Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 4, 1998, Pages 3279-3292

  Rossler T ^a   Indik, R A ^a   Harkness, G K ^a   Moloney, J V ^a   Ning, C Z ^b  

^a University of Arizona   (United States)

^b NASA AMES RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000919518     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.3279     Document Type: Article

References (55)

1. K. Iga, F. Koyama, and S. Kinoshita, IEEE J. Quantum Electron. 24, 1845 (1988).IEJQA7
2. W. W. Chow et al, IEEE J. Quantum Electron. 33, 1810 (1997).IEJQA7
3. Vertical-Cavity Surface-Emitting Lasers, edited by K. D. Choquette, and D. G. Deppe, SPIE Proc. No. 3003 (SPIE, Bellingham, 1997).
4. R. A. Morgan, see Vertical-Cavity Surface-Emitting Lasers (Ref. 3), p. 14, and references therein.
5. D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, Appl. Phys. Lett. 65, 97 (1994).APPLAB
6. K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, Electron. Lett. 30, 2043 (1994).ELLEAK
7. K. L. Lear et al, Electron. Lett. 31, 208 (1995).ELLEAK
8. K. D. Choquette et al, IEEE Photonics Technol. Lett. 7, 1237 (1995).IPTLEL
9. D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, Appl. Phys. Lett. 69, 3477 (1996).APPLAB
10. K. D. Choquette et al, Appl. Phys. Lett. 70, 823 (1997).APPLAB
11. B. Weigl et al, IEEE J. Sel. Top. Quantum Electron. 3, 409 (1997).IJSQEN
12. S. P. Hegarty et al., in Vertical-Cavity Surface-Emitting Lasers II, edited by K. D. Choquette and R. A. Morgan, SPIE Proc. No. 3286 (SPIE, Bellingham, 1998), p. 198.
13. W. Nakwaski and M. Osinski, IEEE J. Quantum Electron. 27, 1391 (1991).IEJQA7
14. J. W. Scott, S. W. Corzine, R. S. Geels, and L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); APPLAB
15. J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, IEEE J. Quantum Electron. 27, 1391 (1993).IEJQA7
16. R. Michalzik and K. J. Ebeling, IEEE J. Quantum Electron. 29, 1963 (1993).IEJQA7
17. J. Piprek, H. Wenzel, and G. Szefka, IEEE Photonics Technol. Lett. 6, 139 (1994).IPTLEL
18. Y.-G. Zhao and J. G. McInerney, IEEE J. Quantum Electron. 31, 1668 (1995).IEJQA7
19. M. Shimizu, F. Koyama, and K. Iga, Trans. Inst. Electron. Inf. Commun. Eng. E 74, 3334 (1991).
20. J.-P. Zhang and K. Petermann, IEEE J. Quantum Electron. 30, 1529 (1994).IEJQA7
21. A. Valle, J. Sarma, and K. A. Shore, Opt. Commun. 115, 297 (1995); OPCOB8
22. A. ValleJ. SarmaK. A. ShoreIEEE J. Quantum Electron. 31, 1423 (1995).
23. J. Y. Law and G. P. Agrawal, IEEE J. Quantum Electron. 33, 462 (1997).IEJQA7
24. H. K. Bissessur, F. Koyama, and K. Iga, IEEE J. Sel. Top. Quantum Electron. 3, 344 (1997).IJSQEN
25. L. E. Thode et al, in Physics and Simulation of Optoelectronic Devices II, edited by W. W. Chow and M. Osinski, SPIE Proc. No. 2146 (SPIE, Bellingham, 1994), p. 174;
26. L. E. Thode et al, in Physics and Simulation of Optoelectronic Devices III, edited by M. Osinski and W. W. Chow, SPIE Proc. No. 2399 (SPIE, Bellingham, 1995), p. 348.
27. G. R. Hadley et al., in Physics and Simulation of Optoelectronic Devices III, (Ref. 23), p. 336;
28. IEEE J. Quantum Electron. 32, 607 (1996).
29. Y.-G. Zhao and J. G. McInerney, IEEE J. Quantum Electron. 32, 1950 (1996).IEJQA7
30. Z.-M. Li, in Physics and Simulation of Optoelectronic Devices V, edited by M. Osinski and W. W. Chow, SPIE Proc. No. 2994 (SPIE, Bellingham, 1997), p. 698.
31. C. Z. Ning, R. A. Indik, and J. V. Moloney, J. Opt. Soc. Am. B 12, 1993 (1995); JOBPDEC. Z. Ning, R. A. Indik, J. V. Moloney, and S. W. Koch, in Physics and Simulation of Optoelectronic Devices III, (Ref. 23), p. 617.
32. C. Z. Ning and J. V. Moloney, Appl. Phys. Lett. 66, 559 (1995).APPLAB
33. C. Z. Ning and J. V. Moloney, Opt. Lett. 20, 1151 (1995).OPLEDP
34. G. R. Hadley, Opt. Lett. 20, 1483 (1995).OPLEDP
35. C. Z. Ning, R. A. Indik, and J. V. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).IEJQA7
36. P. K. Jakobsen, J. V. Moloney, A. C. Newell, and R. Indik, Phys. Rev. A 45, 8129 (1992).PLRAAN
37. D. Burak and R. Binder, IEEE J. Quantum Electron. 33, 1205 (1997).IEJQA7
38. On the other hand, the field polarization has already been treated in the context of a VCSEL model that was originally introduced in Ref. 35 with contributions from one of the present authors (J. V. M.) and recently developed further by San Miguel et al. 36. However, we feel that the four-level system approach to the optical response used in this model is not suited for adequately describing a semiconductor quantum well VCSEL. Since the emphasis of the present paper is the role of gain dispersion in the selection of transverse modes, we found it more important to have a microscopic basis for the susceptibility than to take the vector nature of the field into account. We furthermore note that the case of an index-guided VCSEL — which has not been addressed in the context of this simplified vectorial model — would require a careful consideration of the boundary conditions for the electric field. A notable attempt in that direction is presented in Ref. 37.
39. M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. B 52, 1728 (1995).PRBMDO
40. J. Martín-Regalado et al, Quantum Semiclassic. Opt. 9, 713 (1997), and references therein.QUSOEC
41. D. Burak and R. Binder, in Physics and Simulation of Optoelectronic Devices VI, edited by M. Osinski, P. Blood, and A. Ishibashi, SPIE Proc. No. 3283 (SPIE, Bellingham, 1998), p. 269.
42. See, for instance, W. Rudolph and B. Wilhelmi, Light Pulse Compression (Harwood, Chur, 1989).
43. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 1993).
44. W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, New York, 1994).
45. Y. P. Varshni, Physica 34, 149 (1967).ZZZZZZ
46. F. Jahnke and S. W. Koch, Opt. Lett. 18, 1438 (1993).OPLEDP
47. The error introduced by this procedure is second order in (Formula presented) with a prefactor of order (Formula presented) where (Formula presented) is one of (Formula presented) or (Formula presented) One might also be concerned that roundoff error will accumulate, since (Formula presented) is extremely small compared to (Formula presented) However, (Formula presented) which is still adequately resolved in double precision.
48. Y. Kaneko et al, Jpn. J. Appl. Phys., Part 2 L32, 1612 (1993).JAPLD8
49. T. J. Rogers et al, IEEE Photonics Technol. Lett. 7, 238 (1995).IPTLEL
50. G. Hasnain et al, IEEE J. Quantum Electron. 27, 1377 (1991).IEJQA7
51. For a related discussion of boundary effects in large-aspect-ratio lasers, see G. K. Harkness et al, Phys. Rev. A 50, 4310 (1994).PLRAAN
52. M. Sargent III, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).
53. K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., and S. P. Kilcoyne, Appl. Phys. Lett. 66, 2616 (1995).APPLAB
54. K. D. Choquette and R. E. Leibenguth, IEEE Photonics Technol. Lett. 6, 40 (1994).IPTLEL
55. H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, Chaos Solitons Fractals 4, 1619 (1994). CSFOEH