generation, processing and transmission of microwave signals," IEEE Trans. Microwave Theory Tech. 47, 1257-1264 (1999).
[CrossRef]

J. K. Lawson, D. M. Aikens, R. E. English, Jr., W. T. Whistler, W. House, and M. A. Nichols, "Surface figure and roughness tolerances for NIF optics and the interpretation of the gradient, P-V wavefront, and RMS specifications," Proc. SPIE 3782, 510-517 (1999).
[CrossRef]

1998

L. Moller, "Novel aspects of spectral broadening due to fiber amplifier phase noise," IEEE J. Quantum Electron. 34, 1554-1558 (1998).
[CrossRef]

1994

C. D. Nabors, "Effects of phase errors on coherent emitter arrays," Appl. Opt. 33, 2284-2289 (1994).
[CrossRef] [PubMed]

P. Correc, O. Girard, and I. F. Defaria, "On the thermal contribution to the Fm response of Dfb lasers--theory and experiment," IEEE J. Quantum Electron. 30, 2485-2490 (1994).
[CrossRef]

1990

G. J. Cowle, P. R. Morkel, R. I. Laming, and D. N. Payne, "Spectral broadening due to fiber amplifier phase noise," Electron. Lett. 26, 424-425 (1990).
[CrossRef]

R. T. Ramos and A. J. Seeds, "Delay, linewidth and bandwidth limitations in optical phase-locked loop design," Electron. Lett. 26, 389-391 (1990).
[CrossRef]

1983

R. C. Steele, "Optical phase-locked loop using semiconductor-laser diodes," Electron. Lett. 19, 69-71 (1983).
[CrossRef]

1982

S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, "Direct frequency-modulation in AlGaAs semiconductor-lasers," IEEE J. Quantum Electron. 18, 582-595 (1982).
[CrossRef]

D. S. Elliott, R. Roy, and S. J. Smith, "Extra-cavity laser band-shape and bandwidth modification," Phys. Rev. A 26, 12-18 (1982).
[CrossRef]

1965

L. H. Enloe and J. L. Rodda, "Laser phase-locked loop," Proc. Inst. Electr. Eng. 53, 165-166 (1965).

Appl. Opt.

Electron. Lett.

R. T. Ramos and A. J. Seeds, "Delay, linewidth and bandwidth limitations in optical phase-locked loop design," Electron. Lett. 26, 389-391 (1990).
[CrossRef]

G. J. Cowle, P. R. Morkel, R. I. Laming, and D. N. Payne, "Spectral broadening due to fiber amplifier phase noise," Electron. Lett. 26, 424-425 (1990).
[CrossRef]

C. X. Yu, J. E. Kansky, S. E. J. Shaw, D. V. Murphy, and C. Higgs, "Coherent beam combining of large number of PM fibres in 2-D fibre array," Electron. Lett. 42, 1024-1025 (2006).
[CrossRef]

R. C. Steele, "Optical phase-locked loop using semiconductor-laser diodes," Electron. Lett. 19, 69-71 (1983).
[CrossRef]

IEEE J. Quantum Electron.

S. Kobayashi, Y. Yamamoto, M. Ito, and T. Kimura, "Direct frequency-modulation in AlGaAs semiconductor-lasers," IEEE J. Quantum Electron. 18, 582-595 (1982).
[CrossRef]

Y. Kono, M. Takeoka, K. Uto, A. Uchida, and F. Kannari, "A coherent all-solid-state laser array using the Talbot effect in a three-mirror cavity," IEEE J. Quantum Electron. 36, 607-614 (2000).
[CrossRef]

P. Correc, O. Girard, and I. F. Defaria, "On the thermal contribution to the Fm response of Dfb lasers--theory and experiment," IEEE J. Quantum Electron. 30, 2485-2490 (1994).
[CrossRef]

L. Moller, "Novel aspects of spectral broadening due to fiber amplifier phase noise," IEEE J. Quantum Electron. 34, 1554-1558 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

E. Rochat and R. Dandliker, "New investigations on the effect of fiber amplifier phase noise," IEEE J. Sel. Top. Quantum Electron. 7, 49-54 (2001).
[CrossRef]

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

IEEE Trans. Microwave Theory Tech.

L. N. Langley, M. D. Elkin, C. Edge, M. J. Wale, U. Gliese, X. Huang, and A. J. Seeds, "Packaged semiconductor laser optical phase-locked loop (OPLL) for photonic generation, processing and transmission of microwave signals," IEEE Trans. Microwave Theory Tech. 47, 1257-1264 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

D. S. Elliott, R. Roy, and S. J. Smith, "Extra-cavity laser band-shape and bandwidth modification," Phys. Rev. A 26, 12-18 (1982).
[CrossRef]

Proc. Inst. Electr. Eng.

L. H. Enloe and J. L. Rodda, "Laser phase-locked loop," Proc. Inst. Electr. Eng. 53, 165-166 (1965).

Proc. SPIE

J. K. Lawson, D. M. Aikens, R. E. English, Jr., W. T. Whistler, W. House, and M. A. Nichols, "Surface figure and roughness tolerances for NIF optics and the interpretation of the gradient, P-V wavefront, and RMS specifications," Proc. SPIE 3782, 510-517 (1999).
[CrossRef]

Other

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1996).

D. R. Stephens, Phase-Locked Loops For Wireless Communications (Kluwer Academic, 1998).
[CrossRef]

E. Desurvire, Erbium-Doped Fiber Amplifiers Principles and Applications (Wiley, 1994), pp. 399-404.

S. Demoustier, A. Brignon, E. Lalliere, and J. P. Huignard, "Coherent combining of 1.5 μm Er-Yb doped single mode fiber amplifier," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CThAA5.
[PubMed]

F. M. Gardner, Phaselock Techniques, 3rd ed. (Wiley, 2005).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Schematic of a binary-tree filled-aperture CBC implementation using OPLLs and electric phase shifters.

Fig. 2
Fig. 2

Schematic of a heterodyne OPLL.

Fig. 3
Fig. 3

Schematic of the linearized model of an OPLL.

Fig. 4
Fig. 4

Power spectrum of the locked beat signal between the master laser (NP Photonics fiber laser) and the slave laser (external cavity laser).

Fig. 5
Fig. 5

Schematics of compensation circuits and filters. (a) Passive lag-lead filter, (b) active lag-lead filter, (c) aided acquisition circuit.

Fig. 6
Fig. 6

(a) Schematics of combining two OPLLs without and with a rf phase shifter loop, (b) measured combined signal (PD2) without the rf phase shifter loop.

Fig. 7
Fig. 7

(a) Graphic tool for solving the steady-state phase of the rf phase shifter feedback loop, (b) measured combined signal with the rf phase shifter loop.

Fig. 8
Fig. 8

Schematic of combining two OPLLs using servo system made of VCO.

Fig. 9
Fig. 9

Linearized model of the VCO loop.

Fig. 10
Fig. 10

Measured combined signal. The phase variation in fiber is corrected by the VCO loop.

Fig. 11
Fig. 11

Self-heterodyne fiber amplifier phase noise measurement setup, (b)–(d) predicted beat spectra with (b) no amplifier noise, (c) multiplicative phase noise, and (d) additive phase noise.

Fig. 12
Fig. 12

Experimental results of the self-heterodyne fiber amplifier phase noise measurement with span of (a) 10 MHz and (b) 1 kHz .

Fig. 13
Fig. 13

Example of coherent beam combining using a beam splitter.

Fig. 14
Fig. 14

Maximal combining efficiency limited by the normalized VCO frequency jitter σ ω K v . The number of element beams is 2 n .

Fig. 15
Fig. 15

Two scenarios of phase front deformation caused by the combining system.

Equations (32)

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ω s 0 = ω m ω r ,
ϕ s = ϕ m ϕ r ϕ e 0 ,
sin ( ϕ e 0 ) = ( ω m ω s , f r ω r ) K dc ,
ϕ e ( s ) = ( ϕ m n ( s ) + ϕ s n ( s ) ) H e ( s ) ,
ϕ s ( s ) = ϕ m n ( s ) H o ( s ) + ϕ s n ( s ) H e ( s ) ,
H o ( s ) = G o p ( s ) 1 + G o p ( s ) , H e ( s ) = 1 1 + G o p ( s )
G o p ( s ) = K dc cos ϕ e 0 F f ( s ) F FM ( s ) exp ( s τ ) s
σ ϕ e = ( ϕ e ϕ e 0 ) 2 ¯ = P n P s ,
f ( ϕ e ) = G ( 1 cos ϕ e ) , 0 f ( ϕ e ) 2 π ,
ϕ n f ( ϕ e ) = ϕ e .
( ω m ω v , f ) t K v ( 1 cos ϕ e ) d t ( ω m ω RF ) t ϕ 1 = ϕ e ,
ϕ e , s = cos 1 ( 1 ω RF ω v , f K v ) .
ϕ 2 ( s ) [ K v sin ϕ e , s s ϕ e ( s ) + ϕ v n ( s ) ] ϕ 1 ( s ) + ϕ f n ( s ) = ϕ e ( s ) .
ϕ e ( s ) = ϕ 2 ( s ) + ϕ f n ( s ) ϕ v n ( s ) ϕ 1 ( s ) 1 + K v sin ϕ e , s s .
E out ( t ) = G E 0 e i ϕ ( t ) e i ω t e i ϕ a ( t ) ,
E out ( t ) = G E 0 e i ϕ ( t ) e i ω t + E n e i ω t e i ϕ a ( t ) ,
I p ¯ = i E i [ Φ i ( r , t ) ] 2 ¯ ,
η = I p ¯ I 1 ¯ + I 2 ¯ 1 1 4 ϕ 2 ¯ 1 4 ( r 1 2 ¯ + r 2 2 ¯ ) ,
E t = E 0 i = 1 N exp ( i ϕ i ) .
η = 1 N 2 i , j = 1 N exp [ i ( ϕ i ϕ j ) ] ¯ = 1 N 1 N [ 1 exp ( σ 2 ) ] .
η = 1 ( N 1 ) N σ 2 .
σ ( 1 η ) N N 1 .
F ( x ; 0 , 1 ) = 1 2 π x exp ( u 2 2 ) d u .
P lock = [ 1 F ( x ; 0 , 1 ) ] 2 n 1 .
η lock = ( 1 x σ ω 2 K v ) n .
η = P lock η lock = [ 1 F ( x ; 0 , 1 ) ] 2 n 1 ( 1 x σ ω 2 K v ) n .
η = 1 N 2 i , j = 1 N exp [ i ( ϕ i ϕ j ) ] ¯ = 1 N 2 i , j = 1 N exp [ 1 2 D ( i , j ) σ 2 ] ,
η = 1 [ ( n 2 ) + 2 1 n ] σ 2 .
η = 1 [ n 1 2 + 2 n 1 ] σ 2 .
η = I p ¯ i = 1 N I ¯ i 1 1 N ( 1 1 N ) i = 1 N r i 2 ¯ .
r s = Δ P P 0 = K am P 0 i 0 sin ϕ e ,
K am = P 0 ( I I th ) .

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