Abstract

We discover and theoretically explore self-induced transparency quadratic solitons (SIT-QS) supported by the media with quadratic optical nonlinearities, doped with resonant impurities. The fundamental frequency of input pulses is assumed to be close to the impurity resonance. We envision an ensemble of inhomogeneously broadened semiconductor quantum dots (QD) in the strong confinement regime grown on a substrate with a quadratic nonlinearity to be a promising candidate for the laboratory realization of SIT-QS. We also examine the influence of inhomogeneous broadening as well as wave number and group-velocity mismatches on the salient properties of the introduced solitons.

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  1. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
  2. G. B. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).
  3. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, Boston, 2003).
  4. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford, 2003).
  5. A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
    [CrossRef]
  6. L. A. Ostrovskii, “Propagation of wave packets and space-time self-focusing in a nonlinear medium,” Sov. Phys. JETP 24, 797–800 (1967).
  7. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomenaand their applications to all-optical signal processing, mode-locking, pulse, compression and solitions,” Opt. Quantum Electron. 28, 1691–1740 (1996).
    [CrossRef]
  8. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
    [CrossRef] [PubMed]
  9. R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
    [CrossRef]
  10. P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
    [CrossRef]
  11. A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable Control of Pulse Speed in Parametric Three-Wave Solitons,” Phys. Rev. Lett. 97, 093901 (2006)
    [CrossRef] [PubMed]
  12. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications Inc., New York, 1975).
  13. D. V. Skryabin, A. V. Yulin, and A. I. Maimistov, “Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity,” Phys. Rev. Lett. 96, 163904–163907 (2006).
    [CrossRef] [PubMed]
  14. We assume that a photon of a given circular polarization promotes an electron-hole pair (exciton) creation with a well-defined spin orientation such that only linearly polarized light can generate biexcitons, cf., L. Jacak, P. Hawrylak, and A. Wojs, Optical Properties of Semiconductor Quantum Dots (Springer, Berlin, 1997).
  15. The contributions of cubic and quadratic nonlinearities to the polarization can be roughly estimated as 𝒫(3)/𝒫(2)~χeff(3)ℰm/χeff(2)~5×10−2, using χeff(3)≃10−18m2/V2 for GaAs. Here the peak field amplitude ℰm of a picosecond 2π input pulse was estimated using the known pulse area as ℰm ∼ πh̄/degτp. Thus quadratic nonlinearities indeed dominate in our case.
  16. In the circular polarization basis, the Bloch equations are exact such that no rotating wave approximation is needed.
  17. T. Brunhes, P. Boucaud, and S. Sauvage, “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 61, 5562–5570 (2000).
    [CrossRef]
  18. S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
    [CrossRef]
  19. T. Skauli, K. L. Vodopyanov, T. J. Pinguet, A. Schober, O. Levi, L. A. Eyres, M. M. Fejer, J. S. Harris, B. Gerard, L. Becouarn, E. Lallier, and G. Arisholm, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. 27, 628–630 (2002).
    [CrossRef]
  20. G. Panzarini, U. Hohenester, and E. Molinari, “Self-induced transparency in semiconductor quantum dots,” Phys. Rev. B 65, 165322–165327 (2002).
    [CrossRef]
  21. M. Jütte, H. Stolz, and W. von der Osten, “Linear and nonlinear pulse propagation at bound excitons in CdS,” J. Opt. Soc. Am. B 13, 1205–1210 (1996).
    [CrossRef]
  22. J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
    [CrossRef]
  23. H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
    [CrossRef]
  24. P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401–157404 (2001).
    [CrossRef] [PubMed]
  25. J. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, USA, 2006).
  26. A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Optical solitons supported by competing nonlinearities,” Opt. Lett. 20, 1961–1963 (1995).
    [CrossRef] [PubMed]

2006

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable Control of Pulse Speed in Parametric Three-Wave Solitons,” Phys. Rev. Lett. 97, 093901 (2006)
[CrossRef] [PubMed]

D. V. Skryabin, A. V. Yulin, and A. I. Maimistov, “Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity,” Phys. Rev. Lett. 96, 163904–163907 (2006).
[CrossRef] [PubMed]

2002

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

T. Skauli, K. L. Vodopyanov, T. J. Pinguet, A. Schober, O. Levi, L. A. Eyres, M. M. Fejer, J. S. Harris, B. Gerard, L. Becouarn, E. Lallier, and G. Arisholm, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. 27, 628–630 (2002).
[CrossRef]

G. Panzarini, U. Hohenester, and E. Molinari, “Self-induced transparency in semiconductor quantum dots,” Phys. Rev. B 65, 165322–165327 (2002).
[CrossRef]

2001

P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401–157404 (2001).
[CrossRef] [PubMed]

2000

T. Brunhes, P. Boucaud, and S. Sauvage, “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 61, 5562–5570 (2000).
[CrossRef]

1998

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

1996

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

M. Jütte, H. Stolz, and W. von der Osten, “Linear and nonlinear pulse propagation at bound excitons in CdS,” J. Opt. Soc. Am. B 13, 1205–1210 (1996).
[CrossRef]

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomenaand their applications to all-optical signal processing, mode-locking, pulse, compression and solitions,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

1995

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Optical solitons supported by competing nonlinearities,” Opt. Lett. 20, 1961–1963 (1995).
[CrossRef] [PubMed]

1967

L. A. Ostrovskii, “Propagation of wave packets and space-time self-focusing in a nonlinear medium,” Sov. Phys. JETP 24, 797–800 (1967).

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, Boston, 2003).

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications Inc., New York, 1975).

Antoniades, N.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Arisholm, G.

Baek, Y.

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

Baronio, F.

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable Control of Pulse Speed in Parametric Three-Wave Solitons,” Phys. Rev. Lett. 97, 093901 (2006)
[CrossRef] [PubMed]

Becouarn, L.

Bhat, R.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Borri, P.

P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401–157404 (2001).
[CrossRef] [PubMed]

Boucaud, P.

T. Brunhes, P. Boucaud, and S. Sauvage, “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 61, 5562–5570 (2000).
[CrossRef]

Brunhes, T.

T. Brunhes, P. Boucaud, and S. Sauvage, “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 61, 5562–5570 (2000).
[CrossRef]

Buryak, A. V.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Optical solitons supported by competing nonlinearities,” Opt. Lett. 20, 1961–1963 (1995).
[CrossRef] [PubMed]

Caironi, D.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

Caneau, C.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Conforti, M.

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable Control of Pulse Speed in Parametric Three-Wave Solitons,” Phys. Rev. Lett. 97, 093901 (2006)
[CrossRef] [PubMed]

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Danielius, R.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

Degasperis, A.

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable Control of Pulse Speed in Parametric Three-Wave Solitons,” Phys. Rev. Lett. 97, 093901 (2006)
[CrossRef] [PubMed]

Di Trapani, P.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

Diels, J.

J. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, USA, 2006).

Dubietis, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications Inc., New York, 1975).

Eyres, L. A.

Fejer, M. M.

Gayral, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Gerard, B.

Gérard, J. M.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Giessen, H.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Grün, M.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Haas, S.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomenaand their applications to all-optical signal processing, mode-locking, pulse, compression and solitions,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Harris, J. S.

Hawrylak, P.

We assume that a photon of a given circular polarization promotes an electron-hole pair (exciton) creation with a well-defined spin orientation such that only linearly polarized light can generate biexcitons, cf., L. Jacak, P. Hawrylak, and A. Wojs, Optical Properties of Semiconductor Quantum Dots (Springer, Berlin, 1997).

Hetterich, M.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Hohenester, U.

G. Panzarini, U. Hohenester, and E. Molinari, “Self-induced transparency in semiconductor quantum dots,” Phys. Rev. B 65, 165322–165327 (2002).
[CrossRef]

Jacak, L.

We assume that a photon of a given circular polarization promotes an electron-hole pair (exciton) creation with a well-defined spin orientation such that only linearly polarized light can generate biexcitons, cf., L. Jacak, P. Hawrylak, and A. Wojs, Optical Properties of Semiconductor Quantum Dots (Springer, Berlin, 1997).

Jütte, M.

Kivshar, Y. S.

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Optical solitons supported by competing nonlinearities,” Opt. Lett. 20, 1961–1963 (1995).
[CrossRef] [PubMed]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, Boston, 2003).

Klingshirn, C.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Knorr, A.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Koch, S. W.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Koza, M. A.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Kuhl, J.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Lallier, E.

Lamb, G. B.

G. B. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

Langbein, W.

P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401–157404 (2001).
[CrossRef] [PubMed]

Legrand, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Levi, O.

Linden, S.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

Maimistov, A. I.

D. V. Skryabin, A. V. Yulin, and A. I. Maimistov, “Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity,” Phys. Rev. Lett. 96, 163904–163907 (2006).
[CrossRef] [PubMed]

Molinari, E.

G. Panzarini, U. Hohenester, and E. Molinari, “Self-induced transparency in semiconductor quantum dots,” Phys. Rev. B 65, 165322–165327 (2002).
[CrossRef]

Ostrovskii, L. A.

L. A. Ostrovskii, “Propagation of wave packets and space-time self-focusing in a nonlinear medium,” Sov. Phys. JETP 24, 797–800 (1967).

Panzarini, G.

G. Panzarini, U. Hohenester, and E. Molinari, “Self-induced transparency in semiconductor quantum dots,” Phys. Rev. B 65, 165322–165327 (2002).
[CrossRef]

Pinguet, T. J.

Piskarskas, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

Pitaevskii, L.

L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford, 2003).

Rajhel, A.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Rudolph, W.

J. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, USA, 2006).

Sauvage, S.

T. Brunhes, P. Boucaud, and S. Sauvage, “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 61, 5562–5570 (2000).
[CrossRef]

Schiek, R.

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

Schneider, S.

P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401–157404 (2001).
[CrossRef] [PubMed]

Schober, A.

Sermage, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Skauli, T.

Skryabin, D. V.

D. V. Skryabin, A. V. Yulin, and A. I. Maimistov, “Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity,” Phys. Rev. Lett. 96, 163904–163907 (2006).
[CrossRef] [PubMed]

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomenaand their applications to all-optical signal processing, mode-locking, pulse, compression and solitions,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Stolz, H.

Stringari, S.

L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford, 2003).

Thierry-Mieg, V.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomenaand their applications to all-optical signal processing, mode-locking, pulse, compression and solitions,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Trapani, P. D.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Trillo, S.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Optical solitons supported by competing nonlinearities,” Opt. Lett. 20, 1961–1963 (1995).
[CrossRef] [PubMed]

Valiulis, G.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Vodopyanov, K. L.

von der Osten, W.

Wabnitz, S.

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable Control of Pulse Speed in Parametric Three-Wave Solitons,” Phys. Rev. Lett. 97, 093901 (2006)
[CrossRef] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).

Woggon, U.

P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401–157404 (2001).
[CrossRef] [PubMed]

Wojs, A.

We assume that a photon of a given circular polarization promotes an electron-hole pair (exciton) creation with a well-defined spin orientation such that only linearly polarized light can generate biexcitons, cf., L. Jacak, P. Hawrylak, and A. Wojs, Optical Properties of Semiconductor Quantum Dots (Springer, Berlin, 1997).

Yoo, S. J. B.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

Yulin, A. V.

D. V. Skryabin, A. V. Yulin, and A. I. Maimistov, “Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity,” Phys. Rev. Lett. 96, 163904–163907 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett.

S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. 68, 2609–2611 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Opt. Quantum Electron.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomenaand their applications to all-optical signal processing, mode-locking, pulse, compression and solitions,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Phys. Rep.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Phys. Rev. B

T. Brunhes, P. Boucaud, and S. Sauvage, “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 61, 5562–5570 (2000).
[CrossRef]

G. Panzarini, U. Hohenester, and E. Molinari, “Self-induced transparency in semiconductor quantum dots,” Phys. Rev. B 65, 165322–165327 (2002).
[CrossRef]

Phys. Rev. E

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138–1141 (1996).
[CrossRef]

Phys. Rev. Lett.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, “Observation of temporal solitons in second-harmonic generation with tilted pulses,” Phys. Rev. Lett. 81, 570–573 (1998).
[CrossRef]

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable Control of Pulse Speed in Parametric Three-Wave Solitons,” Phys. Rev. Lett. 97, 093901 (2006)
[CrossRef] [PubMed]

D. V. Skryabin, A. V. Yulin, and A. I. Maimistov, “Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity,” Phys. Rev. Lett. 96, 163904–163907 (2006).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81, 4260–4263 (1998).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, and U. Woggon, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett. 87, 157401–157404 (2001).
[CrossRef] [PubMed]

Sov. Phys. JETP

L. A. Ostrovskii, “Propagation of wave packets and space-time self-focusing in a nonlinear medium,” Sov. Phys. JETP 24, 797–800 (1967).

Other

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).

G. B. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, Boston, 2003).

L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon, Oxford, 2003).

We assume that a photon of a given circular polarization promotes an electron-hole pair (exciton) creation with a well-defined spin orientation such that only linearly polarized light can generate biexcitons, cf., L. Jacak, P. Hawrylak, and A. Wojs, Optical Properties of Semiconductor Quantum Dots (Springer, Berlin, 1997).

The contributions of cubic and quadratic nonlinearities to the polarization can be roughly estimated as 𝒫(3)/𝒫(2)~χeff(3)ℰm/χeff(2)~5×10−2, using χeff(3)≃10−18m2/V2 for GaAs. Here the peak field amplitude ℰm of a picosecond 2π input pulse was estimated using the known pulse area as ℰm ∼ πh̄/degτp. Thus quadratic nonlinearities indeed dominate in our case.

In the circular polarization basis, the Bloch equations are exact such that no rotating wave approximation is needed.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications Inc., New York, 1975).

J. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, USA, 2006).

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Figures (5)

Fig. 1
Fig. 1

Top row: intensity profiles of the FW and SH soliton pair. The parameters are b = 107MHz, δ = 0, and LW = ∞. Bottom row: same as the top row except there is no inhomogeneous broadening.

Fig. 2
Fig. 2

Top row: intensity profiles of the FW and SH soliton pair. The parameters are b = 107MHz, δ = 3, and LW = ∞. Bottom row: same as above except b = 0.

Fig. 3
Fig. 3

Intensity profile of the SH wave for (a) δ = 2, (b) δ = 3, (c) δ = 5 and (d) δ = 7. The other parameters are b = 107MHz and LW = ∞.

Fig. 4
Fig. 4

Intensity profiles of the FW and SH soliton components. The parameters are b = 107MHz, δ = 1, and LW = 1mm.

Fig. 5
Fig. 5

Intensity profiles of the FW and SH soliton pair for secant hyperbolic (top row) and Gaussian (bottom row) input 2π fundamental pulses. The other parameters are b = 107MHz, δ = 0 and LW = ∞.

Equations (11)

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( z + 1 v g 1 t ) 1 = i N d e g ω 2 2 k 1 ɛ 0 c 2 < σ > i ω 2 χ e f f ( 2 ) * 2 k 1 c 2 1 * 2 e i Δ k z ,
( z + 1 v g 2 t ) 2 = i ω 2 χ e f f ( 2 ) k 2 c 2 1 2 e i Δ k z .
τ σ = ( γ + i Δ ) σ i Ω 1 w ,
τ w = γ ( w w eq ) i 2 ( Ω 1 * σ Ω 1 σ * ) .
Ω ¯ 1 Z = i < σ > i L A 4 L NL Ω ¯ 1 * Ω ¯ 2 e i ( δ Z + ϕ 0 ) ,
( Z + s ± L A L W T ) Ω ¯ 2 = i k 1 L A 2 k 2 L NL Ω ¯ 1 2 e i ( δ Z + ϕ 0 ) .
L A = 1 α ; L W = τ p | ν | ; L NL = k 1 c 2 | d e g | τ p h ¯ ω 2 | χ e f f | ,
< σ > d Δ ¯ g ( Δ ¯ ) σ ( Δ ¯ ) .
g ( Δ ¯ ) = 1 2 π b τ p exp ( Δ ¯ 2 2 b 2 τ p 2 ) .
T σ = i Δ ¯ σ i Ω ¯ 1 w ,
T w = i 2 ( Ω ¯ 1 * σ Ω ¯ 1 σ * ) .

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