Abstract

Microscopic simulations on the basis of semiconductor Maxwell-Bloch equations show that in the short-time spatio-temporal dynamics of large aspect vertical cavity surface emitting lasers (VC-SEL) and coupled VCSEL-arrays microscopic and macroscopic effects are intrinsically coupled. The combination of microscopic spatial and spectral dynamics of the carrier distribution functions and the nonlinear polarization of the active semiconductor medium reveal spatio-spectral hole-burning effects as the origin of ultra-fast mode-switching effects. In coupled VCSEL-arrays the simulations predict the emergence of spontaneous ultra-fast spatial switching.

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References

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  1. C. J. Chang-Hasnain, "Vertical cavity surface-emitting laser arrays," in Diode Laser Arrays, D. Botez and D. R. Scrifres, eds., (Cambridge University Press, Cambridge, 1994), pp. 368-413.
    [CrossRef]
  2. O. Buccafusca, J. L. A. Chilla, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, "Ultrahigh frequency oscillations and multimode dynamics in vertical cavity surface emitting lasers," Appl. Phys. Lett. 67, 185-187 (1995).
    [CrossRef]
  3. D. G. H. Nugent, R. G. S. Plumb, M. A. Fischer, and D. A. O. Davies, "Self-pulsations in vertical-cavity surface emitting lasers," Electron. Lett. 31, 43-44 (1995).
    [CrossRef]
  4. J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, "Mode behavior and high resolution spectra of circularly-symmetric GaAs/AlGaAs air-post vertical cavity surface emitting lasers," Appl. Phys. Lett. 69, 2312-2314 (1996).
    [CrossRef]
  5. I. Hoersch, R. Kusche, O. Marti, B. Weigl, and K. J. Ebeling, "Spectrally resolved mode imaging of vertical cavity semiconductor lasers by scanning near-eld optical microscopy," Appl. Phys. Lett. 79, 3831-3833 (1996).
  6. O. Hess and T. Kuhn, "Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers I: Theoretical Description," Phys. Rev. A 54, 3347-3359 (1996).
    [CrossRef] [PubMed]
  7. O. Hess and T. Kuhn, "Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers II: Spatio-temporal dynamics," Phys. Rev. A 54, 3360-3368 (1996).
    [CrossRef] [PubMed]
  8. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. V. Lehmen, 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]
  9. F. Koyama, K. Morito, and K. Iga, "Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasrs," IEEE J. Quantum Electron. QE-27, 1410-1416 (1991).
    [CrossRef]
  10. D. Vakhshoori, "Symmetry considerations in vertical-cavity surface-emitting lasers: Prediction of removal of polarization isotropy on (001) substrates," Appl. Phys. Lett. 65, 259-261 (1995).
    [CrossRef]
  11. K. D. Choquette, J. P. Schneider, K. L. Lear, and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers," IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
    [CrossRef]
  12. A. K. J. van Doorn, M. P. van Exter, and J. P. Woerdman, "Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers," Appl. Phys. Lett. 69, 1041-1043 (1996).
    [CrossRef]
  13. H. F. Hofmann and O. Hess, "Quantum Noise and Polarization Fluctuations in Vertical Cavity Surface Emitting Lasers," Phys. Rev. A 56, 868-876 (1997).
    [CrossRef]
  14. O. Hess and T. Kuhn, "Spatio-Temporal Dynamics of Semiconductor Lasers: Theory, Modeling and Analysis," Prog. Quantum Electron. 20, 85-179 (1996).
    [CrossRef]
  15. O. Hess, Spatio-Temporal Dynamics of Semiconductor Lasers (Wissenschaft und Technik Verlag, Berlin, 1993).

Other

C. J. Chang-Hasnain, "Vertical cavity surface-emitting laser arrays," in Diode Laser Arrays, D. Botez and D. R. Scrifres, eds., (Cambridge University Press, Cambridge, 1994), pp. 368-413.
[CrossRef]

O. Buccafusca, J. L. A. Chilla, J. J. Rocca, C. Wilmsen, S. Feld, and R. Leibenguth, "Ultrahigh frequency oscillations and multimode dynamics in vertical cavity surface emitting lasers," Appl. Phys. Lett. 67, 185-187 (1995).
[CrossRef]

D. G. H. Nugent, R. G. S. Plumb, M. A. Fischer, and D. A. O. Davies, "Self-pulsations in vertical-cavity surface emitting lasers," Electron. Lett. 31, 43-44 (1995).
[CrossRef]

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, "Mode behavior and high resolution spectra of circularly-symmetric GaAs/AlGaAs air-post vertical cavity surface emitting lasers," Appl. Phys. Lett. 69, 2312-2314 (1996).
[CrossRef]

I. Hoersch, R. Kusche, O. Marti, B. Weigl, and K. J. Ebeling, "Spectrally resolved mode imaging of vertical cavity semiconductor lasers by scanning near-eld optical microscopy," Appl. Phys. Lett. 79, 3831-3833 (1996).

O. Hess and T. Kuhn, "Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers I: Theoretical Description," Phys. Rev. A 54, 3347-3359 (1996).
[CrossRef] [PubMed]

O. Hess and T. Kuhn, "Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers II: Spatio-temporal dynamics," Phys. Rev. A 54, 3360-3368 (1996).
[CrossRef] [PubMed]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. V. Lehmen, 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]

F. Koyama, K. Morito, and K. Iga, "Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasrs," IEEE J. Quantum Electron. QE-27, 1410-1416 (1991).
[CrossRef]

D. Vakhshoori, "Symmetry considerations in vertical-cavity surface-emitting lasers: Prediction of removal of polarization isotropy on (001) substrates," Appl. Phys. Lett. 65, 259-261 (1995).
[CrossRef]

K. D. Choquette, J. P. Schneider, K. L. Lear, and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers," IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
[CrossRef]

A. K. J. van Doorn, M. P. van Exter, and J. P. Woerdman, "Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers," Appl. Phys. Lett. 69, 1041-1043 (1996).
[CrossRef]

H. F. Hofmann and O. Hess, "Quantum Noise and Polarization Fluctuations in Vertical Cavity Surface Emitting Lasers," Phys. Rev. A 56, 868-876 (1997).
[CrossRef]

O. Hess and T. Kuhn, "Spatio-Temporal Dynamics of Semiconductor Lasers: Theory, Modeling and Analysis," Prog. Quantum Electron. 20, 85-179 (1996).
[CrossRef]

O. Hess, Spatio-Temporal Dynamics of Semiconductor Lasers (Wissenschaft und Technik Verlag, Berlin, 1993).

Supplementary Material (3)

» Media 1: MOV (347 KB)     
» Media 2: MOV (566 KB)     
» Media 3: MOV (369 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Snapshots of the intensity (left column) and charge carrier density (right column) of a large aspect-ratio (d = 30 μm) VCSEL. The time between successive snapshots is Δt = 3 ps.

Fig. 2.
Fig. 2.

Animation of the spatio-spectral dynamics of the carrier Wigner distribution δfe (k,0,x,t) during a time interval of 200 ps. The horizontal axis shows the momentum (k) dependence of δfe (k,0,x,t), given in units of the inverse exciton Bohr radius a 0 = 1.295 × 10-6 cm of GaAs, i.e. a shift from e.g. ka 0 = 2 to ka 0 = 2.5 corresponds to a wavelength shift of approximately 10 nm. The vertical axis depicts the spatial dependence of δfe and is given in units of μm. [Media 1]

Fig. 3.
Fig. 3.

Animation of the spatio-temporal intensity dynamics of a strongly coupled VCSEL-array consisting of four round large-aspect ratio VCSELs. Each VCSEL has a transverse width w = 30μm and is separated from its neighbor at a distance s = 5μm. The total time sequence shown in the animation displays a typical time-period of 100 ps. [Media 2]

Fig. 4.
Fig. 4.

Self-induced ultrafast spatio-temporal switching of four round small (w = 5μm) VCSELs being separated from each other at a distance s = 5μm. The total time sequence corresponds to a characteristic time-period of 100 ps. [Media 3]

Equations (10)

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t f e , h ( k , x , t ) = g ( k , x , t ) + Λ e , h ( k , x , t ) τ e , h 1 ( k ) [ f e , h ( k , x , t ) f eq e , h ( k , x , t ) ]
Γ sp ( k ) f e ( k , x , t ) f h ( k , x , t ) γ nr f e , h ( k , x , t )
t p nl ( k , x , t ) = [ i ω ¯ ( k ) + τ p 1 ( k ) ] p nl ( k , x , t ) + β Γ sp ( k ) f e ( k , x , t ) f h ( k , x , t )
+ 1 Δ U nl ( x , t ) 1 U ( x , t ) [ f e ( k , x , t ) + f h ( k , x , t ) ]
n l c t E ( x , t ) = i 2 1 K z T 2 E ( x , t ) ( γ m + α ( x ) 2 + ( x ) ) E + i n l 2 ε 0 P nl ( x , t )
t N ( x , t ) = T D f T N ( x , t ) γ nr N ( x , t ) + Λ ( x , t ) + G ( x , t ) W ( x , t )
P nl ( x , t ) = d cv * V k p nl ( k , x , t ) ,
g ( k , x , t ) = χ ˜ ( ω ; k , x , t ) 2 ħ E ( x , t ) 2
1 2 ħ Im [ d cv E ( x , t ) p nl * ( k , x , t ) Δ U ( x , t ) p * ( k , x , t ) ]
G ( x , t ) = χ′′ ħ E ( x , t ) 2 1 2 ħ Im [ E ( x , t ) P nl * ( x , t ) ] ,

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