Abstract

Phase control is crucial to the operation of coherent beam combining systems, whether for laser radar or high-power beam combining. We have recently demonstrated a design for a multi-aperture, coherently combined, synchronized- and phased-array slow light laser radar (SLIDAR) that is capable of scanning in two dimensions with dynamic group delay compensation. Here we describe in detail the optical phase locking system used in the design. The phase locking system achieves an estimated Strehl ratio of 0.8, and signals from multiple emitting apertures are phase locked simultaneously to within π/5 radians (1/10 wave) after propagation through 2.2 km of single-mode fiber per channel. Phase locking performance is maintained even as two independent slow light mechanisms are utilized simultaneously.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. D. Nabors, “Effects of phase errors on coherent emitter arrays,” Appl. Opt.33, 2284–2289 (1994).
    [CrossRef] [PubMed]
  2. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett.29, 474–476 (2004).
    [CrossRef] [PubMed]
  3. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron.11, 567–577 (2005).
    [CrossRef]
  4. N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.46, 5933–5943 (2007).
    [CrossRef] [PubMed]
  5. W. Liang, N. Satyan, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Coherent beam combining with multilevel optical phase-locked loops,” J. Opt. Soc. Am. B24, 2930–2939 (2007).
    [CrossRef]
  6. W. Liang, A. Yariv, A. Kewitsch, and G. Rakuljic, “Coherent combining of the output of two semiconductor lasers using optical phase-lock loops,” Opt. Lett.32, 370–372 (2007).
    [CrossRef] [PubMed]
  7. P. F. McManamon, “Review of ladar: A historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng.51, 060901 (2012).
    [CrossRef]
  8. A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express19, 15760–15769 (2011).
    [CrossRef] [PubMed]
  9. A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar system with two-dimensional scanning,” Opt. Lett.37, 329–331 (2012).
    [CrossRef] [PubMed]
  10. Z. Shi, A. Schweinsberg, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar (SLIDAR),” Opt. Photon. News23, 51–51 (2012).
    [CrossRef]
  11. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London)397, 594–598 (1999).
    [CrossRef]
  12. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science301, 200–202 (2003).
    [CrossRef] [PubMed]
  13. M. González Herráez, K. Y. Song, and L. Thévenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express14, 1395–1400 (2006).
    [CrossRef] [PubMed]
  14. B. Zhang, L. Zhang, L.-S. Yan, I. Fazal, J. Yang, and A. E. Willner, “Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line,” Opt. Express15, 8317–8322 (2007).
    [CrossRef] [PubMed]
  15. F. Öhman, K. Yvind, and J. Mørk, “Slow light in a semiconductor waveguide for true-time delay applications in microwave photonics,” IEEE Photon. Technol. Lett.19, 1145–1147 (2007).
    [CrossRef]
  16. R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett.98, 043902 (2007).
    [CrossRef] [PubMed]
  17. Y. Okawachi, R. Salem, and A. L. Gaeta, “Continuous tunable delays at 10-Gb/s data rates using self-phase modulation and dispersion,” J. Lightwave Technol.25, 3710–3715 (2007).
    [CrossRef]
  18. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol.25, 201–206 (2007).
    [CrossRef]
  19. Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
    [CrossRef]
  20. S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers (Invited),” J. Opt. Soc. Am. B24, 1707–1715 (2007).
    [CrossRef]
  21. P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
    [CrossRef]
  22. A. M. Marino and C. R. Stroud, “Phase-locked laser system for use in atomic coherence experiments,” Rev. Sci. Instrum.79, 013104 (2008).
    [CrossRef] [PubMed]
  23. T. M. Shay and V. Benham, “First experimental demonstration of phase locking of optical fiber arrays by RF phase modulation,” Proc. SPIE5550, 313–319 (2004).
    [CrossRef]
  24. T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14, 12015–12021 (2006).
    [CrossRef] [PubMed]
  25. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett.22, 907–909 (1997).
    [CrossRef] [PubMed]
  26. L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P (2005).
    [CrossRef]
  27. X. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36, 3121–3123 (2011).
    [CrossRef] [PubMed]

2012 (3)

Z. Shi, A. Schweinsberg, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar (SLIDAR),” Opt. Photon. News23, 51–51 (2012).
[CrossRef]

P. F. McManamon, “Review of ladar: A historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng.51, 060901 (2012).
[CrossRef]

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar system with two-dimensional scanning,” Opt. Lett.37, 329–331 (2012).
[CrossRef] [PubMed]

2011 (2)

2010 (1)

Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
[CrossRef]

2009 (1)

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

2008 (1)

A. M. Marino and C. R. Stroud, “Phase-locked laser system for use in atomic coherence experiments,” Rev. Sci. Instrum.79, 013104 (2008).
[CrossRef] [PubMed]

2007 (9)

F. Öhman, K. Yvind, and J. Mørk, “Slow light in a semiconductor waveguide for true-time delay applications in microwave photonics,” IEEE Photon. Technol. Lett.19, 1145–1147 (2007).
[CrossRef]

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett.98, 043902 (2007).
[CrossRef] [PubMed]

W. Liang, A. Yariv, A. Kewitsch, and G. Rakuljic, “Coherent combining of the output of two semiconductor lasers using optical phase-lock loops,” Opt. Lett.32, 370–372 (2007).
[CrossRef] [PubMed]

Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol.25, 201–206 (2007).
[CrossRef]

B. Zhang, L. Zhang, L.-S. Yan, I. Fazal, J. Yang, and A. E. Willner, “Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line,” Opt. Express15, 8317–8322 (2007).
[CrossRef] [PubMed]

S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers (Invited),” J. Opt. Soc. Am. B24, 1707–1715 (2007).
[CrossRef]

N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.46, 5933–5943 (2007).
[CrossRef] [PubMed]

W. Liang, N. Satyan, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Coherent beam combining with multilevel optical phase-locked loops,” J. Opt. Soc. Am. B24, 2930–2939 (2007).
[CrossRef]

Y. Okawachi, R. Salem, and A. L. Gaeta, “Continuous tunable delays at 10-Gb/s data rates using self-phase modulation and dispersion,” J. Lightwave Technol.25, 3710–3715 (2007).
[CrossRef]

2006 (2)

2005 (2)

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P (2005).
[CrossRef]

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

2004 (2)

T. M. Shay and V. Benham, “First experimental demonstration of phase locking of optical fiber arrays by RF phase modulation,” Proc. SPIE5550, 313–319 (2004).
[CrossRef]

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

2003 (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science301, 200–202 (2003).
[CrossRef] [PubMed]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London)397, 594–598 (1999).
[CrossRef]

1997 (1)

1994 (1)

Aflatouni, F.

Ali-Khan, I.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett.98, 043902 (2007).
[CrossRef] [PubMed]

Augst, S. J.

Baker, J. T.

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London)397, 594–598 (1999).
[CrossRef]

Benham, V.

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science301, 200–202 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar system with two-dimensional scanning,” Opt. Lett.37, 329–331 (2012).
[CrossRef] [PubMed]

Z. Shi, A. Schweinsberg, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar (SLIDAR),” Opt. Photon. News23, 51–51 (2012).
[CrossRef]

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express19, 15760–15769 (2011).
[CrossRef] [PubMed]

Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science301, 200–202 (2003).
[CrossRef] [PubMed]

Broadbent, C. J.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett.98, 043902 (2007).
[CrossRef] [PubMed]

Camacho, R. M.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett.98, 043902 (2007).
[CrossRef] [PubMed]

Carhart, G. W.

Culpepper, M. A.

Dawes, A. M. C.

Dierking, M. P.

Duncan, B. D.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London)397, 594–598 (1999).
[CrossRef]

Fan, T. Y.

Fazal, I.

Gaeta, A. L.

Gauthier, D. J.

González Herráez, M.

Guo, S.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London)397, 594–598 (1999).
[CrossRef]

Hashemi, H.

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London)397, 594–598 (1999).
[CrossRef]

Howell, J. C.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett.98, 043902 (2007).
[CrossRef] [PubMed]

Kewitsch, A.

Leng, J.

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science301, 200–202 (2003).
[CrossRef] [PubMed]

Liang, W.

Liu, L.

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P (2005).
[CrossRef]

Liu, Z.

X. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36, 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

Lu, C. A.

Ma, H.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

Ma, Y.

X. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36, 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

Marino, A. M.

A. M. Marino and C. R. Stroud, “Phase-locked laser system for use in atomic coherence experiments,” Rev. Sci. Instrum.79, 013104 (2008).
[CrossRef] [PubMed]

Martínez Gámez, M. A.

Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
[CrossRef]

McManamon, P. F.

P. F. McManamon, “Review of ladar: A historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng.51, 060901 (2012).
[CrossRef]

Miller, N. J.

Mørk, J.

F. Öhman, K. Yvind, and J. Mørk, “Slow light in a semiconductor waveguide for true-time delay applications in microwave photonics,” IEEE Photon. Technol. Lett.19, 1145–1147 (2007).
[CrossRef]

Nabors, C. D.

Nelson, D. J.

Öhman, F.

F. Öhman, K. Yvind, and J. Mørk, “Slow light in a semiconductor waveguide for true-time delay applications in microwave photonics,” IEEE Photon. Technol. Lett.19, 1145–1147 (2007).
[CrossRef]

Okawachi, Y.

Pilkington, D.

Rakuljic, G.

Ranka, J. K.

Ricklin, J. C.

Salem, R.

Sanchez, A.

Sanchez, A. D.

Satyan, N.

Schweinsberg, A.

Z. Shi, A. Schweinsberg, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar (SLIDAR),” Opt. Photon. News23, 51–51 (2012).
[CrossRef]

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar system with two-dimensional scanning,” Opt. Lett.37, 329–331 (2012).
[CrossRef] [PubMed]

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express19, 15760–15769 (2011).
[CrossRef] [PubMed]

Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
[CrossRef]

Shay, T. M.

Shi, Z.

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar system with two-dimensional scanning,” Opt. Lett.37, 329–331 (2012).
[CrossRef] [PubMed]

Z. Shi, A. Schweinsberg, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar (SLIDAR),” Opt. Photon. News23, 51–51 (2012).
[CrossRef]

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express19, 15760–15769 (2011).
[CrossRef] [PubMed]

Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
[CrossRef]

Song, K. Y.

Spring, J.

Stroud, C. R.

A. M. Marino and C. R. Stroud, “Phase-locked laser system for use in atomic coherence experiments,” Rev. Sci. Instrum.79, 013104 (2008).
[CrossRef] [PubMed]

Thévenaz, L.

Vornehm, J. E.

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar system with two-dimensional scanning,” Opt. Lett.37, 329–331 (2012).
[CrossRef] [PubMed]

Z. Shi, A. Schweinsberg, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar (SLIDAR),” Opt. Photon. News23, 51–51 (2012).
[CrossRef]

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express19, 15760–15769 (2011).
[CrossRef] [PubMed]

Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
[CrossRef]

Vorontsov, M. A.

Wang, X.

X. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36, 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

Ward, B.

Willner, A. E.

Xu, X.

X. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36, 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

Yan, L.-S.

Yang, J.

Yariv, A.

Yvind, K.

F. Öhman, K. Yvind, and J. Mørk, “Slow light in a semiconductor waveguide for true-time delay applications in microwave photonics,” IEEE Photon. Technol. Lett.19, 1145–1147 (2007).
[CrossRef]

Zhang, B.

Zhang, L.

Zhou, P.

X. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36, 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[CrossRef]

Zhu, Z.

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (2)

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron.15, 248–256 (2009).
[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 Photon. Technol. Lett. (1)

F. Öhman, K. Yvind, and J. Mørk, “Slow light in a semiconductor waveguide for true-time delay applications in microwave photonics,” IEEE Photon. Technol. Lett.19, 1145–1147 (2007).
[CrossRef]

J. Lightwave Technol. (2)

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

Nature (London) (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London)397, 594–598 (1999).
[CrossRef]

Opt. Eng. (1)

P. F. McManamon, “Review of ladar: A historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng.51, 060901 (2012).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Opt. Photon. News (1)

Z. Shi, A. Schweinsberg, J. E. Vornehm, and R. W. Boyd, “A slow-light laser radar (SLIDAR),” Opt. Photon. News23, 51–51 (2012).
[CrossRef]

Phys. Lett. A (1)

Z. Shi, A. Schweinsberg, J. E. Vornehm, M. A. Martínez Gámez, and R. W. Boyd, “Low distortion, continuously tunable, positive and negative time delays by slow and fast light using stimulated Brillouin scattering,” Phys. Lett. A374, 4071–4074 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett.98, 043902 (2007).
[CrossRef] [PubMed]

Proc. SPIE (2)

T. M. Shay and V. Benham, “First experimental demonstration of phase locking of optical fiber arrays by RF phase modulation,” Proc. SPIE5550, 313–319 (2004).
[CrossRef]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

A. M. Marino and C. R. Stroud, “Phase-locked laser system for use in atomic coherence experiments,” Rev. Sci. Instrum.79, 013104 (2008).
[CrossRef] [PubMed]

Science (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science301, 200–202 (2003).
[CrossRef] [PubMed]

Supplementary Material (1)

» Media 1: MOV (485 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

An 8 ms sample of raw, uncorrected phase noise (black line) and phase error after correction by the phase control system (blue line). The phase error consists of two parts: the zero-mean residual phase error and the 4π snapback event that occurs at 4 ms. (Only the phase error modulo 2π affects system performance.)

Fig. 2
Fig. 2

Schematic diagram of the optical system (see text for details). A fraction of each channel’s output signal is heterodyned with a frequency-shifted reference to monitor the phase. Phase locking electronics (PL) feed back to an electro-optic modulator (EOM) to control the phase. The local oscillator (LO) used to frequency-shift the phase reference is also used by the phase locking electronics. Inset: Emitter configuration, as seen looking into the emitters.

Fig. 3
Fig. 3

Block diagram of the phase control electronics. The 55 MHz local oscillator (LO) is phase-shifted to allow independent, arbitrary phasing of each channel. The heterodyne signal is amplified, its DC bias is removed by the bias T, and it is mixed with the LO and then low-pass filtered (LPF) to perform a phase-sensitive detection of the heterodyne signal. The resulting signal is then fed to the proportional-integral (P-I) controller.

Fig. 4
Fig. 4

Block diagram of the proportional-integral (P-I) controller, including the loop filter and the fast 2nπ-phase snapback circuit. The signal from the low-pass filter (LPF) in Fig. 3 is the primary input to an integrating op-amp that tracks the phase error and drives the EOM. When the op-amp output voltage VEOM exceeds ±3Vπ (nominally ±12 V), a set-reset (S-R) latch engages an analog switch that quickly drives VEOM toward the opposite polarity; the switch disengages once VEOM is within the range ±Vπ (nominally ±4 V). The process typically takes about 1.2 μs. In practice, the comparator bias voltages and the resistor and capacitor values are tuned for optimal snapback performance and are usually selected to provide a 4π snapback. (Some circuit elements are not shown, including buffering op-amps, diodes, and a power-on reset circuit.)

Fig. 5
Fig. 5

RMS residual phase error vs. approximate SBS gain, showing about π/5 radians RMS residual phase error for all SBS gain values, with the SBS pump both broadened and unbroadened. In our system, the dispersion-compensating fiber used to achieve dispersive slow light performs similarly to the dispersion-shifted fiber used here to achieve SBS slow light, including under changes in wavelength.

Fig. 6
Fig. 6

( Media 1) A representative image from a real-time video showing the far-field pattern of the three-channel system, first with phase locking disabled and then with phase locking enabled (image taken when phase locking is enabled). When phase locking is disabled, the bright lobes in the far-field pattern shift rapidly in both transverse dimensions, since the points of constructive interference change with the emitter phases. When phase locking is enabled, the lobes lock into place, with a small but still visible amount of jitter.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

u ( x , y ) = u 0 ( x , y ) * j = 1 N δ ( x x j , y y j ) exp ( i ϕ j ) = u 0 ( x , y ) * g ( x , y ) ,
U 0 ( f x , f y ) = u 0 ( x , y ) exp [ i 2 π ( f x x + f y y ) ] d x d y
G ( f x , f y ) = j = 1 N exp [ i 2 π ( f x x j + f y y j ) + i ϕ j ] .
I ( f x , f y ) = | U ( f x , f y ) | 2 = | U 0 ( f x , f y ) | 2 | G ( f x , f y ) | 2 .
S = I ( 0 , 0 ) I max ( 0 , 0 ) = | U 0 ( 0 , 0 ) | 2 | G ( 0 , 0 ) | 2 | U 0 ( 0 , 0 ) | 2 [ max | G ( 0 , 0 ) | 2 ] = | G ( 0 , 0 ) | 2 max | G ( 0 , 0 ) | 2 ,
G ( 0 , 0 ) G * ( 0 , 0 ) = [ j = 1 N exp ( i ϕ j ) ] [ j = 1 N exp ( i ϕ j ) ] = j = 1 N [ 1 + 2 k = j + 1 N cos ( ϕ j ϕ k ) ] ,
S = 1 N 2 | G ( 0 , 0 ) | 2 = 1 N 2 j = 1 N [ 1 + 2 k = j + 1 N cos ( ϕ j ϕ k ) ] .
cos ( ϕ j ϕ k ) = 1 2 π σ 2 exp ( ϕ j 2 ϕ k 2 2 σ 2 ) cos ( ϕ j ϕ k ) d ϕ j d ϕ k = exp ( σ 2 ) .
S = 1 N 2 j = 1 N [ 1 + 2 k = j + 1 N exp ( σ 2 ) ] = 1 N + N 1 N exp ( σ 2 ) .
ϕ j ( t ) = ϕ R , j ( t ) + ϕ S , j ( t ) ,
P ( m ; T ) = exp ( r T ) ( r T ) m m ! .
S ( t ) t 0 , t 1 = 1 t 1 t 0 t 0 t 1 S ( t ) d t .
S ( t ) t 0 , t 1 = 1 N 2 | G ( 0 , 0 ; t ) | 2 t 0 , t 1 = j = 1 N [ 1 + 2 k = j + 1 N cos ( ϕ j ( t ) ϕ k ( t ) ) ] t 0 , t 1 = 1 N 2 j = 1 N { 1 + 2 k = j + 1 N cos [ ϕ R , j ( t ) ϕ R , k ( t ) + ϕ S , j ( t ) ϕ S , k ( t ) ] t 0 , t 1 } .
cos [ ϕ R , j ( t ) ϕ R , k ( t ) + 2 n π ( t t 0 ) / τ ] t 0 , t 0 + τ = 1 2 π σ 2 exp ( ϕ j 2 ϕ k 2 2 σ 2 ) cos [ ϕ j ϕ k + 2 n π ( t t 0 ) / τ ] d ϕ j d ϕ k t 0 , t 0 + τ = exp ( σ 2 ) cos [ 2 n π ( t t 0 ) / τ ] t 0 , t 0 + τ = 0 .
cos [ ϕ R , j ( t ) ϕ R , k ( t ) ] t 0 , t 0 + τ = exp ( σ 2 ) t 0 , t 0 + τ = exp ( σ 2 ) .
S ( t ) t 0 , t 0 + T = 1 N 2 | G ( 0 , 0 ; t ) | 2 t 0 , t 0 + T = 1 N 2 m = 0 P ( m ; T ) j = 1 N [ 1 + 2 k = j + 1 N ( 1 m τ T ) exp ( σ 2 ) ] = 1 N + N 1 N ( 1 r τ ) exp ( σ 2 ) .

Metrics