Self-induced transparency quadratic solitons |
Optics Express, Vol. 20, Issue 13, pp. 13988-13995 (2012)
http://dx.doi.org/10.1364/OE.20.013988
Acrobat PDF (1357 KB)
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.
© 2012 OSA
1. Introduction
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]
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]
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]
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]
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]
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]
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]
2. Quantitative analysis and physical model
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
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]
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]
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]
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]
20. G. Panzarini, U. Hohenester, and E. Molinari, “Self-induced transparency in semiconductor quantum dots,” Phys. Rev. B 65, 165322–165327 (2002). [CrossRef]
3. Numerical simulations
4. Conclusion
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]
15. The contributions of cubic and quadratic nonlinearities to the polarization can be roughly estimated as
26. A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Optical solitons supported by competing nonlinearities,” Opt. Lett. 20, 1961–1963 (1995). [CrossRef] [PubMed]
References and links
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 |
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] |
OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(260.0260) Physical optics : Physical optics
ToC Category:
Nonlinear Optics
History
Original Manuscript: April 26, 2012
Revised Manuscript: May 22, 2012
Manuscript Accepted: May 23, 2012
Published: June 8, 2012
Citation
Soodeh Haghgoo and Sergey A. Ponomarenko, "Self-induced transparency quadratic solitons," Opt. Express 20, 13988-13995 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-13988
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References
- 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).
- 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]
- L. A. Ostrovskii, “Propagation of wave packets and space-time self-focusing in a nonlinear medium,” Sov. Phys. JETP24, 797–800 (1967).
- 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]
- R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E53, 1138–1141 (1996). [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]
- 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]
- L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications Inc., New York, 1975).
- 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]
- 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}~χ_{eff}^{(3)}ℰ_{m}/χ_{eff}^{(2)}~5×10^{-2}, using χ_{eff}^{(3)}≃10^{-18}m^{2}V^{2} for GaAs. Here the peak field amplitude ℰm of a picosecond 2π input pulse was estimated using the known pulse area as ℰ_{m} ∼ πh̄/d_{eg}τ_{p}. 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.
- T. Brunhes, P. Boucaud, and S. Sauvage, “Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots,” Phys. Rev. B61, 5562–5570 (2000). [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]
- 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. B65, 165322–165327 (2002). [CrossRef]
- M. Jütte, H. Stolz, and W. von der Osten, “Linear and nonlinear pulse propagation at bound excitons in CdS,” J. Opt. Soc. Am. B13, 1205–1210 (1996). [CrossRef]
- 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]
- J. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, USA, 2006).
- A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Optical solitons supported by competing nonlinearities,” Opt. Lett.20, 1961–1963 (1995). [CrossRef] [PubMed]
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