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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 20, Iss. 1 — Jan. 1, 2003
  • pp: 14–26

Coupled-mode structure in oxide aperture vertical-cavity surface-emitting lasers and its effects on lasing threshold

Spilios Riyopoulos  »View Author Affiliations

JOSA B, Vol. 20, Issue 1, pp. 14-26 (2003)

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Mode coupling caused by the presence of an oxide dielectric aperture is addressed. For rays passing through the dielectric, we apply the complex reflection coefficient that corresponds to a Fabry–Perot subcavity formed by a slab dielectric and the nearest distributed Bragg reflector (DBR) mirror. The DBR reflectivity applies to rays passing through the aperture opening. The diffraction effects for curved wave-front incidence are also included. The expansion coefficients of the cavity eigenmodes into pure Gauss–Laguerre (GL) modes are obtained for the lowest eigenmodes in the optimum waist representation. The effects of the aperture location in the cavity standing wave are addressed. Over the entire range of aperture diameters, higher cavity losses and higher threshold currents result for antinode placement, owing to wide-angle scattering. This agrees with experimental results and earlier scattering analysis by use of pure GL (uncoupled) eigenmodes. Mixing with higher modes increases round-trip losses at small apertures, compared with uncoupled-mode results. In the limit of a large aperture diameter, the cavity eigenmodes decouple to pure GL modes.

© 2003 Optical Society of America

OCIS Codes
(140.4780) Lasers and laser optics : Optical resonators
(140.5960) Lasers and laser optics : Semiconductor lasers
(250.7260) Optoelectronics : Vertical cavity surface emitting lasers

Spilios Riyopoulos, "Coupled-mode structure in oxide aperture vertical-cavity surface-emitting lasers and its effects on lasing threshold," J. Opt. Soc. Am. B 20, 14-26 (2003)

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  1. S. Riyopoulos, D. Dialeti s, J-M. Inman, and A. Phillips, “Active cavity vertical-cavity surface-emitting laser eigenmodes with simple analytic representation,” J. Opt. Soc. Am. B 18, 1268–1284 (2001). [CrossRef]
  2. S. Riyopoulos and D. Dialetis, “Radiation scattering by apertures in vertical-cavity surface-emitting laser cavities and its effects on mode structure,” J. Opt. Soc. Am. B 18, 1497–1511 (2001). [CrossRef]
  3. G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607 (1989). [CrossRef]
  4. B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. G. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358 (1999). [CrossRef]
  5. S. Riyopoulos, D. Dialetis, J. Liu, and B. Riely, “Generic representation of active cavity VCSEL eigenmodes by optimized waist gain guided Gauss–Laguerre modes,” IEEE J. Sel. Top. Quantum Electron. (to be published).
  6. K. L. Lear, K. D. Choquette, R. P. Schneider, and S. P. Kilcoyne, Appl. Phys. Lett. 66, 2616 (1994). [CrossRef]
  7. Y. G. Zhao and J. McInerney, “Transverse-mode control of VCSELs,” IEEE J. Quantum Electron. 32, 1950 (1996). [CrossRef]
  8. A. Bond, P. D. Dapkus, and J. D. O’Brien, “Design of low-loss, single-mode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 5, 574 (1999). [CrossRef]
  9. See, for example, C. C. Davis in Lasers and Electro-optics (Cambridge U. Press, Cambridge, UK, 1996), pp. 73–79.
  10. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), pp. 108–118.
  11. S. Mukai, “Non-monotonic threshold size dependence of buried post VCLs,” IEEE J. Quantum Electron. 5, 552 (2001). [CrossRef]
  12. D. I. Babic and S. W. Corzine, “Analytic expressions for reflection delay, penetration depth and absorptance of quarter-wave dielectric mirrors,” IEEE J. Quantum Electron. 28, 514 (1992). [CrossRef]
  13. D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in VCSELs,” IEEE J. Quantum Electron. 29, 1950 (1993). [CrossRef]
  14. The standard FP etalon theory yields reflection maxima for ΔΦ΄=lπ+π/2. In that case, however, ΔΦ΄ gives the phase shift not between the optical element edges but between two reference surfaces located so that T=i|T| and R=−|R|, i.e., T is pure imaginary and R is pure negative (see Ref. 6).
  15. P. Bienstman, R. G. Baets, J. Vukusic, A. Larsson, M. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. Bava, H. Wenzel, B. Klein, R. Pregla, S. Riyopoulos, J.-F. Seurin, and S. L. Chuang, “Comparison of optical VCSEL models of the simulation of position dependent effects of thin oxide apertures,” IEEE J. Quantum Electron. 37, 1618 (2001). [CrossRef]
  16. K. D. Choquette and R. E. Liebenquth, “Control of VCSEL polarization with anisotropic transverse cavity geometries,” IEEE Photonics Technol. Lett. 6, 40–42 (1994). [CrossRef]
  17. E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in VCSELs,” IEEE J. Sel. Top. Quantum Electron. 3, 379 (1997). [CrossRef]
  18. See K. Okamoto, Fundamentals of Optical Waveguides (Academic, San Diego, Calif., 2000), pp. 35–39 and references therein.

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