Abstract

We report results of cold-cavity numerical investigations of vertical-cavity surface-emitting lasers with two-dimensional photonic crystals positioned in the laser cavity. The methodology of mode analysis is based on the computation of a normalized propagation constant that directly defines the number of guided modes in comparison with computation of BV diagrams for the structure investigated. It is theoretically shown that the microcavity made by removing one hole is single mode for larger holes than a cavity made by removing several holes. A map obtained for single-mode conditions in the microcavity made by removing one hole for wavelengths 0.98-μm and 1.3 μm is presented, and it is shown that such lasers are easily accessible to modern fabrication processes. The optimum number of holes in the photonic crystal region and the spot size of the fundamental mode have been identified and are discussed.

© 2003 Optical Society of America

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  1. K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
    [CrossRef]
  2. R. Michalzik and K. J. Ebeling, “Operating principles of VCSELs,” Vertical-Cavity Surface-Emitting Laser Devices, H. Li and K. Iga, eds. (Springer-Verlag, Berlin, 2003), pp. 53–98.
  3. P. S. Ivanov, I. A. Sukhoivanov, and V. V. Lysak, “Extended model of a VCSEL with non-uniform laser structure,” Phys. Status Solidi A 188, 961–966 (2001).
    [CrossRef]
  4. L.-G. Zei, S. Ebers, J.-R. Kropp, and K. Petermann, “Noise performance of multimode VCSELs,” J. Lightwave Technol. 19, 884–892 (2001).
    [CrossRef]
  5. H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
    [CrossRef]
  6. H. J. Unold, M. Golling, R. Michalzik, D. Supper, and K. J. Ebeling, “Photonic crystal surface-emitting lasers: tailoring waveguiding for single-mode emission,” Proceedings of the 27th European Conference on Optical Communication, ECOC 2001 (Eindhoven University of Technology, Eindhoven, The Netherlands, 2001), pp. 520–521.
  7. D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
    [CrossRef]
  8. W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
    [CrossRef]
  9. H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
    [CrossRef]
  10. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef] [PubMed]
  11. O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
    [CrossRef]
  12. N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
    [CrossRef]
  13. N. Yokouchi, A. J. Danner, and K. D. Choquetteb, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3609 (2003).
    [CrossRef]
  14. P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, “Single-mode conditions in photonic crystal vertical cavity surface-emitting lasers,” in Proceedings of the Workshop on Laser and Fiber-Optic Network Modeling, LFNM’02 (Kharkiv National University of Radio Electronics, Kharkiv, Ukraine, 2002), pp. 141–144.
  15. M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).
  16. P. S. Ivanov, A. V. Kublik, I. V. Guryev, A. V. Dyogtev, and S. I. Petrov, “Validity of the effective index model for analysis of photonic crystal crystal fibers,” in Proceedings of the Workshop on Laser and Fiber-Optic Network Modeling, LFNM 2003 (Kharkiv National University of Radio Electronics, Kharkiv, Ukraine, 2003).
  17. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  18. J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
    [CrossRef]
  19. J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Comparative study of absorbing boundary conditions for the time-domain beam propagation method,” IEEE Photon. Technol. Lett. 13, 314–316 (2001).
    [CrossRef]
  20. J. Riishede, S. E. Barkou Libori, A. Bjarklev, J. Broeng, and E. Knudsen, “Photonic crystal fibres and effective index approaches,” in Proceedings of the 27th European Conference on Optical Communication, ECOC 2001 (Eindhoven University of Technology, Eindhoven, The Netherlands, 2001), pp. 519–520.

2003 (2)

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquetteb, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3609 (2003).
[CrossRef]

2002 (4)

M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).

D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

2001 (4)

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

L.-G. Zei, S. Ebers, J.-R. Kropp, and K. Petermann, “Noise performance of multimode VCSELs,” J. Lightwave Technol. 19, 884–892 (2001).
[CrossRef]

P. S. Ivanov, I. A. Sukhoivanov, and V. V. Lysak, “Extended model of a VCSEL with non-uniform laser structure,” Phys. Status Solidi A 188, 961–966 (2001).
[CrossRef]

J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Comparative study of absorbing boundary conditions for the time-domain beam propagation method,” IEEE Photon. Technol. Lett. 13, 314–316 (2001).
[CrossRef]

2000 (3)

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

1997 (2)

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
[CrossRef]

Agrawal, G. P.

J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
[CrossRef]

Berg, E.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

Bhattacharya, P.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

Birks, T. A.

Choquette, K. D.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

Choquetteb, K. D.

N. Yokouchi, A. J. Danner, and K. D. Choquetteb, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3609 (2003).
[CrossRef]

Danner, A. J.

N. Yokouchi, A. J. Danner, and K. D. Choquetteb, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3609 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

Dapkus, P. D.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

Ebeling, K. J.

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

Ebers, S.

Grabherr, M.

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

Huh, J.

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Husain, A.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

Hwang, J.-K.

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Iga, K.

K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

Ivanov, P. S.

P. S. Ivanov, I. A. Sukhoivanov, and V. V. Lysak, “Extended model of a VCSEL with non-uniform laser structure,” Phys. Status Solidi A 188, 961–966 (2001).
[CrossRef]

Jaeger, R.

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

Kim, C.-K.

D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

Kim, I.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

Kim, J.-S.

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Kim, S.-H.

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

Knight, J. C.

Kochman, B.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

Koshiba, M.

M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).

Kropp, J.-R.

Law, J. Y.

J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
[CrossRef]

Lee, P. T.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

Lee, Y.-H.

D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Lysak, V. V.

P. S. Ivanov, I. A. Sukhoivanov, and V. V. Lysak, “Extended model of a VCSEL with non-uniform laser structure,” Phys. Status Solidi A 188, 961–966 (2001).
[CrossRef]

Mahmoud, S. W. Z.

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

Michalzik, R.

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

Mortensen, N. A.

Nakano, H.

J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Comparative study of absorbing boundary conditions for the time-domain beam propagation method,” IEEE Photon. Technol. Lett. 13, 314–316 (2001).
[CrossRef]

OBrien, J. D.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

Painter, O.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

Pang, S.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

Park, H.-G.

D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Petermann, K.

Qasaimeh, O.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

Russell, P. St. J.

Ryu, H.-Y.

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Sabarinathan, J.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

Scherer, A.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

Shibayama, J.

J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Comparative study of absorbing boundary conditions for the time-domain beam propagation method,” IEEE Photon. Technol. Lett. 13, 314–316 (2001).
[CrossRef]

Song, D.-S.

D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

Sukhoivanov, I. A.

P. S. Ivanov, I. A. Sukhoivanov, and V. V. Lysak, “Extended model of a VCSEL with non-uniform laser structure,” Phys. Status Solidi A 188, 961–966 (2001).
[CrossRef]

Takahashi, T.

J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Comparative study of absorbing boundary conditions for the time-domain beam propagation method,” IEEE Photon. Technol. Lett. 13, 314–316 (2001).
[CrossRef]

Unold, H. J.

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

Yamauchi, J.

J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Comparative study of absorbing boundary conditions for the time-domain beam propagation method,” IEEE Photon. Technol. Lett. 13, 314–316 (2001).
[CrossRef]

Yokouchi, N.

N. Yokouchi, A. J. Danner, and K. D. Choquetteb, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3609 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

Zei, L.-G.

Zhou, W. D.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

D.-S. Song, S.-H. Kim, H.-G. Park, C.-K. Kim, and Y.-H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 3901–3903 (2002).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquetteb, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3609 (2003).
[CrossRef]

Electron. Lett. (1)

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, “Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,” Electron. Lett. 36, 1541–1542 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

H. J. Unold, S. W. Z. Mahmoud, R. Jaeger, M. Grabherr, R. Michalzik, and K. J. Ebeling, “Large-area single-mode VCSELs and the self-aligned surface relief,” IEEE J. Sel. Top. Quantum Electron. 7, 386–392 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. OBrien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12, 1126–1128 (2000).
[CrossRef]

J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Comparative study of absorbing boundary conditions for the time-domain beam propagation method,” IEEE Photon. Technol. Lett. 13, 314–316 (2001).
[CrossRef]

IEICE Trans. Electron. (1)

M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Status Solidi A (1)

P. S. Ivanov, I. A. Sukhoivanov, and V. V. Lysak, “Extended model of a VCSEL with non-uniform laser structure,” Phys. Status Solidi A 188, 961–966 (2001).
[CrossRef]

Other (5)

J. Riishede, S. E. Barkou Libori, A. Bjarklev, J. Broeng, and E. Knudsen, “Photonic crystal fibres and effective index approaches,” in Proceedings of the 27th European Conference on Optical Communication, ECOC 2001 (Eindhoven University of Technology, Eindhoven, The Netherlands, 2001), pp. 519–520.

P. S. Ivanov, A. V. Kublik, I. V. Guryev, A. V. Dyogtev, and S. I. Petrov, “Validity of the effective index model for analysis of photonic crystal crystal fibers,” in Proceedings of the Workshop on Laser and Fiber-Optic Network Modeling, LFNM 2003 (Kharkiv National University of Radio Electronics, Kharkiv, Ukraine, 2003).

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Figures (8)

Fig. 1
Fig. 1

PCSEL structure.

Fig. 2
Fig. 2

Effective refractive index of the PC cladding as a function of normalized hole diameters d for three wavelengths λ. Calculations were made for hole pitch Λ=1.6 μm.

Fig. 3
Fig. 3

Bk diagram for samples 1 and 2.

Fig. 4
Fig. 4

Bk diagram for samples 1, 3, and 4.

Fig. 5
Fig. 5

Bk diagram for samples 5 and 6.

Fig. 6
Fig. 6

Border line of true single-mode operation of PCSELs with core type 1.

Fig. 7
Fig. 7

LP01 mode of PCSEL sample 6.

Fig. 8
Fig. 8

Relative spot size w¯/Λ of the LP01 mode as a function of hole-size-to-pitch ratio d/Λ for vacuum wavelength λ=0.98 μm.

Tables (1)

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Table 1 Geometrical Parameters of the PCSEL Structures

Equations (5)

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E(x, y, z)=12j=0n e^jEjψj(x, y)exp[i(βjz-ωjt)],
T2ψj(x, y)+n2(x, y) ωj2c2-βj2ψj(x, y)=0,
B=βj2-βclad2(λ)βcore2-βclad2(λ),
[ψj(x, y)]|b=0
Tψj(x, y)-iωjn(x, y)cb=0,

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