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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 23, Iss. 2 — Feb. 1, 2006
  • pp: 250–256

Effects of nonlinear frequency pulling on the cavity phasing and the collective mode structure in phase-locked VCSEL arrays

Spilios Riyopoulos  »View Author Affiliations

JOSA B, Vol. 23, Issue 2, pp. 250-256 (2006)

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Carrier and gain depletion due to cross-cavity interactions in actively coupled vertical-cavity surface-emitting laser arrays cause nonlinear-cavity frequency pulling. As a result the collective mode structure departs significantly from earlier studied linearly coupled eigenmodes. Theory and simulations find that array eigenmodes have uniform amplitude and density distribution over the interior array sites, accompanied with boundary-layer formation at the edges. Exact zero or π phasing among adjacent sites is achieved, depending on the coupling-strength sign. In contrast, in linearly coupled array modes neglecting cross-cavity hole burning, the phase difference cannot be exactly zero or π, yielding a sinusoidal amplitude distribution over the array sites. The exact zero phasing and the uniform intensity distribution in nonlinearly coupled arrays offer advantages for practical applications.

© 2006 Optical Society of America

OCIS Codes
(140.3290) Lasers and laser optics : Laser arrays
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Lasers and Laser Optics

Original Manuscript: April 7, 2005
Revised Manuscript: July 13, 2005
Manuscript Accepted: September 7, 2005

Spilios Riyopoulos, "Effects of nonlinear frequency pulling on the cavity phasing and the collective mode structure in phase-locked VCSEL arrays," J. Opt. Soc. Am. B 23, 250-256 (2006)

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  1. J. K. Butler, D. E. Ackley, and M. Ettenberg, "Coupled-mode analysis of gain and wavelength oscillation characteristics of diode laser phased arrays," IEEE J. Quantum Electron. 21, 458-464 (1990). [CrossRef]
  2. H.-J. Yoo, J. R. Hayes, E. G. Paek, A. Scherer, and Y.-S. Kwon, "Array mode analysis of two-dimensional phased arrays of VCSELs," IEEE J. Quantum Electron. 26, 1039-1051 (1990). [CrossRef]
  3. S. Riyopoulos, "Coherent phase locking, collective oscillations and stability in coupled VCSEL arrays," Phys. Rev. A 66, 53820 (2002). [CrossRef]
  4. S. Riyopoulos, "Simulations of boundary layers and point defects in coupled VCSEL arrays," IEEE J. Sel. Top. Quantum Electron. (to be published).
  5. D. Zhou, L. J. Mawst, and Z. Dai, "Modal properties of two-dimensional antiguided VCSEL arrays," IEEE J. Quantum Electron. 38, 652-663 (2002). [CrossRef]
  6. D. Botez and A. P. Napartovich, "Phase-locked arrays of anti-guides: analytical theory," IEEE J. Quantum Electron. 30, 975-979 (1994). [CrossRef]
  7. D. Botez and A. P. Napartovich, "Corrections to 'Phase-locked arrays of anti-guides: analytical theory'," IEEE J. Quantum Electron. 32, 2175 (1996) [CrossRef]
  8. G. Hergenhan, B. Lucke, and U. Brauch, "Coherent coupling of VCSELs arrays and efficient beam combining by diffractive optical elements: concept and experimental verification," Appl. Opt. 42, 1667-1680 (2003). [CrossRef] [PubMed]
  9. F. Prati, D. Vecchione, and G. Vendramin, "Frequency locking of supermodes and stability of the out of phase locked state in 1-D and 2-D arrays of VCSELs," Opt. Lett. 22, 1633-1635 (1997). [CrossRef]
  10. P. L. Gourley, M. E. Warren, G. R. Hadley, G. A. Vawter, T. M. Brennan, and B. E. Hammons, "Coherent beams from high efficiency two-dimensional surface-emitting semiconductor laser arrays," Appl. Phys. Lett. 58, 890-892 (1991). [CrossRef]
  11. M. Orenstein, E. Kapon, J. P. Harbison, L. T. Florez, and N. G. Stoffel, "Large two-dimensional arrays of phase-locked VCSELs," Appl. Phys. Lett. 60, 1535-1537 (1992). [CrossRef]
  12. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, "High-power coherently coupled 8×8 VCSEL array," Appl. Phys. Lett. 61, 1160-1162 (1992). [CrossRef]
  13. P. Debernardi, G. P. Bava, F. Monti diSopra, and B. M. Willemsen, "Features of vectorial modes in phase-coupled VCSEL arrays: experiments and theory," IEEE J. Quantum Electron. 39, 109-119 (2003). [CrossRef]

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