Abstract

We give a detailed analysis of the influence of near-resonant self-phase modulation on subpicosecond pulse propagation through bulk GaAs at low temperature. We cover the dependence of the pulse characteristics on the propagation length, the input pulse intensity, the focusing into the sample, and the detuning from the band edge. Numerical simulations based on the nonlinear Schrödinger equation are compared with the experimental observations. Phase-resolved measurements characterize the evolution of the pulse phase during propagation. All experiments are based on a fast-scanning technique that ensures high signal-to-noise ratios.

© 2006 Optical Society of America

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  1. H. Ju, S. Zhang, H. de Waardt, E. Tangdiongga, G. D. Khoe, and H. J. S. Dorren, "SOA-based all-optical switch with subpicosecond full recovery," Opt. Express 13, 942-947 (2005).
  2. M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
    [CrossRef]
  3. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
  4. G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).
  5. Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).
  6. T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).
  7. F. G. Omenetto, B. P. Luce, D. Yarotski, and A. J. Taylor, "Observation of chirped soliton dynamics at lambda=1.55 μm in a single-mode optical fiber with frequency-resolved optical gating," Opt. Lett. 24, 1392-1394 (1999).
  8. K. Tai, S. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986).
  9. J.-F. Lami, S. Petit, and C. Hirlimann, "Self-steepening and self-compression of ultrashort optical pulses in a defocusing CdS crystal," Phys. Rev. Lett. 82, 1032-1035 (1999).
  10. P. Dumais, A. Villeneuve, and J. S. Aitchison, "Bright temporal solitonlike pulses in self-defocusing AlGaAs waveguides near 800 nm," Opt. Lett. 21, 260-262 (1996).
  11. S. Linden, H. Giessen, and J. Kuhl, "XFROG—a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).
  12. N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
    [CrossRef]
  13. N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
    [CrossRef]
  14. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).
  15. P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).
  16. J.-C. Diels and W. Rudoph, Ultrashort Laser Pulse Phenomena (Academic, 1996).
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  18. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

2005 (4)

H. Ju, S. Zhang, H. de Waardt, E. Tangdiongga, G. D. Khoe, and H. J. S. Dorren, "SOA-based all-optical switch with subpicosecond full recovery," Opt. Express 13, 942-947 (2005).

Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

2004 (3)

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

2001 (1)

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

1999 (2)

J.-F. Lami, S. Petit, and C. Hirlimann, "Self-steepening and self-compression of ultrashort optical pulses in a defocusing CdS crystal," Phys. Rev. Lett. 82, 1032-1035 (1999).

F. G. Omenetto, B. P. Luce, D. Yarotski, and A. J. Taylor, "Observation of chirped soliton dynamics at lambda=1.55 μm in a single-mode optical fiber with frequency-resolved optical gating," Opt. Lett. 24, 1392-1394 (1999).

1998 (1)

S. Linden, H. Giessen, and J. Kuhl, "XFROG—a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).

1996 (1)

1992 (1)

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).

1986 (1)

K. Tai, S. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Aitchison, J. S.

Baldassarri, H. V. G.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Bayer, M.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Brown de Colstoun, F.

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

de Waardt, H.

Diels, J.-C.

J.-C. Diels and W. Rudoph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

Dorren, H. J. S.

Dumais, P.

Fafard, S.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Forchel, A.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Förstner, J.

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

Gammon, D.

Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).

Gibbs, H. M.

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Giessen, H.

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

S. Linden, H. Giessen, and J. Kuhl, "XFROG—a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).

Harten, P. A.

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Hasegawa, S.

K. Tai, S. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986).

Hawrylak, P.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Hirlimann, C.

J.-F. Lami, S. Petit, and C. Hirlimann, "Self-steepening and self-compression of ultrashort optical pulses in a defocusing CdS crystal," Phys. Rev. Lett. 82, 1032-1035 (1999).

Hofmann, C.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Höner zu Siederdissen, T.

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).

Jin, R.

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Ju, H.

Keldysh, L. V.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Khitrova, G.

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Khoe, G. D.

Knorr, A.

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Koch, S. W.

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Kuhl, J.

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

S. Linden, H. Giessen, and J. Kuhl, "XFROG—a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).

Kuhn, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Kulakovskii, V. D.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Lami, J.-F.

J.-F. Lami, S. Petit, and C. Hirlimann, "Self-steepening and self-compression of ultrashort optical pulses in a defocusing CdS crystal," Phys. Rev. Lett. 82, 1032-1035 (1999).

Larionov, A.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Lee, S. G.

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Li, X. Q.

Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).

Linden, S.

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

S. Linden, H. Giessen, and J. Kuhl, "XFROG—a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).

Löffler, A.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Luce, B. P.

Nielsen, N. C.

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

Omenetto, F. G.

Ortner, G.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Petit, S.

J.-F. Lami, S. Petit, and C. Hirlimann, "Self-steepening and self-compression of ultrashort optical pulses in a defocusing CdS crystal," Phys. Rev. Lett. 82, 1032-1035 (1999).

Peyghambarian, N.

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Prineas, J. P.

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

Reinecke, T. L.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Reithmaier, J. P.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Reitzenstein, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Rudoph, W.

J.-C. Diels and W. Rudoph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

Schaarschmidt, M.

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

T. Höner zu Siederdissen, N. C. Nielsen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, G. Khitrova, H. M. Gibbs, S. W. Koch, and H. Giessen, "Transition between different coherent light-matter interaction regimes analyzed by phase-resolved pulse propagation," Opt. Lett. 30, 1384-1386 (2005).

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

Sek, G.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Sham, L. J.

Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).

Sheik-Bahae, M.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).

Sokoloff, J. P.

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Steel, D.

Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).

Sutherland, R. L.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

Tai, K.

K. Tai, S. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986).

Tangdiongga, E.

Taylor, A. J.

Tomita, A.

K. Tai, S. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986).

van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).

Villeneuve, A.

Wasilewski, Z.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Wright, E. M.

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Wu, Y. W.

Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).

Yarotski, D.

Yugova, I.

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Zhang, S.

zu Siederdissen, T. Höner

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991).

Nature (1)

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. B (2)

N. C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr, S. W. Koch, and H. Giessen, "Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor," Phys. Rev. B 64, 245202 (2001).
[CrossRef]

M. Schaarschmidt, J. Förstner, A. Knorr, J. P. Prineas, N. C. Nielsen, J. Kuhl, G. Khitrova, H. M. Gibbs, H. Giessen, and S. W. Koch, "Adiabatically driven electron dynamics in a resonant photonic band gap: optical switching of a Bragg periodic semiconductor," Phys. Rev. B 70, 233302 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

K. Tai, S. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986).

J.-F. Lami, S. Petit, and C. Hirlimann, "Self-steepening and self-compression of ultrashort optical pulses in a defocusing CdS crystal," Phys. Rev. Lett. 82, 1032-1035 (1999).

N. C. Nielsen, T. Höner zu Siederdissen, J. Kuhl, M. Schaarschmidt, J. Förstner, A. Knorr, and H. Giessen, "Phase evolution of solitonlike optical pulses during excitonic rabi flopping in a semiconductor," Phys. Rev. Lett. 94, 057406 (2005).
[CrossRef]

P. A. Harten, A. Knorr, J. P. Sokoloff, F. Brown de Colstoun, S. G. Lee, R. Jin, E. M. Wright, G. Khitrova, H. M. Gibbs, S. W. Koch, and N. Peyghambarian, "Propagation-induced escape from adibatic following in a semiconductor," Phys. Rev. Lett. 69, 852-855 (1992).

Phys. Status Solidi B (1)

S. Linden, H. Giessen, and J. Kuhl, "XFROG—a new method for amplitude and phase characterization of weak ultrashort pulses," Phys. Status Solidi B 206, 119-124 (1998).

Physica E (Amsterdam) (2)

G. Ortner, I. Yugova, A. Larionov, H. V. G. Baldassarri, M. Bayer, P. Hawrylak, S. Fafard, and Z. Wasilewski, "Coherent optical control of semiconductor quantum dots for quantum information processing," Physica E (Amsterdam) 25, 242-248 (2004).

Y. W. Wu, X. Q. Li, D. Steel, D. Gammon, and L. J. Sham, "Experimental demonstration of coherent coupling of two quantum dots," Physica E (Amsterdam) 26, 281-285 (2005).

Other (3)

J.-C. Diels and W. Rudoph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

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Figures (14)

Fig. 1
Fig. 1

Experimental setup using high-repetition 100 fs pulses with wavelengths at 830 or 836 nm . The input pulses are spectrally shaped and focused onto the sample. The transmitted pulses can be directly measured with a spectrometer, time resolved by cross correlation, or phase resolved by XFROG.[11] BBO, β-barium borate; PMT, photomultiplier tube; BS, beam splitter.

Fig. 2
Fig. 2

Linear absorption spectra of the bulk GaAs samples with a thickness of 250 μ m (solid curve) and 1000 μ m (dashed curve). Inset: linear absorption spectrum of the optically polished 600 μ m thick GaAs wafer.

Fig. 3
Fig. 3

(a),(b) Normalized cross correlation and (c),(d) spectral intensities for the input pulse at 830 nm (lowest curves) and output pulses after propagation through a 750 μ m thick GaAs sample for different input intensities. (a),(c) Linear and (b),(d) logarithmic scales.

Fig. 4
Fig. 4

(a)–(d) Normalized cross-correlation signals and (e)–(h) spectral intensities for the input pulse at 830 nm (lowest curves) and transmitted pulses for different propagation distances and input intensities from 80 to 540 MW cm 2 .

Fig. 5
Fig. 5

(a)–(d) Normalized cross-correlation signals and (e)–(h) spectral intensities for the input pulse at 836 nm (lowest curves) and transmitted pulses for different propagation distances and input intensities from 80 to 540 MW cm 2 .

Fig. 6
Fig. 6

Pulse widths for different propagation distances at an input intensity of 80 MW cm 2 and wavelengths of 830 nm (upward triangles) and 836 nm (downward triangles). The dashed and solid curves represent fits based on the temporal broadening of a Gaussian pulse with group-velocity dispersion parameter β 2 .

Fig. 7
Fig. 7

Numerical solutions of the NLSE: (a)–(d) Normalized intensity profiles and (e)–(h) spectra for the input pulse at 830 nm (lowest curves) and transmitted pulses for different propagation distances and input intensities from 80 to 540 MW cm 2 (the same parameters as in Fig. 4).

Fig. 8
Fig. 8

XFROG traces for (a) the input pulse at 830 nm and (b)–(f) after propagation through an optically polished 600 μ m thick GaAs wafer at T = 9 K for input intensities from 10 to 580 MW cm 2 . The contour lines range from 95% to 0.5% of the peak intensity and represent an increase or decrease of the intensity by a factor of 1.5 with respect to each other.

Fig. 9
Fig. 9

Normalized retrieved intensities (dashed curves) and phase (solid curves) versus time for (a) the input pulse at 830 nm and (b)–(f) after propagation through an optically polished 600 μ m thick GaAs wafer at T = 9 K for input intensities from 10 to 580 MW cm 2 .

Fig. 10
Fig. 10

Normalized retrieved spectra for (a) the input pulse at 830 nm and (b)–(f) after propagation through an optically polished 600 μ m thick GaAs wafer at T = 9 K for input intensities from 10 to 580 MW cm 2 .

Fig. 11
Fig. 11

Normalized retrieved intensities (dashed curves) and phases (solid curves) versus time for the 600 fs input pulse (top) and after linear propagation at 8 MW cm 2 (middle) and nonlinear propagation at 580 MW cm 2 (bottom) through 600 μ m of bulk GaAs. Input pulse at (a) 836 nm and (b) 830 nm .

Fig. 12
Fig. 12

Normalized measured spectra after linear propagation of 600 fs input pulses at 8 MW cm 2 (dashed curves) and nonlinear propagation at 580 MW cm 2 (solid curves) through 600 μ m of bulk GaAs. Input pulse at (a) 836 nm and (b) 830 nm .

Fig. 13
Fig. 13

(a) Normalized cross-correlation signals and (b) spectral intensities for the input pulse at 836 nm (lowest curves) and after propagation through a 2 mm thick GaAs sample at 970 MW cm 2 for different positions of the sample front surface relative to the focal point of the microscope objective. A negative sign of the position indicates a displacement toward the microscope objective.

Fig. 14
Fig. 14

(a),(c) Normalized cross-correlation signals and (b),(d) spectral intensities for the input pulse at 836 nm (dashed curves) and after propagation at 970 MW cm 2 through a 2 mm thick GaAs sample (solid curves). (a),(b) Position of the front surface at the focal point and (c),(d) displaced by 0.3 mm (closer to the microscope objective).

Equations (12)

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τ p = τ p 4 + 16 [ ln ( 2 ) ] 2 β 2 2 L 2 τ p 2 ,
A z = α 2 A i 2 β 2 2 T 2 A + i γ A 2 A ,
T = t β 1 z ,
E ( t , x , y , z ) = Re [ A ( z , t ) e x 2 + y 2 w 2 e i ω 0 t e i β 0 z ]
A 0 = 32 E pulse π w 0 2 ϵ 0 c 0 n π T 0 .
A z = ( D ̂ + N ̂ ) A ,
D ̂ = α 2 i 2 β 2 2 T 2
N ̂ = i γ A 2 .
A ( z + h , T ) = exp ( h 2 D ̂ ) exp [ z z + h N ̂ ( z ) d z ] exp ( h 2 D ̂ ) A ( z , T ) .
exp ( h D ̂ ) B ( z , T ) = F 1 { exp [ h D ̂ ( T i ω ) ] F [ B ( z , T ) ] } ,
z z + h N ̂ ( z ) d z h 2 [ N ̂ ( z ) + N ̂ ( z + h ) ] .
A z = i γ A 2 A .

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