Abstract

(Al,In)GaN–based laser diodes with ridge widths broader than a few micrometer tend to show filamentation effects in the lateral direction. By time–resolved scanning near–field optical microscopy, we find different kinds of filaments depending on ridge width and lateral position. We investigate these effects systematically and compare them to the results of corresponding simulations, which are based on a simple rate equation model including the lateral dimension. By this comparison we find a consistent and reasonable set of material parameters that can describe the laser diode. Furthermore, we discuss several reasons for filamentation dynamics like ridge asymmetry or spatial hole–burning, as well as critical temperatures that induce filamentation.

© 2008 Optical Society of America

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  3. V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
    [CrossRef]
  4. U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
    [CrossRef]
  5. U. T. Schwarz and M. Pindl, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Proc. SPIE 5738, 229-237 (2005).
    [CrossRef]
  6. U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
    [CrossRef]
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    [CrossRef]
  8. W.W. Chow, H. Amano, and I. Akasaki, "Analysis of lateral-mode Behavior in broad-area InGaN quantum-well lasers," IEEE J. Quantum Electron. 37, 265-273 (2001).
    [CrossRef]
  9. J. Buus, "Models of the static and dynamic behavior of stripe geometry lasers," IEEE J. Quantum Electron. 19, 953-960 (1983).
    [CrossRef]
  10. Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
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    [CrossRef]
  14. M. O. Ziegler, M. M¨unkel, G. Jennemann, I. Fischer, and W. Elsä�?er, "Spatiotemporal emission dynamics of ridge waveguide laser diodes: picosecond pulsing and switching," J. Opt. Soc. Am. B 16, 2015 (1999).
    [CrossRef]
  15. J. Piprekt and S. Nakamura, "Physics of high-power InGaN/GaN lasers," IEE Proc. J.Optoelectron. 149, 145 (2002).
    [CrossRef]
  16. S. Odermatt, B. Witzigmann, and B. Schmithüsen, "Harmonic balance analysis for semiconductor lasers under large-signal modulation," Opt. Quantum Electron. 38, 1039 (2006).
    [CrossRef]
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  18. C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
    [CrossRef]
  19. H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
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  20. Y. P. Varshni, "Temperature dependence of the energy gap in semiconductors," Physica 34, 149 (1967).
    [CrossRef]
  21. G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
    [CrossRef]
  22. U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
    [CrossRef]
  23. M. Pindl and U. T. Schwarz, "Waveguide mode dynamics of blue laser diodes," Phys. Status Solidi A 203, 1787-1791 (2006).
    [CrossRef]

2008

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

2007

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

2006

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

B. Witzigmann, V. Laino, and M. Luisier, "Microscopic analysis of optical gain in InGaN/GaN quantum wells," Appl. Phys. Lett. 88, 021104 (2006).
[CrossRef]

S. Odermatt, B. Witzigmann, and B. Schmithüsen, "Harmonic balance analysis for semiconductor lasers under large-signal modulation," Opt. Quantum Electron. 38, 1039 (2006).
[CrossRef]

M. Pindl and U. T. Schwarz, "Waveguide mode dynamics of blue laser diodes," Phys. Status Solidi A 203, 1787-1791 (2006).
[CrossRef]

2005

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

U. T. Schwarz and M. Pindl, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Proc. SPIE 5738, 229-237 (2005).
[CrossRef]

2004

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

2003

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

2002

J. Piprekt and S. Nakamura, "Physics of high-power InGaN/GaN lasers," IEE Proc. J.Optoelectron. 149, 145 (2002).
[CrossRef]

2001

G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
[CrossRef]

W.W. Chow, H. Amano, and I. Akasaki, "Analysis of lateral-mode Behavior in broad-area InGaN quantum-well lasers," IEEE J. Quantum Electron. 37, 265-273 (2001).
[CrossRef]

2000

W. W. Chow and H. Amano, "Theoretical analysis of filamentation and fundamental-mode operation in InGaN quantum well lasers," Appl. Phys. Lett. 76, 1647-1649 (2000).
[CrossRef]

1999

1996

I. Fischer, O. Hess,W. Elsä�?er, and E. Göbel, "Complex spatio-temporal dynamics in the near-field of a broad-area semiconductor laser," Europhys. Lett. 35, 579 (1996).
[CrossRef]

1983

J. Buus, "Models of the static and dynamic behavior of stripe geometry lasers," IEEE J. Quantum Electron. 19, 953-960 (1983).
[CrossRef]

1967

Y. P. Varshni, "Temperature dependence of the energy gap in semiconductors," Physica 34, 149 (1967).
[CrossRef]

Akasaki, I.

W.W. Chow, H. Amano, and I. Akasaki, "Analysis of lateral-mode Behavior in broad-area InGaN quantum-well lasers," IEEE J. Quantum Electron. 37, 265-273 (2001).
[CrossRef]

Amano, H.

W.W. Chow, H. Amano, and I. Akasaki, "Analysis of lateral-mode Behavior in broad-area InGaN quantum-well lasers," IEEE J. Quantum Electron. 37, 265-273 (2001).
[CrossRef]

W. W. Chow and H. Amano, "Theoretical analysis of filamentation and fundamental-mode operation in InGaN quantum well lasers," Appl. Phys. Lett. 76, 1647-1649 (2000).
[CrossRef]

Ben, Y.

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

Braun, H.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

Brüninghoff, S.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

Buus, J.

J. Buus, "Models of the static and dynamic behavior of stripe geometry lasers," IEEE J. Quantum Electron. 19, 953-960 (1983).
[CrossRef]

Chow, W. W.

W. W. Chow and H. Amano, "Theoretical analysis of filamentation and fundamental-mode operation in InGaN quantum well lasers," Appl. Phys. Lett. 76, 1647-1649 (2000).
[CrossRef]

Chow, W.W.

W.W. Chow, H. Amano, and I. Akasaki, "Analysis of lateral-mode Behavior in broad-area InGaN quantum-well lasers," IEEE J. Quantum Electron. 37, 265-273 (2001).
[CrossRef]

Eichler, C.

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Elsä??er, W.

M. O. Ziegler, M. M¨unkel, G. Jennemann, I. Fischer, and W. Elsä�?er, "Spatiotemporal emission dynamics of ridge waveguide laser diodes: picosecond pulsing and switching," J. Opt. Soc. Am. B 16, 2015 (1999).
[CrossRef]

I. Fischer, O. Hess,W. Elsä�?er, and E. Göbel, "Complex spatio-temporal dynamics in the near-field of a broad-area semiconductor laser," Europhys. Lett. 35, 579 (1996).
[CrossRef]

Fischer, I.

M. O. Ziegler, M. M¨unkel, G. Jennemann, I. Fischer, and W. Elsä�?er, "Spatiotemporal emission dynamics of ridge waveguide laser diodes: picosecond pulsing and switching," J. Opt. Soc. Am. B 16, 2015 (1999).
[CrossRef]

I. Fischer, O. Hess,W. Elsä�?er, and E. Göbel, "Complex spatio-temporal dynamics in the near-field of a broad-area semiconductor laser," Europhys. Lett. 35, 579 (1996).
[CrossRef]

Furitsch, M.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

Göbel, E.

I. Fischer, O. Hess,W. Elsä�?er, and E. Göbel, "Complex spatio-temporal dynamics in the near-field of a broad-area semiconductor laser," Europhys. Lett. 35, 579 (1996).
[CrossRef]

H¨arle, V.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Habel, F.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Härle, V.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

Harrison, I.

G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
[CrossRef]

Hess, O.

I. Fischer, O. Hess,W. Elsä�?er, and E. Göbel, "Complex spatio-temporal dynamics in the near-field of a broad-area semiconductor laser," Europhys. Lett. 35, 579 (1996).
[CrossRef]

Hofstetter, D.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Jennemann, G.

Kümmler, V.

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

Laino, V.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

B. Witzigmann, V. Laino, and M. Luisier, "Microscopic analysis of optical gain in InGaN/GaN quantum wells," Appl. Phys. Lett. 88, 021104 (2006).
[CrossRef]

Larkins, E.

G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
[CrossRef]

Lauterbach, C.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

Laws, G.

G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
[CrossRef]

Leber, A.

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

Lell, A.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

Luisier, M.

B. Witzigmann, V. Laino, and M. Luisier, "Microscopic analysis of optical gain in InGaN/GaN quantum wells," Appl. Phys. Lett. 88, 021104 (2006).
[CrossRef]

Luo, Y.

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

M¨unkel, M.

Meyer, T.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

Miller, S.

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Molloy, C.

G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
[CrossRef]

Nakamura, S.

J. Piprekt and S. Nakamura, "Physics of high-power InGaN/GaN lasers," IEE Proc. J.Optoelectron. 149, 145 (2002).
[CrossRef]

Odermatt, S.

S. Odermatt, B. Witzigmann, and B. Schmithüsen, "Harmonic balance analysis for semiconductor lasers under large-signal modulation," Opt. Quantum Electron. 38, 1039 (2006).
[CrossRef]

Omura, E.

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

Pindl, M.

M. Pindl and U. T. Schwarz, "Waveguide mode dynamics of blue laser diodes," Phys. Status Solidi A 203, 1787-1791 (2006).
[CrossRef]

U. T. Schwarz and M. Pindl, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Proc. SPIE 5738, 229-237 (2005).
[CrossRef]

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

Piprekt, J.

J. Piprekt and S. Nakamura, "Physics of high-power InGaN/GaN lasers," IEE Proc. J.Optoelectron. 149, 145 (2002).
[CrossRef]

Roemer, F.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

Rumbolz, C.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

Schad, S.-S.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Scherer, M.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Schillgalies, M.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

Schillgalies, M. O.

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

Schmithüsen, B.

S. Odermatt, B. Witzigmann, and B. Schmithüsen, "Harmonic balance analysis for semiconductor lasers under large-signal modulation," Opt. Quantum Electron. 38, 1039 (2006).
[CrossRef]

Scholz, D.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

Scholz, F.

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

Schwarz, U. T.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

M. Pindl and U. T. Schwarz, "Waveguide mode dynamics of blue laser diodes," Phys. Status Solidi A 203, 1787-1791 (2006).
[CrossRef]

U. T. Schwarz and M. Pindl, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Proc. SPIE 5738, 229-237 (2005).
[CrossRef]

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

Seyboth, M.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Solowan, H. M.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

Somerford, D.

G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
[CrossRef]

Strau??, U.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

Sturm, E.

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

Sun, C.

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

Varshni, Y. P.

Y. P. Varshni, "Temperature dependence of the energy gap in semiconductors," Physica 34, 149 (1967).
[CrossRef]

Wegscheider, W.

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

Weimar, A.

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Witzigmann, B.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

B. Witzigmann, V. Laino, and M. Luisier, "Microscopic analysis of optical gain in InGaN/GaN quantum wells," Appl. Phys. Lett. 88, 021104 (2006).
[CrossRef]

S. Odermatt, B. Witzigmann, and B. Schmithüsen, "Harmonic balance analysis for semiconductor lasers under large-signal modulation," Opt. Quantum Electron. 38, 1039 (2006).
[CrossRef]

Xue, S.

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

Yagi, T.

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

Ziegler, M. O.

Appl. Phys. Lett.

B. Witzigmann, V. Laino, and M. Luisier, "Microscopic analysis of optical gain in InGaN/GaN quantum wells," Appl. Phys. Lett. 88, 021104 (2006).
[CrossRef]

U. T. Schwarz, M. Pindl, W. Wegscheider, C. Eichler, F. Scholz, M. Furitsch, A. Leber, S. Miller, A. Lell, and V. Härle, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Appl. Phys. Lett. 86, 161112 (2005).
[CrossRef]

W. W. Chow and H. Amano, "Theoretical analysis of filamentation and fundamental-mode operation in InGaN quantum well lasers," Appl. Phys. Lett. 76, 1647-1649 (2000).
[CrossRef]

Europhys. Lett.

I. Fischer, O. Hess,W. Elsä�?er, and E. Göbel, "Complex spatio-temporal dynamics in the near-field of a broad-area semiconductor laser," Europhys. Lett. 35, 579 (1996).
[CrossRef]

IEEE J. Quantum Electron.

V. Laino, F. Roemer, B. Witzigmann, C. Lauterbach, U. T. Schwarz, C. Rumbolz, M. Schillgalies, M. Furitsch, A. Lell, and V. Härle, "Substrate modes of (Al,In)GaN semiconductor laser diodes in SiC and GaN substrates," IEEE J. Quantum Electron. 43, 16-24 (2007).
[CrossRef]

W.W. Chow, H. Amano, and I. Akasaki, "Analysis of lateral-mode Behavior in broad-area InGaN quantum-well lasers," IEEE J. Quantum Electron. 37, 265-273 (2001).
[CrossRef]

J. Buus, "Models of the static and dynamic behavior of stripe geometry lasers," IEEE J. Quantum Electron. 19, 953-960 (1983).
[CrossRef]

Y. Ben, C. Sun, S. Xue, Y. Luo, T. Yagi, and E. Omura, "Nonlinearity in power-current characteristics of narrow-pulse-driven AlGaInP laser diodes," IEEE J. Quantum Electron. 40, 349-353 (2004).
[CrossRef]

J. Appl. Phys.

H. Braun, H. M. Solowan, D. Scholz, T. Meyer, U. T. Schwarz, S. Brüninghoff, A. Lell, and U. Strau�?, "Lateral and longitudinal mode pattern of broad ridge 405 nm (Al,In)GaN laser diodes," J. Appl. Phys. 103, 073102 (2008).
[CrossRef]

G. Laws, E. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlGaN and InGaN alloys," J. Appl. Phys. 189, 1108 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Quantum Electron.

S. Odermatt, B. Witzigmann, and B. Schmithüsen, "Harmonic balance analysis for semiconductor lasers under large-signal modulation," Opt. Quantum Electron. 38, 1039 (2006).
[CrossRef]

Optoelectron.

J. Piprekt and S. Nakamura, "Physics of high-power InGaN/GaN lasers," IEE Proc. J.Optoelectron. 149, 145 (2002).
[CrossRef]

Phys. Status Solidi A

U. T. Schwarz, E. Sturm,W. Wegscheider, V. Kümmler, A. Lell, and V. Härle, "Gain spectra and current-induced change of refractice index in (In/Al)GaN diode lasers," Phys. Status Solidi A 200, 143 (2003).
[CrossRef]

M. Pindl and U. T. Schwarz, "Waveguide mode dynamics of blue laser diodes," Phys. Status Solidi A 203, 1787-1791 (2006).
[CrossRef]

Phys. Status Solidi C

C. Eichler, S.-S. Schad, M. Seyboth, F. Habel, M. Scherer, S. Miller, A. Weimar, A. Lell, V. H¨arle, and D. Hofstetter, "Time resolved study of laser diode characteristics during pulsed operation," Phys. Status Solidi C 0, 2283 (2003).
[CrossRef]

Physica

Y. P. Varshni, "Temperature dependence of the energy gap in semiconductors," Physica 34, 149 (1967).
[CrossRef]

Proc. SPIE

U. T. Schwarz and M. Pindl, "Near-field and far-field dynamics of (Al,In)GaN laser diodes," Proc. SPIE 5738, 229-237 (2005).
[CrossRef]

U. T. Schwarz, C. Lauterbach, M. O. Schillgalies, C. Rumbolz, M. Furitsch, A. Lell, and V. Härle, "Time-resolved scanning near-field microscopy of InGaN laser diode dynamics," Proc. SPIE 6184, 61840K (2006).
[CrossRef]

Other

U. T. Schwarz and B. Witzigmann, "Optical properties of edge-emitting lasers: measurement and simulation," in Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed., (WILEY-VCH, 2007), pp. 405-422.

K. Petermann, Laser diode modulation and noise (Kluver Academic Publishers, 1991).

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Kluver Academic Publishers, 1993).

J. Piprek, "Introduction," in Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (WILEY-VCH, 2007), pp. 3-11.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Time averaged SNOM scan of the facette of a laser diode with w=8 µm. The optical intensity is color coded. (b) Optical intensity distribution of a lateral cross section along the vertical maximum of intensity of the same laser diode. This lateral intensity profile (red curve) is a superposition of three Gaussian modes. (blue curves)

Fig. 2.
Fig. 2.

All figures show measurements at I=1.6 Ith . The intensity scale is normalized in each figure separately. (a) w=1.5 µm, (b) w=2.0 µm, (c) w=2.5 µm: The narrow ridges suppress all high-order lateral modes, the intensity distribution is constricted to a single filament. The beam shape is constant during the pulse. (d) w=5 µm. The figure shows a typical behavior for 5 µm-ridges. The splitting into two separated filaments was observed for all currents and at all samples with this ridge width. The filament widths are comparable to the constricted intensity distribution of the narrow ridge samples in (a,b,c). (e) w=8 µm, (f) w=10 µm: We detect multiple filaments. Their number, position and width vary throughout the pulse. A quasi-static state can be found after the first microsecond. Again, the filament widths are comparable to the constricted intensity distribution of the narrow ridge samples in (a,b,c).

Fig. 3.
Fig. 3.

(a) Starting conditions for the lateral refractive index profile including heating and asymmetry and for the lateral carrier density distribution. (b) Resulting refractive index modulation, carrier distribution and optical output power after five iterations of the self–consistency loop. (c) Contribution from the different simulated lateral modes to the overall intensity distribution. The higher the mode order, the less is the modal intensity amplitude. All simulations take into account the first seven modes, which ensures accurate results, as the contributions of higher order modes is negligible.

Fig. 4.
Fig. 4.

Comparison of simulated and experimental obtained data. (a) Simulated (top) and measured (bottom) lateral intensity profile for a ridge width of w=1.5 µm. The three dimensional surfaces represent an interpolation of the discrete lateral profiles (colored lines) for different currents. Due to the small current steps a continuous evolution of the mode profile can be assumed. The lateral drift of the intensity profiles is a measurement artifact. (b) Analog plot for w=10 µm. One can see a strong influence of the asymmetry effects both in simulation (top) and experiment (bottom). (c) Measured (solid) and simulated (dashed) PI–characteristics of similar samples with ridge widths of 2 µm (red), 5 µm (green) and 10 µm (blue).

Fig. 5.
Fig. 5.

Time-resolved measurements of the lateral intensity profile of a 10 µm laser diode at different currents. (a) I=Ith . At threshold current, most of the different filaments are not occurring yet. However, the filaments B and D are already present. (b) I=1.2 Ith . At higher current, more filaments appear. Filaments, that have already been present at smaller current appear now earlier. From this current on, one can see the right edge channel, too. (c) I=1.4 Ith . Even more filaments appear and the rise of filaments that were present at smaller currents shifts towards the beginning of the pulse. (d) I=1.6 Ith . The time-shifting of filament appearance increases further. On this sample, currents were measured from I=Ith to I=1.6 Ith in steps of 0.1 Ith . To save space, only four currents are illustrated here. The non-depicted measurements are in agreement with the figures (a) to (d). In all four figures, the single filaments are marked by letters in alphabetical order. The position of each letter marks the lateral position of the filament as well as the time, when it occurs during the laser pulse. The filaments D and E will be discussed in-depth as examples for central filaments and edge channels.

Fig. 6.
Fig. 6.

Relation between heating of the laser diode (dashed, temperature scale on the left side) and rising of individual filaments marked as D and E in Fig. 5(c). (a) The optical intensity of the left edge channel E [a.u.] is compared to the calculated temperature inside the ridge. (b) Comparison of the intensity of the central filament D and the temperature. In both figures, the temperature region where the particular filament rises is marked.

Tables (2)

Tables Icon

Table 1. Simulation parameters used for this work. All table entries marked with (*) are the best fitting results from the rate equation simulations (see also table 2).

Tables Icon

Table 2. List of parameters that are not accurately known. The optimum values represent a reasonable set of parameters, which lead to best fitting results for the measured set of different ridge widths. This parameter set was used for all simulations shown in this paper. But also other parameter sets with appropriate modifications within the given variation range can reproduce the experimental data with reasonable accuracy.

Equations (8)

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

δ N ( x , t ) δ t = J ( x , t ) e d N ( x , t ) τ eff + D δ 2 N ( x , t ) δ x 2
c n ~ g ( N ( x , t ) ) Γ p I p ( x , t ) S p ( t )
d S p ( t ) d t = c n ~ ( G p ( t ) α int 1 L ln 1 R m ) S p ( t ) + β N p ( t ) τ eff
ε eff ( x ) = n eff 2 + 2 n eff Δ n ( x ) + 2 Γ n 1 N ( x ) dn dN + i k { Γ n 1 g ( N ( x ) ) ( 1 Γ ) n 2 α int }
Δ n ( x ) = Δ n ridge ( x ) + Δ n asym ( x ) + Δ n therm ( x ) .
δ 2 E p ( x ) δ x 2 + [ ε eff ( x ) k 2 β z p 2 ] E p ( x ) = 0 .
I p ( x ) = E p ( x ) 2 1 w E p ( x ) 2 d x ,
P opt ( x ) = p S p · I p ( x )

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