Abstract

Transverse-mode discrimination in vertical-cavity surface-emitting lasers that contain a patterned phase aperture is analyzed numerically. The two lowest-order modes are calculated for different aperture shapes and sizes. They are then expanded in Laguerre-Gaussian modes to study the power distribution as well as their beam propagation factor. The mode selection depends on the aperture's size and degree of symmetry. The maximum value for the mode discrimination in the case of a specific phase aperture is determined, and an enhancement by a factor of 3, compared to the case without a phase aperture, is found.

© 2006 Optical Society of America

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  2. Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, "Single-mode emission from a passive-antiguide-region vertical-cavity surface-emitting laser," Electron. Lett. 29, 1861-1863 (1993).
  3. R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2005 (1)

2004 (1)

2001 (1)

H. J. Unold, S. W. Z. Mahmoud, R. Jäger, 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]

1999 (1)

H. Martinsson, J. A. Vukusic, M. Grabherr, R. Michalzik, R. Jäger, K. J. Ebeling, and A. Larsson, "Transverse mode selection in large-area oxide-confined vertical-cavity surface-emitting lasers using a shallow surface relief," IEEE Photon. Technol. Lett. 11, 1536-1538 (1999).
[CrossRef]

1998 (3)

T.-H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 11-14 (1998).

A. K. J. van Doorn, M. P. van Exter, and J. P. Woerdman, "Strain-induced birefringence in vertical-cavity semiconductor lasers," IEEE J. Quantum. Electron. 34, 700-706 (1998).
[CrossRef]

S. Saghafi and C. J. R. Sheppard, "The beam propagation factor for higher-order Gaussian beams," Opt. Commun. 153, 207-210 (1998).
[CrossRef]

1997 (4)

A. V. Syrbu, J. Fernandez, J. Behrend, C. A. Berseth, J. F. Carlin, A. Rudra, and E. Kapon, "InGaAs/InGaAsP/InP edge emitting laser diodes on p-GaAs substrates obtained by localized wafer fusion," Electron. Lett. 33, 866-868 (1997).
[CrossRef]

R. F. M. Hendriks, M. P. vanExter, J. P. Woerdman, A. vanGeelen, L. Weegels, K. H. Gulden, and M. Moser, "Electro-optic birefringence in semiconductor vertical-cavity lasers," Appl. Phys. Lett. 71, 2599-2601 (1997).
[CrossRef]

B.-S. Yoo, H. Y. Chu, H.-H. Park, H. G. Lee, and J. Lee, "Transverse mode characteristics of vertical-cavity surface-emitting lasers buried in amorphous GaAs antiguide layer," IEEE J. Quantum. Electron. 33, 1794-1800 (1997).
[CrossRef]

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

1995 (1)

1994 (1)

K. D. Choquette and R. E. Leibenguth, "Control of vertical-cavity laser polarization with anisotropic transverse cavity geometries," IEEE Photon. Technol. Lett. 6, 40-42 (1994).
[CrossRef]

1993 (2)

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, "Single-mode emission from a passive-antiguide-region vertical-cavity surface-emitting laser," Electron. Lett. 29, 1861-1863 (1993).

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

1992 (1)

K. Iga, "Surface emitting lasers and parallel operating devices--fundamentals and prospects, "IEICE Trans. Fundamentals E75A, 12-19 (1992).

1990 (1)

T. F. Johnston, Jr., "M2 concept characterizes beam quality," Laser Focus World 5, 173-183 (1990).

1983 (1)

1961 (1)

A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).

Achtenhagen, M.

Allen, G. C.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Andrews, L. C.

Asghari, M.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Asom, M. T.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

Behrend, J.

A. V. Syrbu, J. Fernandez, J. Behrend, C. A. Berseth, J. F. Carlin, A. Rudra, and E. Kapon, "InGaAs/InGaAsP/InP edge emitting laser diodes on p-GaAs substrates obtained by localized wafer fusion," Electron. Lett. 33, 866-868 (1997).
[CrossRef]

Berseth, C. A.

A. V. Syrbu, J. Fernandez, J. Behrend, C. A. Berseth, J. F. Carlin, A. Rudra, and E. Kapon, "InGaAs/InGaAsP/InP edge emitting laser diodes on p-GaAs substrates obtained by localized wafer fusion," Electron. Lett. 33, 866-868 (1997).
[CrossRef]

Callis, S. E.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

Carlin, J. F.

A. V. Syrbu, J. Fernandez, J. Behrend, C. A. Berseth, J. F. Carlin, A. Rudra, and E. Kapon, "InGaAs/InGaAsP/InP edge emitting laser diodes on p-GaAs substrates obtained by localized wafer fusion," Electron. Lett. 33, 866-868 (1997).
[CrossRef]

Champagne, Y.

Chang-Hasnain, C. J.

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, "Single-mode emission from a passive-antiguide-region vertical-cavity surface-emitting laser," Electron. Lett. 29, 1861-1863 (1993).

Choquette, K. D.

K. D. Choquette and R. E. Leibenguth, "Control of vertical-cavity laser polarization with anisotropic transverse cavity geometries," IEEE Photon. Technol. Lett. 6, 40-42 (1994).
[CrossRef]

Chu, H. Y.

B.-S. Yoo, H. Y. Chu, H.-H. Park, H. G. Lee, and J. Lee, "Transverse mode characteristics of vertical-cavity surface-emitting lasers buried in amorphous GaAs antiguide layer," IEEE J. Quantum. Electron. 33, 1794-1800 (1997).
[CrossRef]

Deppe, D. G.

T.-H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 11-14 (1998).

Dowd, P.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Ebeling, K. J.

H. J. Unold, S. W. Z. Mahmoud, R. Jäger, 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]

H. Martinsson, J. A. Vukusic, M. Grabherr, R. Michalzik, R. Jäger, K. J. Ebeling, and A. Larsson, "Transverse mode selection in large-area oxide-confined vertical-cavity surface-emitting lasers using a shallow surface relief," IEEE Photon. Technol. Lett. 11, 1536-1538 (1999).
[CrossRef]

Fernandez, J.

A. V. Syrbu, J. Fernandez, J. Behrend, C. A. Berseth, J. F. Carlin, A. Rudra, and E. Kapon, "InGaAs/InGaAsP/InP edge emitting laser diodes on p-GaAs substrates obtained by localized wafer fusion," Electron. Lett. 33, 866-868 (1997).
[CrossRef]

Focht, M. W.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

Fox, A. G.

A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).

Grabherr, M.

H. J. Unold, S. W. Z. Mahmoud, R. Jäger, 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]

H. Martinsson, J. A. Vukusic, M. Grabherr, R. Michalzik, R. Jäger, K. J. Ebeling, and A. Larsson, "Transverse mode selection in large-area oxide-confined vertical-cavity surface-emitting lasers using a shallow surface relief," IEEE Photon. Technol. Lett. 11, 1536-1538 (1999).
[CrossRef]

Gulden, K. H.

R. F. M. Hendriks, M. P. vanExter, J. P. Woerdman, A. vanGeelen, L. Weegels, K. H. Gulden, and M. Moser, "Electro-optic birefringence in semiconductor vertical-cavity lasers," Appl. Phys. Lett. 71, 2599-2601 (1997).
[CrossRef]

Guth, G. D.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

Hardy, A.

Heard, P. J.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Hendriks, R. F. M.

R. F. M. Hendriks, M. P. vanExter, J. P. Woerdman, A. vanGeelen, L. Weegels, K. H. Gulden, and M. Moser, "Electro-optic birefringence in semiconductor vertical-cavity lasers," Appl. Phys. Lett. 71, 2599-2601 (1997).
[CrossRef]

Huffaker, D. L.

T.-H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 11-14 (1998).

Iga, K.

K. Iga, "Surface emitting lasers and parallel operating devices--fundamentals and prospects, "IEICE Trans. Fundamentals E75A, 12-19 (1992).

Jäger, R.

H. J. Unold, S. W. Z. Mahmoud, R. Jäger, 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]

H. Martinsson, J. A. Vukusic, M. Grabherr, R. Michalzik, R. Jäger, K. J. Ebeling, and A. Larsson, "Transverse mode selection in large-area oxide-confined vertical-cavity surface-emitting lasers using a shallow surface relief," IEEE Photon. Technol. Lett. 11, 1536-1538 (1999).
[CrossRef]

Johnston, T. F.

T. F. Johnston, Jr., "M2 concept characterizes beam quality," Laser Focus World 5, 173-183 (1990).

Kapon, E.

Kojima, K.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

Larsson, A.

H. Martinsson, J. A. Vukusic, M. Grabherr, R. Michalzik, R. Jäger, K. J. Ebeling, and A. Larsson, "Transverse mode selection in large-area oxide-confined vertical-cavity surface-emitting lasers using a shallow surface relief," IEEE Photon. Technol. Lett. 11, 1536-1538 (1999).
[CrossRef]

Lee, H. G.

B.-S. Yoo, H. Y. Chu, H.-H. Park, H. G. Lee, and J. Lee, "Transverse mode characteristics of vertical-cavity surface-emitting lasers buried in amorphous GaAs antiguide layer," IEEE J. Quantum. Electron. 33, 1794-1800 (1997).
[CrossRef]

Lee, J.

B.-S. Yoo, H. Y. Chu, H.-H. Park, H. G. Lee, and J. Lee, "Transverse mode characteristics of vertical-cavity surface-emitting lasers buried in amorphous GaAs antiguide layer," IEEE J. Quantum. Electron. 33, 1794-1800 (1997).
[CrossRef]

Leibenguth, R. E.

K. D. Choquette and R. E. Leibenguth, "Control of vertical-cavity laser polarization with anisotropic transverse cavity geometries," IEEE Photon. Technol. Lett. 6, 40-42 (1994).
[CrossRef]

Li, T.

A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).

Mahmoud, S. W. Z.

H. J. Unold, S. W. Z. Mahmoud, R. Jäger, 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]

Martinsson, H.

H. Martinsson, J. A. Vukusic, M. Grabherr, R. Michalzik, R. Jäger, K. J. Ebeling, and A. Larsson, "Transverse mode selection in large-area oxide-confined vertical-cavity surface-emitting lasers using a shallow surface relief," IEEE Photon. Technol. Lett. 11, 1536-1538 (1999).
[CrossRef]

McDaniel, M. R.

T.-H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 11-14 (1998).

Michalzik, R.

H. J. Unold, S. W. Z. Mahmoud, R. Jäger, 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]

H. Martinsson, J. A. Vukusic, M. Grabherr, R. Michalzik, R. Jäger, K. J. Ebeling, and A. Larsson, "Transverse mode selection in large-area oxide-confined vertical-cavity surface-emitting lasers using a shallow surface relief," IEEE Photon. Technol. Lett. 11, 1536-1538 (1999).
[CrossRef]

Morgan, R. A.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

Moser, M.

R. F. M. Hendriks, M. P. vanExter, J. P. Woerdman, A. vanGeelen, L. Weegels, K. H. Gulden, and M. Moser, "Electro-optic birefringence in semiconductor vertical-cavity lasers," Appl. Phys. Lett. 71, 2599-2601 (1997).
[CrossRef]

Nabiev, R.

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, "Single-mode emission from a passive-antiguide-region vertical-cavity surface-emitting laser," Electron. Lett. 29, 1861-1863 (1993).

Oh, T.-H.

T.-H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 11-14 (1998).

Park, H.-H.

B.-S. Yoo, H. Y. Chu, H.-H. Park, H. G. Lee, and J. Lee, "Transverse mode characteristics of vertical-cavity surface-emitting lasers buried in amorphous GaAs antiguide layer," IEEE J. Quantum. Electron. 33, 1794-1800 (1997).
[CrossRef]

Penty, R. V.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Phillips, R. L.

Raddatz, L.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Rogers, L. E.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, "Tranverse mode control of vertical-cavity top-surface-emitting lasers," IEEE Photon. Technol . Lett. 4, 374-377 (1993).
[CrossRef]

Rudra, A.

A. V. Syrbu, J. Fernandez, J. Behrend, C. A. Berseth, J. F. Carlin, A. Rudra, and E. Kapon, "InGaAs/InGaAsP/InP edge emitting laser diodes on p-GaAs substrates obtained by localized wafer fusion," Electron. Lett. 33, 866-868 (1997).
[CrossRef]

Saghafi, S.

S. Saghafi and C. J. R. Sheppard, "The beam propagation factor for higher-order Gaussian beams," Opt. Commun. 153, 207-210 (1998).
[CrossRef]

Schneider, R. P.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Sheppard, C. J. R.

S. Saghafi and C. J. R. Sheppard, "The beam propagation factor for higher-order Gaussian beams," Opt. Commun. 153, 207-210 (1998).
[CrossRef]

Sumaila, Y.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Syrbu, A. V.

A. V. Syrbu, J. Fernandez, J. Behrend, C. A. Berseth, J. F. Carlin, A. Rudra, and E. Kapon, "InGaAs/InGaAsP/InP edge emitting laser diodes on p-GaAs substrates obtained by localized wafer fusion," Electron. Lett. 33, 866-868 (1997).
[CrossRef]

Tan, M. R. T.

P. Dowd, L. Raddatz, Y. Sumaila, M. Asghari, I. H. White, R. V. Penty, P. J. Heard, G. C. Allen, R. P. Schneider, M. R. T. Tan, and S. Y. Wang, "Mode control in vertical-cavity surface-emitting lasers by postprocessing using focused ion-beam etching," IEEE Photon. Technol. Lett. 9, 1193-1195 (1997).
[CrossRef]

Unold, H. J.

H. J. Unold, S. W. Z. Mahmoud, R. Jäger, 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]

van Doorn, A. K. J.

A. K. J. van Doorn, M. P. van Exter, and J. P. Woerdman, "Strain-induced birefringence in vertical-cavity semiconductor lasers," IEEE J. Quantum. Electron. 34, 700-706 (1998).
[CrossRef]

van Exter, M. P.

A. K. J. van Doorn, M. P. van Exter, and J. P. Woerdman, "Strain-induced birefringence in vertical-cavity semiconductor lasers," IEEE J. Quantum. Electron. 34, 700-706 (1998).
[CrossRef]

vanExter, M. P.

R. F. M. Hendriks, M. P. vanExter, J. P. Woerdman, A. vanGeelen, L. Weegels, K. H. Gulden, and M. Moser, "Electro-optic birefringence in semiconductor vertical-cavity lasers," Appl. Phys. Lett. 71, 2599-2601 (1997).
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