Abstract

Lateral loss causes optical energy to leave the laser cavity in the transverse, lateral, direction, and is sometimes neglected to simplify the numerical simulations. However, in contrast to outcoupling and absorption losses, we show that the lateral loss can change drastically with only nanometer-sized changes of the cavity structure, from being virtually zero to becoming the major source of cavity loss, since the cavity becomes antiguiding. This can be explained as the opening of a channel of efficient resonant lateral leakage of optical power at a certain oblique propagation angle. A number of different realizations of current apertures and top mirror designs in GaN-based VCSEL cavities, which have been suggested for realization of microcavity lasers emitting in the blue wavelength range, are simulated. Many of these are shown to lead to unintentional antiguiding, which can more than double the threshold gain for lasing. Notably, for strong enough antiguiding the resonant lateral leakage decreases so that the threshold gain values might again be tolerable. This regime has been suggested for robust single-mode operation since earlier predictions, building on analogies with slab waveguides, hinted at a very strong suppression of higher order modes. However, our simulations indicate that for the VCSEL cavities the derived formulas grossly overestimate the modal discrimination.

© 2014 Optical Society of America

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  1. G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
    [CrossRef]
  2. C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
    [CrossRef]
  3. T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
    [CrossRef]
  4. D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
    [CrossRef]
  5. T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. T. Czyszanowski, M. Wasiak, R. P. Sarzala, W. Nakwaski, “Exactness of simplified scalar optical approaches in modeling a threshold operation of possible nitride vertical-cavity surface-emitting lasers,” Phys. Stat. Sol. A 204(10), 3562–3573 (2007).
    [CrossRef]
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    [CrossRef]
  17. S. C. Wang, T. C. Lu, H. C. Kuo, “Recent advances on CW current injection blue VCSELs,” Proc. SPIE 8276, 827607 (2012).
    [CrossRef]
  18. B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
    [CrossRef]
  19. M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
    [CrossRef]
  20. W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
    [CrossRef]
  21. R. W. H. Engelmann, D. Kerps, “Leaky modes in active three-layer slab waveguides,” IEE Proc. 127(6), 330–336 (1980).
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    [CrossRef]

2013 (1)

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

2012 (5)

G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
[CrossRef]

C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
[CrossRef]

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

S. C. Wang, T. C. Lu, H. C. Kuo, “Recent advances on CW current injection blue VCSELs,” Proc. SPIE 8276, 827607 (2012).
[CrossRef]

2011 (2)

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

2010 (2)

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

J. Piprek, S. Li, “GaN-based VCSELs: Analysis of internal device physics and performance limitations,” Proc. SPIE 7602, 760217 (2010).
[CrossRef]

2009 (2)

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

2008 (2)

2007 (2)

T. Czyszanowski, M. Wasiak, R. P. Sarzala, W. Nakwaski, “Exactness of simplified scalar optical approaches in modeling a threshold operation of possible nitride vertical-cavity surface-emitting lasers,” Phys. Stat. Sol. A 204(10), 3562–3573 (2007).
[CrossRef]

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

2002 (2)

J. S. Gustavsson, J. Vukusic, J. Bengtsson, A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(2), 203–212 (2002).
[CrossRef]

D. Zhou, L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(12), 1599–1606 (2002).
[CrossRef]

1995 (1)

1980 (1)

R. W. H. Engelmann, D. Kerps, “Leaky modes in active three-layer slab waveguides,” IEE Proc. 127(6), 330–336 (1980).

Akagawa, T.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Altoukhov, A.

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Amann, M.-C.

Ariyoshi, A.

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Bachmann, A.

Bengtsson, J.

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

J. Bengtsson, J. Gustavsson, Å. Haglund, A. Larsson, A. Bachmann, K. Kashani-Shirazi, M.-C. Amann, “Diffraction loss in long-wavelength buried tunnel junction VCSELs analyzed with a hybrid coupled-cavity transfer-matrix model,” Opt. Express 16(25), 20789–20802 (2008).
[CrossRef] [PubMed]

J. S. Gustavsson, J. Vukusic, J. Bengtsson, A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(2), 203–212 (2002).
[CrossRef]

Bousquet, V.

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Butté, R.

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Carlin, J. F.

G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
[CrossRef]

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Castiglia, A.

G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
[CrossRef]

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Chang, C. Y.

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Chen, C. H.

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Chen, C-H.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Chen, C-K.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Chen, S-W.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Cheng, B. S.

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Chiu, C. H.

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Christmann, G.

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Cosendey, G.

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
[CrossRef]

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Czyszanowski, T.

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

T. Czyszanowski, M. Wasiak, R. P. Sarzala, W. Nakwaski, “Exactness of simplified scalar optical approaches in modeling a threshold operation of possible nitride vertical-cavity surface-emitting lasers,” Phys. Stat. Sol. A 204(10), 3562–3573 (2007).
[CrossRef]

W. Nakwaski, T. Czyszanowski, R. P. Sarzala, Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (Wiley, 2007).

Dems, M.

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

DenBaars, S. P.

C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
[CrossRef]

Engelmann, R. W. H.

R. W. H. Engelmann, D. Kerps, “Leaky modes in active three-layer slab waveguides,” IEE Proc. 127(6), 330–336 (1980).

Feezell, D.

C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
[CrossRef]

Feltin, E.

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Fukuda, K.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grandjean, N.

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
[CrossRef]

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Gustavsson, J.

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

J. Bengtsson, J. Gustavsson, Å. Haglund, A. Larsson, A. Bachmann, K. Kashani-Shirazi, M.-C. Amann, “Diffraction loss in long-wavelength buried tunnel junction VCSELs analyzed with a hybrid coupled-cavity transfer-matrix model,” Opt. Express 16(25), 20789–20802 (2008).
[CrossRef] [PubMed]

Gustavsson, J. S.

J. S. Gustavsson, J. Vukusic, J. Bengtsson, A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(2), 203–212 (2002).
[CrossRef]

Hadley, G. R.

Haglund, Å.

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

J. Bengtsson, J. Gustavsson, Å. Haglund, A. Larsson, A. Bachmann, K. Kashani-Shirazi, M.-C. Amann, “Diffraction loss in long-wavelength buried tunnel junction VCSELs analyzed with a hybrid coupled-cavity transfer-matrix model,” Opt. Express 16(25), 20789–20802 (2008).
[CrossRef] [PubMed]

Hashemi, E.

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

Higuchi, Y.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Y. Higuchi, K. Omae, H. Matsumura, T. Mukai, “Room-temperature cw lasing of a GaN-based vertical-cavity surface-emitting laser by current injection,” Appl. Phys. Expr. 1, 121102 (2008).
[CrossRef]

Holder, C.

C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
[CrossRef]

Imafuji, O.

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

Kasahara, D.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Kashani-Shirazi, K.

Kauer, M.

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Kawaguchi, M.

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

Kawamata, J.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Kerps, D.

R. W. H. Engelmann, D. Kerps, “Leaky modes in active three-layer slab waveguides,” IEE Proc. 127(6), 330–336 (1980).

Kohmoto, S.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Kosugi, T.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Kuo, H. C.

S. C. Wang, T. C. Lu, H. C. Kuo, “Recent advances on CW current injection blue VCSELs,” Proc. SPIE 8276, 827607 (2012).
[CrossRef]

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Kuo, H-C.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Larsson, A.

J. Bengtsson, J. Gustavsson, Å. Haglund, A. Larsson, A. Bachmann, K. Kashani-Shirazi, M.-C. Amann, “Diffraction loss in long-wavelength buried tunnel junction VCSELs analyzed with a hybrid coupled-cavity transfer-matrix model,” Opt. Express 16(25), 20789–20802 (2008).
[CrossRef] [PubMed]

J. S. Gustavsson, J. Vukusic, J. Bengtsson, A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(2), 203–212 (2002).
[CrossRef]

Levrat, J.

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

Li, S.

J. Piprek, S. Li, “GaN-based VCSELs: Analysis of internal device physics and performance limitations,” Proc. SPIE 7602, 760217 (2010).
[CrossRef]

Li, Z-Y.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Lu, T. C.

S. C. Wang, T. C. Lu, H. C. Kuo, “Recent advances on CW current injection blue VCSELs,” Proc. SPIE 8276, 827607 (2012).
[CrossRef]

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Lu, T-C.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Masumoto, I.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Matsudate, M.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Matsumura, H.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Y. Higuchi, K. Omae, H. Matsumura, T. Mukai, “Room-temperature cw lasing of a GaN-based vertical-cavity surface-emitting laser by current injection,” Appl. Phys. Expr. 1, 121102 (2008).
[CrossRef]

Mawst, L. J.

D. Zhou, L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(12), 1599–1606 (2002).
[CrossRef]

Morita, D.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Mukai, T.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Y. Higuchi, K. Omae, H. Matsumura, T. Mukai, “Room-temperature cw lasing of a GaN-based vertical-cavity surface-emitting laser by current injection,” Appl. Phys. Expr. 1, 121102 (2008).
[CrossRef]

Nagamatsu, K.

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

Nakagawa, K.

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

Nakamura, S.

C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
[CrossRef]

Nakwaski, W.

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

T. Czyszanowski, M. Wasiak, R. P. Sarzala, W. Nakwaski, “Exactness of simplified scalar optical approaches in modeling a threshold operation of possible nitride vertical-cavity surface-emitting lasers,” Phys. Stat. Sol. A 204(10), 3562–3573 (2007).
[CrossRef]

W. Nakwaski, T. Czyszanowski, R. P. Sarzala, Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (Wiley, 2007).

Naniwae, K.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Ohta, M.

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Ohya, M.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Omae, K.

Y. Higuchi, K. Omae, H. Matsumura, T. Mukai, “Room-temperature cw lasing of a GaN-based vertical-cavity surface-emitting laser by current injection,” Appl. Phys. Expr. 1, 121102 (2008).
[CrossRef]

Onishi, T.

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

Panajotov, K.

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

Piprek, J.

J. Piprek, S. Li, “GaN-based VCSELs: Analysis of internal device physics and performance limitations,” Proc. SPIE 7602, 760217 (2010).
[CrossRef]

Piskorski, L.

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

Rossbach, G.

G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
[CrossRef]

Sarzala, R.

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

Sarzala, R. P.

T. Czyszanowski, M. Wasiak, R. P. Sarzala, W. Nakwaski, “Exactness of simplified scalar optical approaches in modeling a threshold operation of possible nitride vertical-cavity surface-emitting lasers,” Phys. Stat. Sol. A 204(10), 3562–3573 (2007).
[CrossRef]

W. Nakwaski, T. Czyszanowski, R. P. Sarzala, Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (Wiley, 2007).

Sasaoka, C.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Speck, J. S.

C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
[CrossRef]

Stattin, M.

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

Takahashi, K.

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Takigawa, S.

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

Tan, W. S.

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Tsuda, Y.

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Tsukuda, T.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Tu, P. M.

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Tu, P-M.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Vukusic, J.

J. S. Gustavsson, J. Vukusic, J. Bengtsson, A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(2), 203–212 (2002).
[CrossRef]

Wang, S. C.

S. C. Wang, T. C. Lu, H. C. Kuo, “Recent advances on CW current injection blue VCSELs,” Proc. SPIE 8276, 827607 (2012).
[CrossRef]

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Wang, S-C.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Wasiak, M.

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

T. Czyszanowski, M. Wasiak, R. P. Sarzala, W. Nakwaski, “Exactness of simplified scalar optical approaches in modeling a threshold operation of possible nitride vertical-cavity surface-emitting lasers,” Phys. Stat. Sol. A 204(10), 3562–3573 (2007).
[CrossRef]

Wu, T-T.

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Wu, Y. L.

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

Yamada, M.

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

Yamanaka, K.

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

Zhou, D.

D. Zhou, L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(12), 1599–1606 (2002).
[CrossRef]

Adv. Opt. Technol. (1)

R. Sarzala, T. Czyszanowski, M. Wasiak, M. Dems, L. Piskorski, W. Nakwaski, K. Panajotov, “Numerical self-consistent analysis of VCSELs,” Adv. Opt. Technol. 2012, ID 689519 (2012).
[CrossRef]

Appl Phys. Lett. (1)

T-C. Lu, S-W. Chen, T-T. Wu, P-M. Tu, C-K. Chen, C-H. Chen, Z-Y. Li, H-C. Kuo, S-C. Wang, “Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature,” Appl Phys. Lett. 97(7), 071114 (2010).
[CrossRef]

Appl. Phys. Expr. (4)

Y. Higuchi, K. Omae, H. Matsumura, T. Mukai, “Room-temperature cw lasing of a GaN-based vertical-cavity surface-emitting laser by current injection,” Appl. Phys. Expr. 1, 121102 (2008).
[CrossRef]

C. Holder, J. S. Speck, S. P. DenBaars, S. Nakamura, D. Feezell, “Demonstration of nonpolar GaN-based vertical-cavity surface-emitting lasers,” Appl. Phys. Expr. 5, 092104 (2012).
[CrossRef]

D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, H. Matsumura, T. Mukai, “Demonstration of blue and green GaN-based vertical-cavity surface-emitting lasers by current injection at room temperature,” Appl. Phys. Expr. 4, 072103 (2011).
[CrossRef]

W. S. Tan, K. Takahashi, V. Bousquet, A. Ariyoshi, Y. Tsuda, M. Ohta, M. Kauer, “Blue-violet inner stripe laser diodes using lattice matched AlInN as current confinement layer for high power operation,” Appl. Phys. Expr. 2, 112101 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

G. Cosendey, A. Castiglia, G. Rossbach, J. F. Carlin, N. Grandjean, “Blue monolithic AlInN-based vertical cavity surface emitting laser diode on free-standing GaN substrate,” Appl. Phys. Lett. 101(15), 151113 (2012).
[CrossRef]

B. S. Cheng, Y. L. Wu, T. C. Lu, C. H. Chiu, C. H. Chen, P. M. Tu, H. C. Kuo, S. C. Wang, C. Y. Chang, “High Q microcavity light emitting diodes with buried AlN current apertures,” Appl. Phys. Lett. 99(4), 041101 (2011).
[CrossRef]

IEE Proc. (1)

R. W. H. Engelmann, D. Kerps, “Leaky modes in active three-layer slab waveguides,” IEE Proc. 127(6), 330–336 (1980).

IEEE J. Quantum Electron. (3)

D. Zhou, L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(12), 1599–1606 (2002).
[CrossRef]

J. S. Gustavsson, J. Vukusic, J. Bengtsson, A. Larsson, “A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(2), 203–212 (2002).
[CrossRef]

T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Yamanaka, S. Takigawa, “Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature,” IEEE J. Quantum Electron. 48(9), 1107–1112 (2012).
[CrossRef]

Jap. J. Appl. Phys. (1)

E. Hashemi, J. Gustavsson, J. Bengtsson, M. Stattin, G. Cosendey, N. Grandjean, Å. Haglund, “Engineering the lateral optical guiding in gallium nitride-based vertical-cavity surface-emitting laser cavities to reach the lowest threshold gain,” Jap. J. Appl. Phys. 52, 08JG04 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Stat. Sol. A (1)

T. Czyszanowski, M. Wasiak, R. P. Sarzala, W. Nakwaski, “Exactness of simplified scalar optical approaches in modeling a threshold operation of possible nitride vertical-cavity surface-emitting lasers,” Phys. Stat. Sol. A 204(10), 3562–3573 (2007).
[CrossRef]

Proc. SPIE (4)

M. Ohya, K. Fukuda, I. Masumoto, S. Kohmoto, K. Naniwae, M. Yamada, M. Matsudate, T. Tsukuda, T. Akagawa, C. Sasaoka, “High-power operation of inner-stripe GaN-based blue-violet laser diodes,” Proc. SPIE 6485, 648505 (2007).
[CrossRef]

R. Butté, G. Christmann, E. Feltin, A. Castiglia, J. Levrat, G. Cosendey, A. Altoukhov, J. F. Carlin, N. Grandjean, “Room temperature polariton lasing in III-nitride microcavities: a comparison with blue GaN-based vertical cavity surface emitting lasers,” Proc. SPIE 7216, 721619 (2009).
[CrossRef]

S. C. Wang, T. C. Lu, H. C. Kuo, “Recent advances on CW current injection blue VCSELs,” Proc. SPIE 8276, 827607 (2012).
[CrossRef]

J. Piprek, S. Li, “GaN-based VCSELs: Analysis of internal device physics and performance limitations,” Proc. SPIE 7602, 760217 (2010).
[CrossRef]

Other (2)

W. Nakwaski, T. Czyszanowski, R. P. Sarzala, Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (Wiley, 2007).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (8)

Fig. 1
Fig. 1

Schematic of one simulated laser cavity (left) and composite figure showing the rotationally symmetric refractive index variation in a small part of the cavity (shown color-coded above the indicated optical axis) and the rotationally symmetric intracavity field for the fundamental mode. Different subcavities are labeled by integers and their boundaries are marked with vertical dashed lines. The inset shows an example of the convergence of the QW gain towards the threshold value in the iterative 3D cavity simulation algorithm. The symbols in subcavity 2 refer to the treatment in the Appendix.

Fig. 2
Fig. 2

Structures for the different types of current aperture realizations that have been analyzed.

Fig. 3
Fig. 3

Calculated threshold gain for the fundamental mode in the different laser cavities. The number at each marker is the structural depression parameter δ, and the plus sign below each marker indicates the threshold gain multiplied by the modal lateral overlap with the gain region. The inset shows six different mode profiles of the intracavity field amplitude at the position of the QWs, in the radial direction from the indicated optical axis plotted either to the left or right in the inset, for the displayed values of δ.

Fig. 4
Fig. 4

Results of loss analysis for the fundamental mode in the studied VCSEL cavities.

Fig. 5
Fig. 5

A simplified model of the laser cavity as a hard-mirror model with a central depression, and filled with a homogeneous medium of refractive index ncav. Dashed lines perpendicular to the k-vectors denote wavefronts.

Fig. 6
Fig. 6

Calculated propagation angle in air, measured from the optical axis, for the main side lobe in the output field distributions from antiguided cavities. All studied antiguided cavities are represented in this figure, both their fundamental and their first higher order modes (the latter does not exist for the cavity with the lowest δ). The solid line is the result of the resonance analysis for the simplified hard-mirror model. Insets show field distribution in the far-field for a few cases, with image saturation increasing with δ to be able to see the side lobe. All insets cover the same angular range (35 degrees from optical axis in the horizontal and vertical directions).

Fig. 7
Fig. 7

Calculated threshold gain for the first higher order mode. The threshold gain for the fundamental mode from Fig. 3 is also plotted here for convenient comparison (larger markers of same shape and color). The vertical lines connecting the threshold gain values for the fundamental and first higher order mode for the same cavity thus indicate the modal discrimination of this cavity. Insets show cross sections of the intracavity fields above the bottom DBR in the indicated cavity for the fundamental and higher order mode.

Fig. 8
Fig. 8

Results of loss analysis for the first higher order mode in the studied VCSEL cavities. The indicated percentages are the relative change in the lateral loss compared to the case for the fundamental mode.

Tables (1)

Tables Icon

Table 1 Investigated epitaxial layer structures and assumed material parameters.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

k 2 L = m c 2 π ; k = 2 π λ ,
k long 2 ( L + δ ) = m p 2 π ,
cos θ p = L L + δ cav .
sin θ air = n cav sin θ p ,
E act ( x , y ) = κ E 0 ( x , y ) + E 1 ( x , y ) + E other ( x , y ) ,
κ = x , y E act ( x , y ) E 0 * ( x , y ) d x d y x , y E 0 ( x , y ) E 0 * ( x , y ) d x d y .
S ¯ = ( E ¯ + E ¯ ) × ( H ¯ + H ¯ ) = E ¯ × H ¯ + E ¯ × H ¯ + E ¯ × H ¯ + E ¯ × H ¯ ,
E ¯ = x ^ E 0 e γ 2 z ˜ cos ( k z ˜ ω t ) E ¯ = x ^ E 0 e γ 2 z ˜ cos ( k z ˜ ω t + Δ φ ) H ¯ = y ^ H 0 e γ 2 z ˜ cos ( k z ˜ ω t + φ H ) H ¯ = y ^ H 0 e γ 2 z ˜ cos ( k z ˜ ω t + Δ φ + φ H ) ,
S ¯ = z ^ 1 2 { E 0 H 0 cos φ H + E 0 H 0 cos φ H + E 0 H 0 ( cos φ H cos Δ φ sin φ H sin Δ φ ) + E 0 H 0 ( cos φ H cos Δ φ + sin φ H sin Δ φ ) z ^ S .
E x z ˜ = μ 0 H y t ,
H 0 cos φ H = E 0 k μ 0 ω H 0 cos φ H = E 0 k μ 0 ω H 0 sin φ H = E 0 γ 2 μ 0 ω H 0 sin φ H = E 0 γ 2 μ 0 ω .
S = 1 2 μ 0 c 0 { ( E 0 ) 2 n ( E 0 ) 2 n + 2 E 0 E 0 n sin Δ φ } ,
P s c = { S ( x , y ) z = b } d x d y + { S ( x , y ) z = a } d x d y ,

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