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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 29, Iss. 34 — Dec. 1, 1990
  • pp: 5080–5085

Effective reflectivity from self-imaging in a Talbot cavity and its effect on the threshold of a finite 2-D surface emitting laser array

Easen Ho, Fumio Koyama, and Kenichi Iga  »View Author Affiliations


Applied Optics, Vol. 29, Issue 34, pp. 5080-5085 (1990)
http://dx.doi.org/10.1364/AO.29.005080


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Abstract

Using a self-imaged diffraction coupled model in a Talbot cavity for vertical cavity surface emitting laser arrays, the effect of self-imaged reflections on the lasing threshold of a finite 2-D array was investigated. Array size and the ratio defined by the element diameter/element spacing were found to affect the effective reflectivity as seen from the laser cavities and, ultimately, the device threshold. A general curve showing the dependence of the 2-D coupling coefficient on the array fill factor and array size has been found. Minimum levels of laser facet reflectivities have been obtained as a function of the array fill factor for practical devices with low threshold current densities.

© 1990 Optical Society of America

History
Original Manuscript: November 20, 1989
Published: December 1, 1990

Citation
Easen Ho, Fumio Koyama, and Kenichi Iga, "Effective reflectivity from self-imaging in a Talbot cavity and its effect on the threshold of a finite 2-D surface emitting laser array," Appl. Opt. 29, 5080-5085 (1990)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-29-34-5080


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References

  1. C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979). [CrossRef]
  2. P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977). [CrossRef]
  3. See, e.g., D. Botez, “Phased-Locked Arrays of Semiconductor Diode Lasers,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThAl and references therein.
  4. See, e.g., K. Iga, F. Koyama, S. Kinoshita, “Surface Emitting Semiconductor Lasers,” IEEE J. Quantum Electron. QE-24, 1845–1855 (1988) and references therein. [CrossRef]
  5. J. L. Jewell et al., “Low Threshold Electrically-Pumped Vertical-Cavity Surface Emitting MicroLasers,” in Postdeadline Papers, Seventh International Conference on Integrated Optics and Optical Fiber Communication, Kobe, Japan (1989), Session 18B2-6.
  6. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: An Application of the Planar Micro-lens,” Appl. Opt. 21, 3456–3460 (1982). [CrossRef] [PubMed]
  7. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 403–410 (1936).
  8. J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent Addition of AlGaAs Lasers Using Microlenses and Diffractive Coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988). [CrossRef]
  9. J. R. Leger, “Lateral Mode Control of an AlGaAs Laser Array in a Talbot Cavity,” Appl. Phys. Lett. 55, 334–336 (1989). [CrossRef]
  10. F. X. D’Amato, E. T. Siebert, C. Royshoudhuri, “Coherent Operation of an Array of Diode Lasers Using a Spatial Filter in a Talbot Cavity,” Appl. Phys. Lett. 55, 816–818 (1989). [CrossRef]
  11. F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers With Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988). [CrossRef]
  12. For simplicity, only the magniude of κ is used throughout this paper by assuming that the phase part of κ, together with the propagation phase, can be arbitrarily adjusted near the vicinity of Talbot planes. In actuality, κ contains rapid oscillations due to the reflection phase term. Some slight phase curvature due to finite self-imaging also introduces a phase shift in κ, but at Talbot planes this phase shift is small.
  13. H. Soda, Y. Motegi, K. Iga, “GaInAsP/InP Surface Emitting Injection Laser with a Ring Electrode,” IEEE J. Quantum Electron. QE-19, 1035–1041 (1983). [CrossRef]
  14. Hysteresis in the I–L curve may be expected as self-imaging only occurs for coherent light; i.e., κ will be small before phase-locked operation of individual elements. After the onset of phase locking, self-imaged feedback causes the effective reflectivity to increase and the array will effectively have a lower threshold. For each lasing element without self-imaged feedback, Reff ≈ R2, and the initial lasing threshold will be determined mainly by R1,R2.

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