Full-vectorial three-dimensional finite element optical simulation of vertical-cavity surface-emitting lasers

Journal of Lightwave Technology

Volumn 25, Issue 9, 2007, Pages 2427-2434

  Nyakas, Péter ^a  

^a Furukawa Electric Institute of Technology Hungary   (Hungary)

Author keywords

Finite element method (FEM); Numerical modeling; Photonic crystal (PhC); Polarization; Vertical cavity surface emitting laser (VCSEL)

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; HELMHOLTZ EQUATION; MATHEMATICAL MODELS; PHOTONIC CRYSTALS; POLARIZATION; SEMICONDUCTOR LASERS;

FULL-VECTORIAL TREATMENT; SURFACE RELIEFS;

SURFACE EMITTING LASERS;

EID: 34548648255     PISSN: 07338724     EISSN: None     Source Type: Journal    
DOI: 10.1109/JLT.2007.902742     Document Type: Article

References (32)

1. K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, T. J. Drummond, and R. Hull, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett., vol. 69, no. 10, pp. 1385-1387, Sep. 1996.
2. Å. Haglund, J. S. Gustavsson, J. A. Vukušić, P. Modh, and A. Larsson, "Single fundamental-mode output power exceeding 6 mW from VCSELs with a shallow surface relief," IEEE Photon. Technol. Lett. vol. 16, no. 2, pp. 368-370, Feb. 2004.
3. A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emmitting lasers with triangular holey structure," Appl. Phys. Lett., vol. 85, no. 22, pp. 5161-5163, Nov. 2004.
4. N. Yokouchi, A. J. Danner, and K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Topics Quantum Electron., vol. 9, no. 5, pp. 1439-1445, Sep./Oct. 2003.
5. H. Liu, M. Yan, P. Shum, H. Ghafouri-Shiraz, and D. Liu, "Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers," Opt. Express, vol. 12, no. 18, pp. 4269-4274, Sep. 2004.
6. M. P. van Exter, A. K. J. van Doorn, and J. P. Woerdman, "Electro-optic effect and birefringence in semiconductor vertical-cavity lasers," Phys. Rev. A, At. Mol. Opt. Phys., vol. 56, no. 1, pp. 845-853, Jul. 1997.
7. K. D. Choquette and R. E. Leibenguth, "Control of vertical cavity laser polarization with anisotropic transverse cavities," IEEE Photon. Technol. Lett., vol. 6, no. 1, pp. 40-42, Jan. 1994.
8. H. J. Unold, M. C. Riedl, R. Michalzik, and K. J. Ebeling, "Polarisation control in VCSELs by elliptic surface etching," Electron. Lett., vol. 38, no. 2, pp. 77-78, Jan. 2002.
9. Y. Kaneko, D. Mars, S. Nakagawa, Y. Ichimura, and N. Yamada, "Vertical-cavity surface-emitting lasers with stable polarization grown on (411)a - oriented substrates," Jpn. J. Appl. Phys., vol. 38, no. 8A, pp. 864-866, Aug. 1999.
10. H. Uenohara, K. Tateno, T. Kagawa, Y. Ohiso, H. Tsuda, T. Kurokawa, and C. Amano, "Polarization-controlled 850-nm-wavelength vertical-cavity surface-emitting lasers grown on (311)B substrates by metal-organic chemical vapor deposition," IEEE J. Sel. Topics Quantum Electron. vol. 5, no. 3, pp. 537-545, May/Jun. 1999.
11. B. S. Ryvkin, E. A. Avrutin, and A. C. Walker, "Current-directionality-induced giant absorption dichroism in III-V semiconductors and its potential for polarization control in vertical cavity surface-emitting lasers," J. Appl. Phys., vol. 91, no. 6, pp. 3516-3521, Mar. 2002.
12. G. Verschaffelt, W. van der Vleuten, M. Creusen, E. Smalbrugge, T. G. van de Roer, F. Karouta, R. C. Strijbos, J. Danckaert, I. Veretennicoff, B. Ryvkin, H. Thiepont, and G. A. Acket, "Polarization stabilization in vertical-cavity surface-emitting lasers through asymmetric current injection," IEEE Photon. Technol. Lett., vol. 12, no. 8, pp. 945-947, Aug. 2000.
13. T. Mukaihara, N. Ohnoki, Y. Hayashi, N. Hatori, F. Koyama, and K. Iga, "Polarization control of vertical-cavity surface emitting lasers using a birefringent metal/dielectric polarizer loaded on top distributed Bragg reflector," IEEE J. Sel. Topics Quantum Electron., vol. 1, no. 2, pp. 667-673, Jun. 1995.
14. S. J. Schablitsky, L. Zhuang, R. C. Shi, and S. Y. Chou, "Controlling polarization of vertical-cavity surface-emitting lasers using amorphous silicon subwavelength transmission gratings," Appl. Phys. Lett., vol. 69, no. 1, pp. 7-9, Jul. 1996.
15. P. Bienstman, R. Baets, J. Vukusic, 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., vol. 37, no. 12, pp. 1618-1631, Dec. 2001.
16. G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A, At. Mol. Opt. Phys., vol. 63, no. 2, p. 023 816, Feb. 2001.
17. P. Debernardi and G. P. Bava, "Coupled mode theory: A powerful tool for analyzing complex VCSELs and designing advanced device features," IEEE J. Sel. Topics Quantum Electron., vol. 9, no. 3, pp. 905-917, May/Jun. 2003.
18. P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: Experiments and theory," IEEE J. Sel. Topics Quantum Electron., vol. 9, no. 5, pp. 1394-1404, Sep./Oct. 2003.
19. P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: A comparative theoretical and experimental study," IEEE J. Sel. Topics Quantum Electron., vol. 11, no. 1, pp. 107-116, Jan./Feb. 2005.
20. P. Nyakas, G. Varga, Z. Puskás, N. Hashizume, T. Kárpáti, T. Veszprémi, and G. Zsombok, "Self-consistent real three-dimensional simulation of vertical-cavity surface-emitting lasers," J. Opt. Soc. Amer. B, Opt. Phys., vol. 23, no. 9, pp. 1761-1769, Sep. 2006.
21. D.-S. Song, Y-J. Lee, H.-W. Choi, and Y.-H. Lee, "Polarization-controlled, single-transverse-mode, photonic-crystal, vertical-cavity, surface-emitting lasers," Appl. Phys. Lett., vol. 82, no. 19, pp. 3182-3184, May 2003.
22. M. Streiff, A. Witzig, M. Pfeiffer, P. Royo, and W. Fichtner, "A comprehensive VCSEL device simulator," IEEE J. Sel. Topics Quantum Electron., vol. 9, no. 3, pp. 879-891, May/Jun. 2003.
23. R. D. Graglia, D. R. Wilton, A. F. Peterson, and I.-L. Gheorma, "Higher order interpolatory vector bases on prism elements," IEEE Trans. Antennas Propag., vol. 46, no. 3, pp. 442-450, Mar. 1998.
24. R. D. Graglia, D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 329-342, Mar. 1997.
25. G. A. Baraff and R. K. Smith, "Nonadiabatic semiconductor laser rate equations for the large-signal, rapid-modulation regime," Phys. Rev. A, At. Mol. Opt. Phys., vol. 61, no. 4, p. 043 808, Apr. 2000.
26. S. D. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propag. vol. 44, no. 12, pp. 1630-1639, Dec. 1996.
27. T. Özdemir and J. L. Volakis, "Triangular prisms for edge-based vector finite element analysis of conformal antennas," IEEE Trans. Antennas Propag., vol. 45, no. 5, pp. 788-797, May 1997.
28. D. R. Fokkema, G. L. G. Sleijpen, and H. A. van der Vorst, "Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 94-125, Aug. 1998.
29. H. A. van der Vorst and J. B. M. Melissen, "A Petrov-Galerkin type method for solving Ax = b, where A is symmetric complex," IEEE Trans. Magn., vol. 26, no. 2, pp. 706-708, Mar. 1990.
30. A. Christ, N. Kuster, M. Streiff, A. Witzig, and W. Fichtner, "Correction of the numerical reflection coefficient of the finite-difference time-domain method for efficient simulation of vertical-cavity surface-emitting lasers," J. Opt. Soc. Amer. B, Opt. Phys., vol. 20, no. 7, pp. 1401-1408, Jul. 2003.
31. P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, "Theoretical study of cold-cavity single-mode conditions in vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals" J. Opt. Soc. Amer. B, Opt. Phys. vol. 20, no. 12, pp. 2442-2447, Dec. 2003.
32. A. J. Danner, J. J. Raftery, Jr., P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett., vol. 88, no. 9, p. 091114, Feb. 2006.