OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 25 — Dec. 8, 2008
  • pp: 20789–20802

Diffraction loss in long-wavelength buried tunnel junction VCSELs analyzed with a hybrid coupled-cavity transfer-matrix model

Jörgen Bengtsson, Johan Gustavsson, Å sa Haglund, Anders Larsson, Alexander Bachmann, Kaveh Kashani-Shirazi, and Markus-Christian Amann  »View Author Affiliations

Optics Express, Vol. 16, Issue 25, pp. 20789-20802 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (774 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Intra-cavity diffraction in VCSELs is a loss mechanism that potentially can cause a significant decrease in efficiency and a rise in the threshold current, particularly in cavities with small lateral features with a high index contrast. One such VCSEL type is the 2.3 µm GaSb-based buried tunnel junction (BTJ) VCSEL studied in this work, where the BTJ induced topology of the top layers gives rise to excess loss through diffraction. Diffraction loss is difficult to measure, and also the numerical estimation must be done with care because of the non-axial propagation of the diffracted fields. We present a simulation method with spatially varying dimensionality, such that the field is three-dimensional (3D) in the entire cavity, whereas the material structure of the cavity is modelled in 3D near the BTJ and the layers with a varying topology, but elsewhere is assumed to be 1D like in a regular DBR structure. We find that the diffraction loss displays a non-monotonic behaviour as a function of the BTJ diameter, but as expected it rapidly increases below a certain diameter of the BTJ and may even become the dominant cause of loss in some device designs. We also show that the diffraction loss can be much reduced if the layers above the BTJ can be deposited such that the surface profile becomes smoother with increasing distance from the BTJ.

© 2008 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(140.3410) Lasers and laser optics : Laser resonators
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.0250) Optical devices : Optoelectronics
(140.7260) Lasers and laser optics : Vertical cavity surface emitting lasers

ToC Category:
Optical Devices

Original Manuscript: October 20, 2008
Revised Manuscript: November 25, 2008
Manuscript Accepted: November 25, 2008
Published: December 1, 2008

Jörgen Bengtsson, Johan Gustavsson, Åsa Haglund, Anders Larsson, Alexander Bachmann, Kaveh Kashani-Shirazi, and Markus-Christian Amann, "Diffraction loss in long-wavelength buried tunnel junction VCSELs analyzed with a hybrid coupled-cavity transfer-matrix model," Opt. Express 16, 20789-20802 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Ortsiefer, G. Böhm, M. Grau, K. Windhorn, E. R¨onneberg, J. Rosskopf, R. Shau, O. Dier, and M.-C. Amann, "Electrically pumped room temperature CW VCSELs with 2.3 μm emission wavelength," Electron. Lett. 42,640-641 (2006). [CrossRef]
  2. A. Krier, Mid-infrared semiconductor optoelectronics, (Springer-Verlag 2006). [CrossRef]
  3. A. Bachmann, T. Lim, K. Kashani-Shirazi, O. Dier, C. Lauer, and M.-C. Amann, "Continuous-wave operation of electrically pumped GaSb-based vertical cavity surface emitting laser at 2.3 μm," Electron. Lett. 44,202-203 (2008). [CrossRef]
  4. P. A. Roos, J. L. Carlsten, D. C. Kilper, and K. L. Lear,"Diffraction from oxide confinement apertures in verticalcavity lasers," Appl. Phys. Lett. 75, 754-756 (1999). [CrossRef]
  5. E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, "Scattering losses from dielectric apertures in vertical-cavity lasers," J. Sel. Top. Quantum Electron. 3, 379-389 (1997). [CrossRef]
  6. G. R. Hadley and K. L. Lear, "Diffraction loss of confined modes in microcavities," 1997 Digest of the IEEE/LEOS Summer Topical Meetings (Cat. No. 97TH8276), 65-66 (1997).
  7. R. R. Burton, M. S. Stern, P. C. Kendall, and P. N. Robson, "VCSEL diffraction-loss theory," IEE Proc. Optoelectron. 142, 77-81 (1995). [CrossRef]
  8. G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," J. Quantum Electron. 32, 607-616 (1996). [CrossRef]
  9. M. J. Noble, J. P. Loehr, and J. A. Lott, "Semi-analytic calculation of diffraction losses and threshold currents in microcavity VCSELs," Proc. LEOS’98. IEEE Lasers and Electro-Optics Society 1998 Annual Meeting (Cat. No. 98CH36243) 1, 212-213 (1998).
  10. P. Mackowiak, R. P. Sarzala, M. Wasiak and W. Nakwaski, "Radial optical confinement in nitride VCSELs," J. Phys. D 36, 2041-2045 (2003). [CrossRef]
  11. 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]
  12. P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001). [CrossRef]
  13. A. G. Fox and T. Li, "Resonant modes in maser interferometer," Bell System Tech. J. 40, 453-488 (1961).
  14. D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, "Modal reflection of quarter-wave mirrors in vertical-cavity lasers," J. Quantum Electron. 29, 1950-1962 (1993). [CrossRef]
  15. P. Yeh, Optical waves in layered media, (Wiley 2005).
  16. J. W. Goodman, Introduction to Fourier optics, (McGraw-Hill 1996).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited