## Three-dimensional analysis of mode discrimination in vertical-cavity surface-emitting lasers

Applied Optics, Vol. 44, Issue 14, pp. 2832-2838 (2005)

http://dx.doi.org/10.1364/AO.44.002832

Acrobat PDF (522 KB)

### Abstract

Optical mode discrimination in vertical-cavity surface-emitting lasers that contain distributed Bragg reflectors (DBRs) and a spatially limited gain medium is analyzed numerically. It is assumed that the output field is linearly polarized owing to gain selectivity. The analysis employs a three-dimensional model and an angular spectrum of plane-wave decomposition with the proper polarizations. Two types of round aperture are considered, namely, a Gaussian aperture and a ring-peak aperture that represents gain saturation. Coupled with the DBRs, the former aperture yields nearly Laguerre-Gaussian modes, whereas the latter aperture significantly distorts the mode shapes. In both cases, narrowband DBRs provide the best mode discrimination.

© 2005 Optical Society of America

**OCIS Codes**

(140.0140) Lasers and laser optics : Lasers and laser optics

(230.0250) Optical devices : Optoelectronics

**Citation**

Martin Achtenhagen, Amos Hardy, and Eli Kapon, "Three-dimensional analysis of mode discrimination in vertical-cavity surface-emitting lasers," Appl. Opt. **44**, 2832-2838 (2005)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-14-2832

Sort: Year | Journal | Reset

### References

- P. Bienstman, R. Baets, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
- A. Valle, "Selection and modulation of higher-order transverse modes in vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 34, 1924-1932 (1998).
- G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A 63, 23816 (2001).
- P. Debernardi and G. P. Bava, "Coupled mode theory: a powerful tool for analyzing complex VCSELs and designing advanced device features," IEEE J. Sel. Top. Quantum Electron. 9, 905-917 (2003).
- D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, "Modal reflection of quarter-wave mirrors in vertical-cavity lasers," IEEE J. Quantum Electron. 29, 1950-1962 (1993).
- M. Achtenhagen, A. A. Hardy, and E. Kapon, "Design of distributed Bragg reflector structures for transverse-mode discrimination in vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 22, 1962-1967 (2004).
- A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).
- J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
- M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).
- S. H. Friedberg and A. J. Insel, Introduction to Linear Algebra with Applications (Prentice-Hall, Englewood Cliffs, N.J., 1986).
- H. K. Bissessur, F. Koyama, and K. Iga, "Modeling of oxide-confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 3, 344-352 (1997).
- M. Jungo, D. Erni, and W. Baechtold, "Quasi-analytic steady-state solution of VCSEL rate equations including spatial hole burning and carrier diffusion losses," Int. J. Numer. Model. 16, 143-159 (2003).
- A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
- T. F. Johnston, Jr., "M2 concept characterizes beam quality," Laser Focus 5, 173-183 (1990).
- A. E. Siegman, "Defining the effective radius of curvature for a nonideal optical beam," IEEE J. Quantum Electron. 27, 1146-1148 (1991).

## 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.