Abstract

We report a strong reduction of spatial coherence of the emission of large aperture vertical-cavity surface-emitting lasers when they are driven by microsecond electrical pulses. We give evidence that this is due to a breakdown of the modal emission of these lasers. The spatial decoherence manifests itself in the formation of a Gaussian far field intensity distribution. The coherence radius we extract is 1.4 micrometer under these operating conditions, irrespective of the Fresnel number of the vertical-cavity surface-emitting laser. Finally, the spatial coherence properties can be varied by changing the pulse duration or pulse amplitude.

© 2005 Optical Society of America

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References

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  2. T. E. Sale, Vertical Cavity Surface Emitting Lasers, Optoelectronic series; 2 (John Wiley&Sons inc., New York, 1995). ISBN 0 86380 174 9.
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    [CrossRef]
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    [CrossRef]
  5. P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Els�er, �??Influence of anisotropies on transverse modes in oxide-confined VCSELs,�?? IEEE J. Quantum Electron. 38, 73�??84 (2002).
    [CrossRef]
  6. S. F. Pereira, M. B.Willemsen, M. P. van Exter, and J. P.Woerdman, �??Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 73, 2239�??2241 (1998).
    [CrossRef]
  7. S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, �??Pattern Formation in the Transverse Section of a Laser with a Large Fresnel Number,�?? Phys. Rev. Lett. 82, 1434�??1437 (1999).
    [CrossRef]
  8. S. Hegarty, G. Huyet, P. Porta, J. McInerney, K. Choquette, K. M. Geib, and H. Hou, �??Transverse-mode structure and pattern formation in oxide-confined vertical-cavity semiconductor lasers,�?? J. Opt. Soc. Am. B 16, 2060�??2071 (1999).
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  9. K. Huang, Y. Chen, and L. Lai, �??Observation of the Wave Function of a Quantum Billiard from the Transverse Patterns of Vertical Cavity Surface Emitting Lasers,�?? Phys. Rev. Lett. 89, 224,102 (2002).
    [CrossRef]
  10. T. Gensty, K. Becker, I. Fischer,W. Els�er, C. Degen, P. Debernardi, and G. P. Bava, �??Wave Chaos in Real-World Vertical-Cavity Surface-Emitting Laser,�?? Phys. Rev. Lett. 94, 233,901 (2005).
    [CrossRef]
  11. S. Barland, F. Marino, M. Giudici, J. Tredicce, and S. Balle, �??In situ measurement of cavity length variations across the transverse section of broad-area vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 83, 2303�??2305 (2003).
    [CrossRef]
  12. M. C. Cross and P. C. Hohenberg, �??Pattern formation outside of equilibrium,�?? Rev. Mod. Phys. 65, 851�??1124 (1993).
    [CrossRef]
  13. A. Schell, �??A Technique for the Determination of the Radiation Pattern of a Partially Coherent Aperture,�?? IEEE Trans. Antennas Propag. AP-15, 187�??188 (1967).
    [CrossRef]
  14. E. Collett and E. Wolf, �??Is complete spatial coherence necessary for the generation of highly directional light beams?�?? Opt. Lett. 27, 27�??29 (1978).
    [CrossRef]
  15. M. von Waldkirch, P. Lukowicz, and T. Gerhard, �??Effect of light coherence on depth of focus in head-mounted retinal projection displays,�?? Optical Engineering 43, 1552�??1560 (2004).
    [CrossRef]
  16. M. Grabherr, R. Jäger, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, �??Efficient Single-Mode Oxide-Confined GaAs VCSEL�??s Emitting in the 850-nm Wavelength Regime,�?? IEEE Phot. Tech. Lett. 9, 1304�??1306 (1997)
    [CrossRef]
  17. M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, �??High-Power VCSEL�??s: Single Devices and Densely Packed 2-D-Arrays,�?? IEEE J. Sel. Top. Quantum Electron. 5, 495�??502 (1999).
    [CrossRef]
  18. M. Miller, M. Grabherr, R. King, R. Jäger, R. Michalzik, and K. J. Ebeling, �??Improved Output Performance of High-Power VCSELs,�?? IEEE J. Sel. Top. Quantum Electron. 7, 210�??216 (2001).
    [CrossRef]
  19. W. Nakwaski, �??Thermal aspects of efficient operation of vertical-cavity surface-emitting lasers,�?? Opt. Quantum Electron. 28, 335�??352 (1996).
    [CrossRef]
  20. C. Degen, I. Fischer, and W. Els�er, �??Thermally induced local gain suppression in vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 76, 3352�??3354 (2000).
    [CrossRef]
  21. F. Zernike, �??The concept of degree of coherence and its applications to optical problems,�?? Physica 5, 785�??795 (1938).
    [CrossRef]
  22. M. Born and E. Wolf, Principles of optics, 7th Edition (Cambridge Press, 1999).
  23. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  24. Q. Lin and L.Wang, �??Generation of partially coherent laser beam directly from spatial-temporal phase modulated optical resonators,�?? J. Modern Opt. 50, 743�??754 (2003).
  25. S. V. Kukhlevsky and L. Kozma, �??Optical characteristics of pulsed capillary gas lasers with waveguide resonators,�?? Opt. Commun. 115, 425�??428 (1995).
    [CrossRef]
  26. R. Tommasini, S. Insam, and E. Fill, �??Coherence properties of an amplified spontaneous emission laser: experiments on a 10 Hz vacuum-ultraviolet H2-laser,�?? Opt. Commun. 180, 277�??283 (2000).
    [CrossRef]

Appl. Phys. Lett.

S. Barland, F. Marino, M. Giudici, J. Tredicce, and S. Balle, �??In situ measurement of cavity length variations across the transverse section of broad-area vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 83, 2303�??2305 (2003).
[CrossRef]

C. Degen, I. Fischer, and W. Els�er, �??Thermally induced local gain suppression in vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 76, 3352�??3354 (2000).
[CrossRef]

S. F. Pereira, M. B.Willemsen, M. P. van Exter, and J. P.Woerdman, �??Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 73, 2239�??2241 (1998).
[CrossRef]

IEEE J. Quantum Electron.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, �??Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,�?? IEEE J. Quantum Electron. 27, 1402�??1409 (1991).
[CrossRef]

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Els�er, �??Influence of anisotropies on transverse modes in oxide-confined VCSELs,�?? IEEE J. Quantum Electron. 38, 73�??84 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Grabherr, M. Miller, R. Jäger, R. Michalzik, U. Martin, H. J. Unold, and K. J. Ebeling, �??High-Power VCSEL�??s: Single Devices and Densely Packed 2-D-Arrays,�?? IEEE J. Sel. Top. Quantum Electron. 5, 495�??502 (1999).
[CrossRef]

M. Miller, M. Grabherr, R. King, R. Jäger, R. Michalzik, and K. J. Ebeling, �??Improved Output Performance of High-Power VCSELs,�?? IEEE J. Sel. Top. Quantum Electron. 7, 210�??216 (2001).
[CrossRef]

IEEE Phot. Tech. Lett.

M. Grabherr, R. Jäger, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, �??Efficient Single-Mode Oxide-Confined GaAs VCSEL�??s Emitting in the 850-nm Wavelength Regime,�?? IEEE Phot. Tech. Lett. 9, 1304�??1306 (1997)
[CrossRef]

IEEE Trans. Antennas Propag.

A. Schell, �??A Technique for the Determination of the Radiation Pattern of a Partially Coherent Aperture,�?? IEEE Trans. Antennas Propag. AP-15, 187�??188 (1967).
[CrossRef]

J. Modern Opt.

Q. Lin and L.Wang, �??Generation of partially coherent laser beam directly from spatial-temporal phase modulated optical resonators,�?? J. Modern Opt. 50, 743�??754 (2003).

J. Opt. Soc. Am. B

Opt. Commun.

S. V. Kukhlevsky and L. Kozma, �??Optical characteristics of pulsed capillary gas lasers with waveguide resonators,�?? Opt. Commun. 115, 425�??428 (1995).
[CrossRef]

R. Tommasini, S. Insam, and E. Fill, �??Coherence properties of an amplified spontaneous emission laser: experiments on a 10 Hz vacuum-ultraviolet H2-laser,�?? Opt. Commun. 180, 277�??283 (2000).
[CrossRef]

Opt. Lett.

E. Collett and E. Wolf, �??Is complete spatial coherence necessary for the generation of highly directional light beams?�?? Opt. Lett. 27, 27�??29 (1978).
[CrossRef]

Opt. Quantum Electron.

W. Nakwaski, �??Thermal aspects of efficient operation of vertical-cavity surface-emitting lasers,�?? Opt. Quantum Electron. 28, 335�??352 (1996).
[CrossRef]

Optical Engineering

M. von Waldkirch, P. Lukowicz, and T. Gerhard, �??Effect of light coherence on depth of focus in head-mounted retinal projection displays,�?? Optical Engineering 43, 1552�??1560 (2004).
[CrossRef]

Phys. Rev. Lett.

K. Huang, Y. Chen, and L. Lai, �??Observation of the Wave Function of a Quantum Billiard from the Transverse Patterns of Vertical Cavity Surface Emitting Lasers,�?? Phys. Rev. Lett. 89, 224,102 (2002).
[CrossRef]

T. Gensty, K. Becker, I. Fischer,W. Els�er, C. Degen, P. Debernardi, and G. P. Bava, �??Wave Chaos in Real-World Vertical-Cavity Surface-Emitting Laser,�?? Phys. Rev. Lett. 94, 233,901 (2005).
[CrossRef]

S. Hegarty, G. Huyet, J. McInerney, and K. Choquette, �??Pattern Formation in the Transverse Section of a Laser with a Large Fresnel Number,�?? Phys. Rev. Lett. 82, 1434�??1437 (1999).
[CrossRef]

Physica

F. Zernike, �??The concept of degree of coherence and its applications to optical problems,�?? Physica 5, 785�??795 (1938).
[CrossRef]

Rev. Mod. Phys.

M. C. Cross and P. C. Hohenberg, �??Pattern formation outside of equilibrium,�?? Rev. Mod. Phys. 65, 851�??1124 (1993).
[CrossRef]

Other

M. Born and E. Wolf, Principles of optics, 7th Edition (Cambridge Press, 1999).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Press, 1995).

T. E. Sale, Vertical Cavity Surface Emitting Lasers, Optoelectronic series; 2 (John Wiley&Sons inc., New York, 1995). ISBN 0 86380 174 9.

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Figures (5)

Fig. 1.
Fig. 1.

An overview of the normalized intensity distribution in the near and far field. The intensity scale is logarithmic. Panels (a) and (b) depict the near and far fields in the CW case at an injection current of 39mA. Panels (c) and (d) show the near and far fields in the pulsed case at a pulse amplitude of 39mA, a pulse length of 1μs and a duty cycle of 2 percent. Panels (e) and (f) depict the near and far fields in the pulsed case at a pulse amplitude of 320mA, other parameters remain the same. The scale is in μm for the near fields, in cm for the far fields. Angles correspond to the full opening of the cones.

Fig. 2.
Fig. 2.

A transverse cut through the far field of the pulsed device, corresponding to case (f) of Fig. 1. The solid line is the measurement, the dashed line a Gaussian fit with a estimated variance of 3.2 × 10-4. The full far field opening is 22 degrees (1/e 2).

Fig. 3.
Fig. 3.

The calculated angular coherence for a quasi-homogeneous source with the intensity distribution as in Fig. 1(e) is indicated by the solid line. The crosses are measurements at different slit separations. Measurements at slit separations larger than 7 degrees (outside of the plot range) show almost zero visibility. The shaded area corresponds to the measured visibility range for CW multimode emission.

Fig. 4.
Fig. 4.

A plot of the visibility of the fringes for different values of (a) the pulse duration at a pulse amplitude of 110mA, duty cycle 2%. (b) the pulse amplitude at a pulse duration of 1μs, duty cycle 2%

Fig. 5.
Fig. 5.

A density plot of the visibility of the fringes for different values of the pulse duration and pulse amplitude. The duty cycle was 2% is all cases. White means high visibility C=0.7 and black low C=0.04; the dashed area corresponds to points where we do not observe sustained laser operation for the entire pulse duration.

Equations (5)

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

J ( s ) ~ A g ( 0 ) ( ρ ) C ( ρ ) e i f . ρ d A
g ( 0 ) ( ρ ) = exp ( ρ 2 2 ξ 2 ) .
J ( θ ) = J ( 0 ) exp ( 1 2 ( 2 π λ ξ sin θ ) 2 )
j ( 0 ) exp ( 2 θ 2 θ 1 e 2 2 )
θ 1 e 2 = λ π ξ .

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