Abstract

The first theory for two novel coherent beam combination architectures that are the first electronic beam combination architectures that completely eliminate the need for a separate reference beam are presented. Detailed theoretical models are developed and presented for the first time.

© 2006 Optical Society of America

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References

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  1. V. P. Gapontsev, "New milestones in the development of super high power fiber lasers," presented at Photonics West, OE/LASE 2006, San Jose, CA, Jan 21-26, 2006.
  2. P. K Cheo, A. Liu, and G. G. King, "A high brightness laser beam from a Phase-Locked Multicore Yb-Doped Fiber Laser Array," IEEE Photon. Technol. Lett. 13, 439-441 (2001).
    [CrossRef]
  3. E. J. Bochove, P. K. Cheo, and G. G. King, "Self-organization in a multicore fiber laser array," Opt. Lett. 28, 1200-1202 (2003).
    [CrossRef] [PubMed]
  4. H. Bruesselbach, D. C. Jones, M. S. Mangir, M. I. Minden, and J. L. Rogers, "Self-organized coherence in fiber laser arrays," Opt. Lett. 30, 1339-1341 (2003).
    [CrossRef]
  5. R. J. Beach, M. D. Feit, S. C. Mitchell, K. P. Culter, J. W. Dawson, S. A. Payne, R. W. Mead, J. S. Hayden, D. Krashkevich, and D. A. Alunni, "Ribbon fiber with multiple phase-locked gain cores," in Advances in Fiber Lasers, L. N. Durvasula, ed., Proc. SPIE 4974, 7-16 (2003).
    [CrossRef]
  6. R. A. Beach, M. D. Feit, R. H. Page, L. D. Brasure, R. Wilcox, and S. A. Payne, "Scalable antiguided ribbon laser," J. Opt. Soc. Am. B 19, 1521-1534 (2002).
    [CrossRef]
  7. C. J. Corcoran, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118-201121 (2005).
    [CrossRef]
  8. B. W. Grimes, W. B. Roh, and T. G. Alley, "Beam phasing multiple fiber amplifiers using a fiber phase conjugate mirror," in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds., Proc. SPIE 6102, 61021C-1 to 61021C-8 (2006).
  9. R. R. Rice et, J. A. Davis, J. S. Whitely, J. H. Hollister, and N. F. Ruggieri, "Coherent Fiber MOPA," Presented at 14th Annual Solid State and Diode Laser Technology Review, Sean Ross, ed., Albuquerque, NM (2001).
  10. J. Abderegg, S. J. Brosnan, M. E. Weber, H. Komine, and M. G. Wickham, "8-watt coherently-phased 4-element fiber array," in Advances in Fiber Lasers, L. N. Durvasula, ed., Proc. SPIE 4974, 1-6 (2003).
    [CrossRef]
  11. S. J. Augst, T. Y. Fan, and A. Sanchez, "Coherent beam combining and phase noise measurements of Yt fiber amplifiers," Opt. Lett. 29, 474-476 (2004).
    [CrossRef] [PubMed]
  12. M. Wickham, "Coherently coupled high power fiber arrays," in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds., Proc. SPIE 6102, 61020U-1 to 61020U-5 (2006).
  13. "A novel technique for phase locking Optical Fiber Arrays," T. M. Shay and V. Benham, in Free-Space Laser Communications IV, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 313-319 (2004).
    [CrossRef]
  14. "First experimental demonstration of fiber array phase locking by RF phase modulation," T. M. Shay and V. Benham, Proceedings of the 17th Solid State and Diode Laser Technology Review, S. Ross, ed., pg. BEAM-7 (2004).
  15. "Self-synchronous locking of optical coherence by single-detector electronic-frequency tagging," T. M. Shay, US Patent 7,058,098, June 2006.
  16. Note that in principle any odd harmonic of the modulation frequency, ωi, can be used to demodulate the phase error signal. However, the fundamental frequency generally produces the highest signal-to-noise ratio. Therefore, in this analysis the demodulation the fundamental frequency is always used for demodulation of the phase error signals.

2005 (1)

C. J. Corcoran, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118-201121 (2005).
[CrossRef]

2004 (1)

2003 (2)

2002 (1)

2001 (1)

P. K Cheo, A. Liu, and G. G. King, "A high brightness laser beam from a Phase-Locked Multicore Yb-Doped Fiber Laser Array," IEEE Photon. Technol. Lett. 13, 439-441 (2001).
[CrossRef]

Augst, S. J.

Beach, R. A.

Bochove, E. J.

Brasure, L. D.

Bruesselbach, H.

Cheo, P. K

P. K Cheo, A. Liu, and G. G. King, "A high brightness laser beam from a Phase-Locked Multicore Yb-Doped Fiber Laser Array," IEEE Photon. Technol. Lett. 13, 439-441 (2001).
[CrossRef]

Cheo, P. K.

Corcoran, C. J.

C. J. Corcoran, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118-201121 (2005).
[CrossRef]

Fan, T. Y.

Feit, M. D.

Jones, D. C.

King, G. G.

E. J. Bochove, P. K. Cheo, and G. G. King, "Self-organization in a multicore fiber laser array," Opt. Lett. 28, 1200-1202 (2003).
[CrossRef] [PubMed]

P. K Cheo, A. Liu, and G. G. King, "A high brightness laser beam from a Phase-Locked Multicore Yb-Doped Fiber Laser Array," IEEE Photon. Technol. Lett. 13, 439-441 (2001).
[CrossRef]

Liu, A.

P. K Cheo, A. Liu, and G. G. King, "A high brightness laser beam from a Phase-Locked Multicore Yb-Doped Fiber Laser Array," IEEE Photon. Technol. Lett. 13, 439-441 (2001).
[CrossRef]

Mangir, M. S.

Minden, M. I.

Page, R. H.

Payne, S. A.

Rogers, J. L.

Sanchez, A.

Wilcox, R.

Appl. Phys. Lett. (1)

C. J. Corcoran, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118-201121 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. K Cheo, A. Liu, and G. G. King, "A high brightness laser beam from a Phase-Locked Multicore Yb-Doped Fiber Laser Array," IEEE Photon. Technol. Lett. 13, 439-441 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Other (10)

V. P. Gapontsev, "New milestones in the development of super high power fiber lasers," presented at Photonics West, OE/LASE 2006, San Jose, CA, Jan 21-26, 2006.

B. W. Grimes, W. B. Roh, and T. G. Alley, "Beam phasing multiple fiber amplifiers using a fiber phase conjugate mirror," in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds., Proc. SPIE 6102, 61021C-1 to 61021C-8 (2006).

R. R. Rice et, J. A. Davis, J. S. Whitely, J. H. Hollister, and N. F. Ruggieri, "Coherent Fiber MOPA," Presented at 14th Annual Solid State and Diode Laser Technology Review, Sean Ross, ed., Albuquerque, NM (2001).

J. Abderegg, S. J. Brosnan, M. E. Weber, H. Komine, and M. G. Wickham, "8-watt coherently-phased 4-element fiber array," in Advances in Fiber Lasers, L. N. Durvasula, ed., Proc. SPIE 4974, 1-6 (2003).
[CrossRef]

M. Wickham, "Coherently coupled high power fiber arrays," in Fiber Lasers III: Technology, Systems, and Applications, A. J. W. Brown, J. Nilsson, D. J. Harter, and A. Tunnermann, eds., Proc. SPIE 6102, 61020U-1 to 61020U-5 (2006).

"A novel technique for phase locking Optical Fiber Arrays," T. M. Shay and V. Benham, in Free-Space Laser Communications IV, J. C. Ricklin and D. G. Voelz, eds., Proc. SPIE 5550, 313-319 (2004).
[CrossRef]

"First experimental demonstration of fiber array phase locking by RF phase modulation," T. M. Shay and V. Benham, Proceedings of the 17th Solid State and Diode Laser Technology Review, S. Ross, ed., pg. BEAM-7 (2004).

"Self-synchronous locking of optical coherence by single-detector electronic-frequency tagging," T. M. Shay, US Patent 7,058,098, June 2006.

Note that in principle any odd harmonic of the modulation frequency, ωi, can be used to demodulate the phase error signal. However, the fundamental frequency generally produces the highest signal-to-noise ratio. Therefore, in this analysis the demodulation the fundamental frequency is always used for demodulation of the phase error signals.

R. J. Beach, M. D. Feit, S. C. Mitchell, K. P. Culter, J. W. Dawson, S. A. Payne, R. W. Mead, J. S. Hayden, D. Krashkevich, and D. A. Alunni, "Ribbon fiber with multiple phase-locked gain cores," in Advances in Fiber Lasers, L. N. Durvasula, ed., Proc. SPIE 4974, 7-16 (2003).
[CrossRef]

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Figures (1)

Fig. 1.
Fig. 1.

A linear control loop model for self-synchronous LOCSET.

Equations (27)

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E u ( t ) = E u 0 · Cos ( ω L · t + ϕ u ) and
E i ( t ) = E i 0 · Cos ( ω L · t + ϕ i + β i · Sin ( ω i · t ) ) ,
E i ( t ) = E i 0 · [ Cos ( ω L · t + ϕ i ) Cos ( β i · Sin ( ω i · t ) ) Sin ( ω L · t + ϕ i ) Sin ( β i · Sin ( ω i · t ) ) ] ,
i PD ( t ) = R PD · A · μ o ε o · { E u 2 ( t ) + ( l = 1 N E l ( t ) ) ( j = 1 N E j ( t ) ) + 2 · E u ( t ) · j = 1 N E j ( t ) } ,
i u 2 ( t ) = ε o μ o · R PD · A · E u 2 ( t ) ,
i uj ( t ) = ε o μ o · R PD · A · 2 · E u ( t ) · j = 1 N E j ( t ) .
i ij ( t ) = ε o μ o · R PD · A · ( l = 1 N E l ( t ) ) ( j = 1 , j l N E j ( t ) ) .
i u 2 ( t ) = R PD · P u 2 .
i lj ( t ) = R PD 2
l = 1 N P l · j = 1 j l N P j [ { Cos ( ϕ l ϕ j ) ( J 0 ( β l ) + 2 · n l = 1 J 2 n l ( β l ) · Cos ( 2 · n l · ω l · t ) ) ( J 0 ( β j ) + 2 · n j = 1 J 2 n j ( β j ) · Cos ( 2 · n j · ω j · t ) ) } { Sin ( ϕ l ϕ j ) · 2 · n l = 1 J 2 n l 1 ( β l ) · Sin ( ( 2 · n l 1 ) · ω l · t ) ) ( J 0 ( β j ) + 2 · n j = 1 J 2 n j ( β j ) · Cos ( 2 · n j · ω j · t ) ) } + { Sin ( ϕ l ϕ j ) ( J 0 ( β l ) + 2 · n j = 1 J 2 n j ( β j ) · Cos ( 2 · n j · ω j · t ) ) 2 · n j = 1 J 2 n j 1 ( β j ) · Sin ( ( 2 · n j 1 ) · ω j · t ) } + { Cos ( ϕ l ϕ j ) ( 2 · n j = 1 J 2 n j 1 ( β j ) ·Sin ( ( 2 · n j 1 ) · ω j · t ) ) 2 · n l = 1 J 2 n l 1 ( β l ) ·Sin ( ( 2 · n l 1 ) · ω l · t ) } ] ,
i uj ( t ) = R PD · P u ·
j = 1 N P j · [ { Cos ( ϕ j ϕ u ) ( J 0 ( β j ) + 2 · n j = 1 J 2 n j ( β j ) · Cos ( 2 · n j · ω j · t ) ) } + { Sin ( ϕ j ϕ u ) · 2 · n j = 1 J 2 n j 1 ( β j ) · Sin ( ( 2 · n j 1 ) · ω j · t ) } ] ,
S uic = 1 τ · 0 τ i ui ( t ) · Sin ( ω c · t ) · dt =
1 τ · 0 τ { 2 · R PD · P u · Sin ( ω c · t ) i = 1 N P i · [ { Cos ( ϕ i ϕ u ) ( J 0 ( β i ) + 2 · n i = 1 J 2 n i ( β i ) · Cos ( 2 · n i · ω i · t ) ) } + { Sin ( ϕ u ϕ i ) · 2 · n i = 1 J 2 n i 1 ( β i ) · Sin ( ( 2 · n i 1 ) · ω i · t ) } ] } · dt .
S uii = R PD · P u · P i · Sin ( ϕ u ϕ i ) · J 1 ( β i ) ,
S ijc = 1 τ 0 τ i ij ( t ) · Sin ( ω c · t ) · dt =
S iji = R PD · p i · J 1 ( β i ) · j = 1 N p j · J 0 ( β j ) · Sin ( ϕ j ϕ i ) ,
S SRi = S uii + S iji
S SRi = R PD · P i · J 1 ( β i ) ( P u · Sin ( ϕ u ϕ i ) + j = 1 N P j · J 0 ( β j ) · Sin ( ϕ j ϕ i ) ) ,
S SSi = S iji = R PD · P i · J 1 ( β i ) ( j = 1 N P j · J 0 ( β j ) · Sin ( ϕ j ϕ i ) ) ,
ϕ j ( t ) = ϕ jo + Δ ϕ j ( t ) ,
S SSi = R PD · P i · J 1 ( β i ) ( j = 1 N P j · J 0 ( β j ) · Sin ( ϕ jo ϕ io + δ ϕ j ( t ) Δ ϕ i ( t ) ) ) ,
S SSi = R PD · P i · J 1 ( β i ) ( j = 1 N P j · J 0 ( β j ) · [ δ ϕ je ( t ) Δ ϕ i ( t ) ] ) .
K ij = R PD · P i · J 1 ( β i ) · P j · J 0 ( β j ) .
δ ϕ ie _ i ( s ) = s · Δ ϕ i s + A e · K PM τ · j = 1 j i N K ij ,
SNR i = ( δ ϕ ie _ rms · R PD · J 1 ( β i ) · P i · j = 1 j 1 N J 0 ( β j ) · P j ) 2 2 · q · B · R PD · j = 1 N P j ,
SNR i δ ϕ ie _ rms 2 · R PD · J 1 ( β i ) 2 · P i · π · τ q · A e · K PM · K ij ,

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