Abstract

We report the production of stable, coherent, and same-phase states in arrays of fiber lasers. Provided that proper interactions between the lasers are present, arrays will spontaneously self-organize into stable coherent same-phase states. There is no need for active control. Power scaling, power spectra, spatial interference fringes, and temporal data all support this conclusion.

© 2005 Optical Society of America

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  1. V. A. Kozlov, J. Hernandez-Cordero, and T. F. Morse, Opt. Lett. 24, 1814 (1999).
    [CrossRef]
  2. T. B. Simpson, A. Gavrielides, and P. Peterson, in The 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), p. 62.
  3. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
    [CrossRef]
  4. D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
    [CrossRef]
  5. A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, Opt. Express 10, 1167 (2002).
    [CrossRef] [PubMed]
  6. P. K. Cheo, A. Liu, and G. G. King, IEEE Photonics Technol. Lett. 13, 439 (2001).
    [CrossRef]
  7. M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).
  8. Gould Electronics, Inc., Chandler, Ariz.
  9. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge U. Press, New York, 2001).
    [CrossRef]

2003

M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).

2002

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
[CrossRef]

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, Opt. Express 10, 1167 (2002).
[CrossRef] [PubMed]

2001

P. K. Cheo, A. Liu, and G. G. King, IEEE Photonics Technol. Lett. 13, 439 (2001).
[CrossRef]

1999

Barthelemy, A.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

Barthélémy, A.

D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
[CrossRef]

Bruesselbach, H. W.

M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).

Cheo, P. K.

P. K. Cheo, A. Liu, and G. G. King, IEEE Photonics Technol. Lett. 13, 439 (2001).
[CrossRef]

Desfarges-Berthelemot, A.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
[CrossRef]

Gavrielides, A.

T. B. Simpson, A. Gavrielides, and P. Peterson, in The 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), p. 62.

Hernandez-Cordero, J.

Jones, D. C.

M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).

Kermene, V.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

Kermène, V.

D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
[CrossRef]

King, G. G.

P. K. Cheo, A. Liu, and G. G. King, IEEE Photonics Technol. Lett. 13, 439 (2001).
[CrossRef]

Kozlov, V. A.

Kurths, J.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge U. Press, New York, 2001).
[CrossRef]

Lefort, L.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

Liu, A.

P. K. Cheo, A. Liu, and G. G. King, IEEE Photonics Technol. Lett. 13, 439 (2001).
[CrossRef]

Mahodaux, C.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

Mangir, M. S.

M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).

Minden, M. L.

M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).

Morse, T. F.

Peterson, P.

T. B. Simpson, A. Gavrielides, and P. Peterson, in The 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), p. 62.

Pikovsky, A.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge U. Press, New York, 2001).
[CrossRef]

Pureur, D.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

Rogers, J.

M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).

Rosenblum, M.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge U. Press, New York, 2001).
[CrossRef]

Sabourdy, D.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
[CrossRef]

Saitou, T.

Sekiguchi, T.

Shirakawa, A.

Simpson, T. B.

T. B. Simpson, A. Gavrielides, and P. Peterson, in The 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), p. 62.

Ueda, K.

Vampouille, M.

D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
[CrossRef]

Appl. Phys. B

D. Sabourdy, V. Kermène, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthélémy, Appl. Phys. B 75, 503 (2002).
[CrossRef]

Electron. Lett.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, Electron. Lett. 38, 692 (2002).
[CrossRef]

IEEE Photonics Technol. Lett.

P. K. Cheo, A. Liu, and G. G. King, IEEE Photonics Technol. Lett. 13, 439 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

M. S. Mangir, M. L. Minden, J. Rogers, H. W. Bruesselbach, and D. C. Jones, Proc. SPIE 4974, 251 (2003).

Other

Gould Electronics, Inc., Chandler, Ariz.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge U. Press, New York, 2001).
[CrossRef]

T. B. Simpson, A. Gavrielides, and P. Peterson, in The 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), p. 62.

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Figures (5)

Fig. 1
Fig. 1

Diagrams of two experiments for all-fiber combination of five or four lasers. Gain is provided by 2 - m -long neodymium-doped fibers, each core pumped by an 813-nm laser diode through a wavelength division multiplexer. The 875 ± 6 - nm cutoff, 0.19-N.A. fiber has a 4.0 - μ m core diameter, with 12.6 - dB m absorption at 807 nm and 6.1 - dB km background absorption at 1150 nm. The fiber resonator cavities include polarization paddles and are 12.8 m long, equalized to ± 0.1 m . The lasers are all-to-all coupled; each interacts with all the others through a 1-to-5 coupler,[8] the shaded box. In (a) each laser cavity is defined by a 98% reflectivity fiber grating ( 0.5 - nm width) spliced to the end of each gain section and by the partial reflectivity of the flat face on the standard FC/PC flat-polished connector spliced onto the fiber on the right; this is the output. Although all the gratings are made with the same mask and are kept at the same temperature, the lasing frequencies are a few tenths of a nanometer different. Inverting this produces the setup in (b), where only four gain sections are used. Diagnostics are attached to the coupler’s fifth fiber. The output, indicated by the arrow on the left, is now from a linear array of adjacent, coaligned 1.25-mm-diameter graded-index lens fiber collimators. The setup in (b) allows spatial coherence to be investigated.

Fig. 2
Fig. 2

Experimental measurements of output power as the number of simultaneously turned-on lasers is increased for the setup in Fig. 1(a). Expectations for an incoherent array and an in-phase array (curves) are compared with the experimental measurements (symbols). The measured power agrees with predictions for an in-phase array. The incoherent expectation is the calculated sum of nonsimultaneous individual laser powers, measured when the lasers are turned on one at time in the same setup. The total available power, five times the incoherent power (see text), is also plotted.

Fig. 3
Fig. 3

Measured power spectra when individual fiber lasers are pumped or when all five are pumped simultaneously; nothing else was changed between measurements. Each spectrum is an average of 100 readings. Center wavelengths and variances (a measure of the linewidths), calculated from the data files, are listed. The lowest five curves are recorded when the five are turned on individually. The highest curve is measured when all five are on simultaneously. Note that it is 25 times higher than any individual laser. For comparison, the intermediate curve, simply the calculated sum of the lower five curves, is the power spectrum expected if the lasers were incoherent. There is a fixed attenuation between the output from the connector and the optical spectrum analyzer used for these measurements; the ordinate is scaled by aiming the connector into a powermeter for reference instead of connecting it to the spectrum analyzer.

Fig. 4
Fig. 4

Three transections, taken at the indicated times, of the far-field fringe patterns, inserts, for the Fig. 1(b) setup with four lasers on. Intensity is plotted versus spatial position; both scales are arbitrary. The fringe pattern spacings are consistent with the array dimensions.

Fig. 5
Fig. 5

Homodyne spectrum for the Fig. 1(b) setup. The signal from a fast fiber-coupled photodiode is fed to a rf spectrum analyzer. The horizontal scale is 0-500 MHz, and the vertical scale is 0 - 90 μ V . Closer examination at other sweep rates and resolutions shows that the closely spaced peaks are 8.2 MHz apart; they are observed even when the rf sweep time is only 30 ms.

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