Abstract

We propose, analyze and demonstrate the optoelectronic phase-locking of optical waves whose frequencies are chirped continuously and rapidly with time. The optical waves are derived from a common optoelectronic swept-frequency laser based on a semiconductor laser in a negative feedback loop, with a precisely linear frequency chirp of 400 GHz in 2 ms. In contrast to monochromatic waves, a differential delay between two linearly chirped optical waves results in a mutual frequency difference, and an acoustooptic frequency shifter is therefore used to phase-lock the two waves. We demonstrate and characterize homodyne and heterodyne optical phase-locked loops with rapidly chirped waves, and show the ability to precisely control the phase of the chirped optical waveform using a digital electronic oscillator. A loop bandwidth of ∼ 60 kHz, and a residual phase error variance of < 0.01 rad2 between the chirped waves is obtained. Further, we demonstrate the simultaneous phase-locking of two optical paths to a common master waveform, and the ability to electronically control the resultant two-element optical phased array. The results of this work enable coherent power combining of high-power fiber amplifiers—where a rapidly chirping seed laser reduces stimulated Brillouin scattering—and electronic beam steering of chirped optical waves.

© 2012 OSA

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2012 (1)

2011 (1)

2010 (1)

2009 (4)

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express17, 15991–15999 (2009).
[CrossRef] [PubMed]

T. von Lerber, S. Honkanen, A. Tervonen, H. Ludvigsen, and F. Küppers, “Optical clock recovery methods: Review (Invited),” Opt. Fiber Technol.15, 363–372 (2009).
[CrossRef]

N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron.45, 755–761 (2009).
[CrossRef]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers Using optical phase-lock loops (Invited),” IEEE J. Sel. Top. Quantum Electron.15, 240–247 (2009).
[CrossRef]

2007 (2)

2006 (2)

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]

S. Takasaka, Y. Ozeki, S. Namiki, and M. Sakano, “External synchronization of 160-GHz optical beat signal by optical phase-locked loop technique,” IEEE Photon. Technol. Lett.18, 2457–2459 (2006).
[CrossRef]

2005 (3)

2004 (2)

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

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]

2001 (1)

2000 (2)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

L. A. Johansson and A. J. Seeds, “Millimeter-wave modulated optical signal generation with high spectral purity and wide-locking bandwidth using a fiber-integrated optical injection phase-lock loop,” IEEE Photon. Technol. Lett.12, 690–692 (2000).
[CrossRef]

1999 (2)

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

1996 (1)

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol.14, 50 –57 (1996).
[CrossRef]

1994 (1)

1992 (1)

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

1990 (1)

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, and B. L. Kasper, “4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers,” IEEE Photon. Technol. Lett.2, 285–287 (1990).
[CrossRef]

1988 (1)

Y. Aoki, K. Tajima, and I. Mito, “Input power limits of single-mode optical fibers due to stimulated Brillouin scattering in optical communication systems,” J. Lightwave Technol.6, 710 –719 (1988).
[CrossRef]

1986 (1)

L. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communications systems,” J. Lightwave Technol.4, 415–425 (1986).
[CrossRef]

1984 (1)

S. Saito, O. Nilsson, and Y. Yamamoto, “Coherent FSK transmitter using a negative feedback stabilised semiconductor laser,” Electron. Lett.20, 703–704 (1984).
[CrossRef]

1983 (1)

H. Philipp, A. Scholtz, E. Bonek, and W. Leeb, “Costas loop experiments for a 10.6 μm communications receiver,” IEEE Trans. Commun.31, 1000–1002 (1983).
[CrossRef]

Aflatouni, F.

Andrekson, P. A.

Aoki, Y.

Y. Aoki, K. Tajima, and I. Mito, “Input power limits of single-mode optical fibers due to stimulated Brillouin scattering in optical communication systems,” J. Lightwave Technol.6, 710 –719 (1988).
[CrossRef]

Augst, S. J.

Bächtold, W.

Bartels, A.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Bartelt-Berger, L.

Bi, Z.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Boggio, J. M. C.

Bonek, E.

H. Philipp, A. Scholtz, E. Bonek, and W. Leeb, “Costas loop experiments for a 10.6 μm communications receiver,” IEEE Trans. Commun.31, 1000–1002 (1983).
[CrossRef]

Brauch, U.

Breitkopf, S.

Broberg, B.

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

Bruun, M.

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

Cahill, J. P.

Cundiff, S. T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Diddams, S. A.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Dross, F.

Edge, C.

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

Elkin, M. D.

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

Erni, D.

Fan, T. Y.

Fragnito, H. L.

Gardner, F. M.

F. M. Gardner, Phaselock Techniques (Hoboken, NJ: John Wiley and Sons, 2005).
[CrossRef]

Giesen, A.

Gliese, U.

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

Gnauck, A. H.

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, and B. L. Kasper, “4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers,” IEEE Photon. Technol. Lett.2, 285–287 (1990).
[CrossRef]

Goodno, G. D.

G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett.35, 1542–1544 (2010).
[CrossRef] [PubMed]

S. B. Weiss, M. E. Weber, and G. D. Goodno, “Group delay locking of broadband phased lasers,” in “Lasers, Sources, and Related Photonic Devices,” (Optical Society of America, 2012), p. AM3A.5.

Hall, J. L.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Hansryd, J.

Hashemi, H.

Herzog, F.

Higgs, C.

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]

Hollberg, L.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Holzwarth, R.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Honkanen, S.

T. von Lerber, S. Honkanen, A. Tervonen, H. Ludvigsen, and F. Küppers, “Optical clock recovery methods: Review (Invited),” Opt. Fiber Technol.15, 363–372 (2009).
[CrossRef]

Huang, X.

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

Huegel, H.

Johansson, L. A.

L. A. Johansson and A. J. Seeds, “Millimeter-wave modulated optical signal generation with high spectral purity and wide-locking bandwidth using a fiber-integrated optical injection phase-lock loop,” IEEE Photon. Technol. Lett.12, 690–692 (2000).
[CrossRef]

Jones, D. J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Kahn, J. M.

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, and B. L. Kasper, “4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers,” IEEE Photon. Technol. Lett.2, 285–287 (1990).
[CrossRef]

Kansky, J. E.

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]

Kasper, B. L.

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, and B. L. Kasper, “4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers,” IEEE Photon. Technol. Lett.2, 285–287 (1990).
[CrossRef]

Kazovsky, L.

L. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communications systems,” J. Lightwave Technol.4, 415–425 (1986).
[CrossRef]

Kewitsch, A.

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers Using optical phase-lock loops (Invited),” IEEE J. Sel. Top. Quantum Electron.15, 240–247 (2009).
[CrossRef]

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. Express15, 3201–3205 (2007).
[CrossRef] [PubMed]

Klenke, A.

Knudsen, S. N.

Korotky, S. K.

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, and B. L. Kasper, “4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers,” IEEE Photon. Technol. Lett.2, 285–287 (1990).
[CrossRef]

Kudielka, K.

Küppers, F.

T. von Lerber, S. Honkanen, A. Tervonen, H. Ludvigsen, and F. Küppers, “Optical clock recovery methods: Review (Invited),” Opt. Fiber Technol.15, 363–372 (2009).
[CrossRef]

Langley, L. N.

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

Leeb, W.

H. Philipp, A. Scholtz, E. Bonek, and W. Leeb, “Costas loop experiments for a 10.6 μm communications receiver,” IEEE Trans. Commun.31, 1000–1002 (1983).
[CrossRef]

Leyva, V.

Liang, W.

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers Using optical phase-lock loops (Invited),” IEEE J. Sel. Top. Quantum Electron.15, 240–247 (2009).
[CrossRef]

N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron.45, 755–761 (2009).
[CrossRef]

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. Express15, 3201–3205 (2007).
[CrossRef] [PubMed]

Limpert, J.

Lindgren, S.

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

Lintz Christensen, E.

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

Ludvigsen, H.

T. von Lerber, S. Honkanen, A. Tervonen, H. Ludvigsen, and F. Küppers, “Optical clock recovery methods: Review (Invited),” Opt. Fiber Technol.15, 363–372 (2009).
[CrossRef]

Ma, L.-S.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Marconi, J. D.

McComb, T. S.

McNaught, S. J.

Mito, I.

Y. Aoki, K. Tajima, and I. Mito, “Input power limits of single-mode optical fibers due to stimulated Brillouin scattering in optical communication systems,” J. Lightwave Technol.6, 710 –719 (1988).
[CrossRef]

Mungan, C. E.

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express20, 15872–15881 (2012).
[CrossRef] [PubMed]

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron. (to be published).

Murphy, D. V.

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]

Nabors, C. D.

Namiki, S.

S. Takasaka, Y. Ozeki, S. Namiki, and M. Sakano, “External synchronization of 160-GHz optical beat signal by optical phase-locked loop technique,” IEEE Photon. Technol. Lett.18, 2457–2459 (2006).
[CrossRef]

Nielsen, T. N.

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

Nilsson, O.

S. Saito, O. Nilsson, and Y. Yamamoto, “Coherent FSK transmitter using a negative feedback stabilised semiconductor laser,” Electron. Lett.20, 703–704 (1984).
[CrossRef]

Oates, C.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Ohashi, M.

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol.14, 50 –57 (1996).
[CrossRef]

Okusaga, O.

Opower, H.

Ozeki, Y.

S. Takasaka, Y. Ozeki, S. Namiki, and M. Sakano, “External synchronization of 160-GHz optical beat signal by optical phase-locked loop technique,” IEEE Photon. Technol. Lett.18, 2457–2459 (2006).
[CrossRef]

Philipp, H.

H. Philipp, A. Scholtz, E. Bonek, and W. Leeb, “Costas loop experiments for a 10.6 μm communications receiver,” IEEE Trans. Commun.31, 1000–1002 (1983).
[CrossRef]

Plötner, M.

Rakuljic, G.

Ranka, J. K.

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]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Robertsson, L.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Rogers, S. D.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron. (to be published).

Rothenberg, J. E.

Saito, S.

S. Saito, O. Nilsson, and Y. Yamamoto, “Coherent FSK transmitter using a negative feedback stabilised semiconductor laser,” Electron. Lett.20, 703–704 (1984).
[CrossRef]

Sakano, M.

S. Takasaka, Y. Ozeki, S. Namiki, and M. Sakano, “External synchronization of 160-GHz optical beat signal by optical phase-locked loop technique,” IEEE Photon. Technol. Lett.18, 2457–2459 (2006).
[CrossRef]

Sanchez, A.

Satyan, N.

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express20, 15872–15881 (2012).
[CrossRef] [PubMed]

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express17, 15991–15999 (2009).
[CrossRef] [PubMed]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers Using optical phase-lock loops (Invited),” IEEE J. Sel. Top. Quantum Electron.15, 240–247 (2009).
[CrossRef]

N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron.45, 755–761 (2009).
[CrossRef]

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. Express15, 3201–3205 (2007).
[CrossRef] [PubMed]

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron. (to be published).

N. Satyan, A. Vasilyev, G. Rakuljic, J. O. White, and A. Yariv, “Phase-locking and coherent power combining of linearly chirped optical waves,” in “CLEO:2012 - Laser Science to Photonic Applications,” (Optical Society of America, 2012), p. CF2N.1.

Scholtz, A.

H. Philipp, A. Scholtz, E. Bonek, and W. Leeb, “Costas loop experiments for a 10.6 μm communications receiver,” IEEE Trans. Commun.31, 1000–1002 (1983).
[CrossRef]

Seeds, A. J.

L. A. Johansson and A. J. Seeds, “Millimeter-wave modulated optical signal generation with high spectral purity and wide-locking bandwidth using a fiber-integrated optical injection phase-lock loop,” IEEE Photon. Technol. Lett.12, 690–692 (2000).
[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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

Seise, E.

Shaw, S. E. J.

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]

Shiraki, K.

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol.14, 50 –57 (1996).
[CrossRef]

Stubkjaer, K. E.

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

Tajima, K.

Y. Aoki, K. Tajima, and I. Mito, “Input power limits of single-mode optical fibers due to stimulated Brillouin scattering in optical communication systems,” J. Lightwave Technol.6, 710 –719 (1988).
[CrossRef]

Takasaka, S.

S. Takasaka, Y. Ozeki, S. Namiki, and M. Sakano, “External synchronization of 160-GHz optical beat signal by optical phase-locked loop technique,” IEEE Photon. Technol. Lett.18, 2457–2459 (2006).
[CrossRef]

Tateda, M.

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol.14, 50 –57 (1996).
[CrossRef]

Tervonen, A.

T. von Lerber, S. Honkanen, A. Tervonen, H. Ludvigsen, and F. Küppers, “Optical clock recovery methods: Review (Invited),” Opt. Fiber Technol.15, 363–372 (2009).
[CrossRef]

Thielen, P. A.

Tünnermann, A.

Udem, T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Ungar, J.

Vasilyev, A.

Veselka, J. J.

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, and B. L. Kasper, “4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers,” IEEE Photon. Technol. Lett.2, 285–287 (1990).
[CrossRef]

von Lerber, T.

T. von Lerber, S. Honkanen, A. Tervonen, H. Ludvigsen, and F. Küppers, “Optical clock recovery methods: Review (Invited),” Opt. Fiber Technol.15, 363–372 (2009).
[CrossRef]

Wale, M. J.

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

Weber, M. E.

G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett.35, 1542–1544 (2010).
[CrossRef] [PubMed]

S. B. Weiss, M. E. Weber, and G. D. Goodno, “Group delay locking of broadband phased lasers,” in “Lasers, Sources, and Related Photonic Devices,” (Optical Society of America, 2012), p. AM3A.5.

Weiss, S. B.

S. B. Weiss, M. E. Weber, and G. D. Goodno, “Group delay locking of broadband phased lasers,” in “Lasers, Sources, and Related Photonic Devices,” (Optical Society of America, 2012), p. AM3A.5.

Westlund, M.

White, J. O.

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express20, 15872–15881 (2012).
[CrossRef] [PubMed]

N. Satyan, A. Vasilyev, G. Rakuljic, J. O. White, and A. Yariv, “Phase-locking and coherent power combining of linearly chirped optical waves,” in “CLEO:2012 - Laser Science to Photonic Applications,” (Optical Society of America, 2012), p. CF2N.1.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron. (to be published).

Wickham, M. G.

Wilpers, G.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Windeler, R. S.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Yamamoto, Y.

S. Saito, O. Nilsson, and Y. Yamamoto, “Coherent FSK transmitter using a negative feedback stabilised semiconductor laser,” Electron. Lett.20, 703–704 (1984).
[CrossRef]

Yariv, A.

J. O. White, A. Vasilyev, J. P. Cahill, N. Satyan, O. Okusaga, G. Rakuljic, C. E. Mungan, and A. Yariv, “Suppression of stimulated Brillouin scattering in optical fibers using a linearly chirped diode laser,” Opt. Express20, 15872–15881 (2012).
[CrossRef] [PubMed]

N. Satyan, A. Vasilyev, G. Rakuljic, V. Leyva, and A. Yariv, “Precise control of broadband frequency chirps using optoelectronic feedback,” Opt. Express17, 15991–15999 (2009).
[CrossRef] [PubMed]

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers Using optical phase-lock loops (Invited),” IEEE J. Sel. Top. Quantum Electron.15, 240–247 (2009).
[CrossRef]

N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron.45, 755–761 (2009).
[CrossRef]

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. Express15, 3201–3205 (2007).
[CrossRef] [PubMed]

N. Satyan, A. Vasilyev, G. Rakuljic, J. O. White, and A. Yariv, “Phase-locking and coherent power combining of linearly chirped optical waves,” in “CLEO:2012 - Laser Science to Photonic Applications,” (Optical Society of America, 2012), p. CF2N.1.

Ye, J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Yu, C. X.

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]

Zucco, M.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Appl. Opt. (2)

Electron. Lett. (2)

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]

S. Saito, O. Nilsson, and Y. Yamamoto, “Coherent FSK transmitter using a negative feedback stabilised semiconductor laser,” Electron. Lett.20, 703–704 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. Satyan, W. Liang, and A. Yariv, “Coherence cloning using semiconductor laser optical phase-lock loops,” IEEE J. Quantum Electron.45, 755–761 (2009).
[CrossRef]

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

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

N. Satyan, W. Liang, A. Kewitsch, G. Rakuljic, and A. Yariv, “Coherent power combination of semiconductor lasers Using optical phase-lock loops (Invited),” IEEE J. Sel. Top. Quantum Electron.15, 240–247 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, and B. L. Kasper, “4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers,” IEEE Photon. Technol. Lett.2, 285–287 (1990).
[CrossRef]

U. Gliese, T. N. Nielsen, M. Bruun, E. Lintz Christensen, K. E. Stubkjaer, S. Lindgren, and B. Broberg, “A wideband heterodyne optical phase-locked loop for generation of 3–18 GHz microwave carriers,” IEEE Photon. Technol. Lett.4, 936–938 (1992).
[CrossRef]

L. A. Johansson and A. J. Seeds, “Millimeter-wave modulated optical signal generation with high spectral purity and wide-locking bandwidth using a fiber-integrated optical injection phase-lock loop,” IEEE Photon. Technol. Lett.12, 690–692 (2000).
[CrossRef]

S. Takasaka, Y. Ozeki, S. Namiki, and M. Sakano, “External synchronization of 160-GHz optical beat signal by optical phase-locked loop technique,” IEEE Photon. Technol. Lett.18, 2457–2459 (2006).
[CrossRef]

IEEE Trans. Commun. (1)

H. Philipp, A. Scholtz, E. Bonek, and W. Leeb, “Costas loop experiments for a 10.6 μm communications receiver,” IEEE Trans. Commun.31, 1000–1002 (1983).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

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. Microw. Theory Tech.47, 1257–1264 (1999).
[CrossRef]

J. Lightwave Technol. (5)

K. Shiraki, M. Ohashi, and M. Tateda, “SBS threshold of a fiber with a Brillouin frequency shift distribution,” J. Lightwave Technol.14, 50 –57 (1996).
[CrossRef]

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol.19, 1691–1697 (2001).
[CrossRef]

J. M. C. Boggio, J. D. Marconi, and H. L. Fragnito, “Experimental and numerical investigation of the SBS-threshold increase in an optical fiber by applying strain distributions,” J. Lightwave Technol.23, 3808–3814 (2005).
[CrossRef]

Y. Aoki, K. Tajima, and I. Mito, “Input power limits of single-mode optical fibers due to stimulated Brillouin scattering in optical communication systems,” J. Lightwave Technol.6, 710 –719 (1988).
[CrossRef]

L. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communications systems,” J. Lightwave Technol.4, 415–425 (1986).
[CrossRef]

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

Opt. Express (4)

Opt. Fiber Technol. (1)

T. von Lerber, S. Honkanen, A. Tervonen, H. Ludvigsen, and F. Küppers, “Optical clock recovery methods: Review (Invited),” Opt. Fiber Technol.15, 363–372 (2009).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett.84, 5102–5105 (2000).
[CrossRef] [PubMed]

Science (1)

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 Level,” Science303, 1843–1845 (2004).
[CrossRef] [PubMed]

Other (4)

S. B. Weiss, M. E. Weber, and G. D. Goodno, “Group delay locking of broadband phased lasers,” in “Lasers, Sources, and Related Photonic Devices,” (Optical Society of America, 2012), p. AM3A.5.

F. M. Gardner, Phaselock Techniques (Hoboken, NJ: John Wiley and Sons, 2005).
[CrossRef]

N. Satyan, A. Vasilyev, G. Rakuljic, J. O. White, and A. Yariv, “Phase-locking and coherent power combining of linearly chirped optical waves,” in “CLEO:2012 - Laser Science to Photonic Applications,” (Optical Society of America, 2012), p. CF2N.1.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron. (to be published).

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Figures (10)

Fig. 1
Fig. 1

Concept of phase-synchronization of linearly chirped waves. A time delay between the master and slave arms is equivalent to a frequency delay, and can be compensated using an optical frequency shifter.

Fig. 2
Fig. 2

(a) Schematic diagram of an optoelectronic SFL using a semiconductor laser in a negative feedback loop. SCL: Semiconductor laser, MZI: Mach-Zehnder interferometer, PD: Photodetector. (b) and (c) Measured slope of the optical frequency chirp during the up- and down-chirps respectively, for an optoelectronic SFL using a vertical cavity surface emitting laser. The chirp rate is ±2× 1014 Hz/s, corresponding to a frequency excursion of ±400 GHz in 2 ms.

Fig. 3
Fig. 3

(a) Fiber-based homodyne phase-locking configuration. The upper and lower arms are the master and slave waveforms respectively. SFL: swept-frequency laser, PD: photodetector. (b) Small signal model of phase propagation in the loop. The variables are the Fourier transforms of the deviations of the phases from their steady-state values.

Fig. 4
Fig. 4

Experimental results of homodyne phase-locking of two chirped optical waves. (a) Unlocked combining, where the path-length mismatch results in a rapid oscillation of the combined power. (b) Phase-locked operation, for different values of the free-running frequency difference Δωfr. The SFL chirps +400 GHz in the first 2 ms, and −400 GHz in the next 2 ms.

Fig. 5
Fig. 5

Fiber-based heterodyne phase-locking configuration. The offset frequency of the loop is 100 MHz. SFL: swept-frequency laser, PD: photodetector.

Fig. 6
Fig. 6

Fourier spectrum of the measured beat signal between the master and phase-locked slave arms, over a 2 ms chirp interval. The nominal loop delay parameters are τd = 20 m and τ = 0 m of fiber. A Hamming window was used in the calculation to eliminate the spectral sidebands due to the finite measurement time.

Fig. 7
Fig. 7

(a) Algorithm for calculation of the relative phase between the master and phase-locked slave beams from the measurement of the beat signal between the two waves. LPF: Low-pass filter. (b) Phase difference between the master and slave arms for different values of the loop delay τd and the path-length mismatch τ. (c) Transient during the switching of the chirp from an SFL down-chirp to up-chirp. The bandwidth (locking time) is limited by the AOFS driver used in the experiment.

Fig. 8
Fig. 8

Measured optical beat signals between the slave and master chirped waves in two distinct phase-locked loops, with synchronized offset electronic signals with a frequency ωos = 100 MHz. The phase ϕos of one of the electronic oscillators was set to 0°, 90° and 180° in the three panels, which is reflected in a change in the optical phase of the slave laser phase by the same amount. The delays in each loop were τd = 2 m and τ ≈ 0.

Fig. 9
Fig. 9

(a) Schematic diagram of a tiled-aperture coherent combining experiment with multiple chirped amplifiers. (b) Schematic diagram of a proof-of-concept passive fiber-based experiment to demonstrate electronic beam steering. The fiber path-length mismatches not corrected by the optical phase-locked loops are shown in red. The camera is placed in the far field of the output aperture.

Fig. 10
Fig. 10

Experimental demonstration of electronic phase control and beam steering of chirped optical waves. (a) Far-field intensity profiles for the unlocked and phase-locked cases. The position of the fringes is controlled by varying the phase of the electronic oscillator in one loop. (b) Horizontal cross-section of the far-field intensity pattern.

Tables (1)

Tables Icon

Table 1 Measured residual phase error and phase-locking efficiency for different values of the loop delay τd and the path-length mismatch τ.

Equations (9)

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

ω L ( t ) = ω 0 + ξ t , t [ 0 , T ] ,
ξ = ω R τ M , ω 0 = ϕ R + 2 m π τ M ,
Δ θ ( t ) = [ ( ω 0 + ω m ) t + 1 2 ξ t 2 + ϕ m ] [ ( ω 0 + ω s ) ( t τ ) + 1 2 ξ ( t τ ) 2 + 0 t τ d K ( 1 cos Δ θ ( t ) ) d t ] ,
Δ θ 0 = cos 1 [ 1 ( ω m ω s + ξ τ ) K ] cos 1 ( 1 Δ ω fr K ) .
K ( f ) = K el ( f ) exp ( j 2 π f τ d ) j 2 π f .
Δ θ ( f ) = ϕ m ( f ) ϕ s ( f ) 1 + K ( f ) sin Δ θ 0 + ϕ L ( f ) ( 1 e j 2 π f τ ) 1 + K ( f ) sin Δ θ 0 ϕ m ( f ) ϕ s ( f ) 1 + K ( f ) sin Δ θ 0 + τ [ j 2 π f ϕ L ( f ) ] 1 + K ( f ) sin Δ θ 0 .
Δ θ 0 = ω os t ϕ os sin 1 ( ω s ξ τ ω os K ) ω os t ϕ os sin 1 ( Δ ω fr K ) .
Δ θ ( f ) = ϕ m ( f ) ϕ s ( f ) 1 + K ( f ) cos θ loop + τ [ j 2 π f ϕ L ( f ) ] 1 + K ( f ) cos θ loop ϕ os ( f ) K ( f ) cos θ loop 1 + K ( f ) cos θ loop .
i ( t ) cos ( Δ θ 0 + Δ θ ( t ) ) = cos ( ω os t + ϕ os + θ loop Δ θ ( t ) ) ,

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