Abstract

We study theoretically four-wave parametric amplification arising from the nonlinear optical response of hybrid molecules composed of semiconductor quantum dots and metallic nanoparticles. It is shown that highly efficient four-wave parametric amplification can be achieved by adjusting the frequency and intensity of the pump field and the distance between the quantum dot and the metallic nanoparticle. Specifically, the induced probe-wave gain is tunable in a large range from 1 to 1.43 × 105. This gain reaches its maximum at the position of three-photon resonance. Our findings hold great promise for developing four-wave parametric oscillators.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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2014 (2)

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

E. Paspalakis, S. Evangelou, S. G. Kosionis, and A. F. Terzis, “Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system,” J. Appl. Phys. 115(8), 083106 (2014).
[Crossref]

2013 (5)

S. M. Sadeghi, “Ultrafast plasmonic field oscillations and optics of molecular resonances caused by coherent exciton-plasmon coupling,” Phys. Rev. A 88(1), 013831 (2013).
[Crossref]

M. R. Singh, “Enhancement of the second-harmonic generation in a quantum dot-metallic nanoparticle hybrid system,” Nanotechnology 24(12), 125701 (2013).
[Crossref] [PubMed]

C. H. R. Ooi and K. S. Tan, “Controlling double quantum coherence and electromagnetic induced transparency with plasmonic metallic nanoparticle,” Plasmonics 8(2), 891–898 (2013).
[Crossref]

R. A. Shah, N. F. Scherer, M. Pelton, and S. K. Gray, “Ultrafast reversal of a Fano resonance in a plasmon-exciton system,” Phys. Rev. B 88(7), 075411 (2013).
[Crossref]

X. N. Liu, D. Z. Yao, H. M. Zhou, F. Chen, and G. G. Xiong, “Third-order nonlinear optical response in quantum dot-metal nanoparticle hybrid structures,” Appl. Phys. B 113(4), 603–610 (2013).
[Crossref]

2012 (5)

A. V. Malyshev, “Condition for resonant optical bistability,” Phys. Rev. A 86(6), 065804 (2012).
[Crossref]

S. Evangelou, V. Yannopapas, and E. Paspalakis, “Transparency and slow light in a four-level quantum system near a plasmonic nanostructure,” Phys. Rev. A 86(5), 053811 (2012).
[Crossref]

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Z. H. Xiao, L. Zheng, and H. Z. Lin, “Photoinduced diffraction grating in hybrid artificial molecule,” Opt. Express 20(2), 1219–1229 (2012).
[Crossref] [PubMed]

J. B. Li, N. C. Kim, M. T. Cheng, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Optical bistability and nonlinearity of coherently coupled exciton-plasmon systems,” Opt. Express 20(2), 1856–1861 (2012).
[Crossref] [PubMed]

2011 (2)

S. M. Sadeghi, “Plasmonic meta-resonance nanosensors: ultrasensitive sensors based on nanoparticle molecules,” IEEE Trans. NanoTechnol. 10(3), 566–571 (2011).
[Crossref]

A. V. Malyshev and V. A. Malyshev, “Optical bistability and hysteresis of a hybrid metal-semiconductor nanodimer,” Phys. Rev. B 84(3), 035314 (2011).
[Crossref]

2010 (3)

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
[Crossref] [PubMed]

S. M. Sadeghi, “Gain without inversion in hybrid quantum dot-metallic nanoparticle systems,” Nanotechnology 21(45), 455401 (2010).
[Crossref] [PubMed]

2009 (1)

Z. Lu and K. D. Zhu, “Slow light in an artificial hybrid nanocrystal complex,” J. Phys. B 42(1), 015502 (2009).
[Crossref]

2008 (4)

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: Double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
[Crossref] [PubMed]

H. I. Elim, W. Ji, J. Yang, and J. Y. Lee, “Intensity-dependent enhancement of saturable absorption in PbS–Au4 nanohybrid composites: evidence for resonant energy transfer by Auger recombination,” Appl. Phys. Lett. 92(25), 251106 (2008).
[Crossref]

J. Y. Yan, W. Zhang, S. Q. Duan, X. G. Zhao, and A. O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77(16), 165301 (2008).
[Crossref]

Z. E. Lu and K. D. Zhu, “Enhancing Kerr nonlinearity of a strong coupled exciton-plasmon in hybrid nanocrystal molecules,” J. Phys. B 41(18), 185503 (2008).
[Crossref]

2007 (4)

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photon. 1(7), 402–406 (2007).
[Crossref]

M. T. Cheng, S. D. Liu, H. J. Zhou, Z. H. Hao, and Q. Q. Wang, “Coherent exciton-plasmon interaction in the hybrid semiconductor quantum dot and metal nanoparticle complex,” Opt. Lett. 32(15), 2125–2127 (2007).
[Crossref] [PubMed]

Y. Fedutik, V. V. Temnov, O. Schöps, U. Woggon, and M. V. Artemyev, “Exciton-plasmon-photon conversion in plasmonic nanostructures,” Phys. Rev. Lett. 99(13), 136802 (2007).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007).
[Crossref]

2006 (3)

W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

1981 (1)

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).
[Crossref]

Afshinmanesh, F.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Antón, M. A.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

Artemyev, M. V.

Y. Fedutik, V. V. Temnov, O. Schöps, U. Woggon, and M. V. Artemyev, “Exciton-plasmon-photon conversion in plasmonic nanostructures,” Phys. Rev. Lett. 99(13), 136802 (2007).
[Crossref] [PubMed]

Artuso, R. D.

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: Double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
[Crossref] [PubMed]

Atwater, H. A.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photon. 1(7), 402–406 (2007).
[Crossref]

Boyd, R. W.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).
[Crossref]

Brongersma, M. L.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Bryant, G. W.

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: Double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
[Crossref] [PubMed]

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006).
[Crossref] [PubMed]

Cabrera-Granado, E.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

Calderón, O. G.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

Cao, L.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Carreño, F.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

Chang, D. E.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Chen, F.

X. N. Liu, D. Z. Yao, H. M. Zhou, F. Chen, and G. G. Xiong, “Third-order nonlinear optical response in quantum dot-metal nanoparticle hybrid structures,” Appl. Phys. B 113(4), 603–610 (2013).
[Crossref]

Cheng, M. T.

Chettiar, U. K.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Cox, J.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

Demler, E. A.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007).
[Crossref]

Duan, S. Q.

J. Y. Yan, W. Zhang, S. Q. Duan, X. G. Zhao, and A. O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77(16), 165301 (2008).
[Crossref]

Egatz-Gómez, A.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

Elim, H. I.

H. I. Elim, W. Ji, J. Yang, and J. Y. Lee, “Intensity-dependent enhancement of saturable absorption in PbS–Au4 nanohybrid composites: evidence for resonant energy transfer by Auger recombination,” Appl. Phys. Lett. 92(25), 251106 (2008).
[Crossref]

Engheta, N.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Evangelou, S.

E. Paspalakis, S. Evangelou, S. G. Kosionis, and A. F. Terzis, “Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system,” J. Appl. Phys. 115(8), 083106 (2014).
[Crossref]

S. Evangelou, V. Yannopapas, and E. Paspalakis, “Transparency and slow light in a four-level quantum system near a plasmonic nanostructure,” Phys. Rev. A 86(5), 053811 (2012).
[Crossref]

Fan, P.

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Fedutik, Y.

Y. Fedutik, V. V. Temnov, O. Schöps, U. Woggon, and M. V. Artemyev, “Exciton-plasmon-photon conversion in plasmonic nanostructures,” Phys. Rev. Lett. 99(13), 136802 (2007).
[Crossref] [PubMed]

García-Vidal, F. J.

D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
[Crossref] [PubMed]

Govorov, A. O.

J. Y. Yan, W. Zhang, S. Q. Duan, X. G. Zhao, and A. O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77(16), 165301 (2008).
[Crossref]

W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006).
[Crossref] [PubMed]

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Gray, S. K.

R. A. Shah, N. F. Scherer, M. Pelton, and S. K. Gray, “Ultrafast reversal of a Fano resonance in a plasmon-exciton system,” Phys. Rev. B 88(7), 075411 (2013).
[Crossref]

Hao, Z. H.

Harter, D. J.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).
[Crossref]

Hemmer, P. R.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Ji, W.

H. I. Elim, W. Ji, J. Yang, and J. Y. Lee, “Intensity-dependent enhancement of saturable absorption in PbS–Au4 nanohybrid composites: evidence for resonant energy transfer by Auger recombination,” Appl. Phys. Lett. 92(25), 251106 (2008).
[Crossref]

Kim, N. C.

J. B. Li, N. C. Kim, M. T. Cheng, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Optical bistability and nonlinearity of coherently coupled exciton-plasmon systems,” Opt. Express 20(2), 1856–1861 (2012).
[Crossref] [PubMed]

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Kosionis, S. G.

E. Paspalakis, S. Evangelou, S. G. Kosionis, and A. F. Terzis, “Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system,” J. Appl. Phys. 115(8), 083106 (2014).
[Crossref]

Kotov, N. A.

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Lee, J.

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Lee, J. Y.

H. I. Elim, W. Ji, J. Yang, and J. Y. Lee, “Intensity-dependent enhancement of saturable absorption in PbS–Au4 nanohybrid composites: evidence for resonant energy transfer by Auger recombination,” Appl. Phys. Lett. 92(25), 251106 (2008).
[Crossref]

Lezec, H. J.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photon. 1(7), 402–406 (2007).
[Crossref]

Li, J. B.

J. B. Li, N. C. Kim, M. T. Cheng, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Optical bistability and nonlinearity of coherently coupled exciton-plasmon systems,” Opt. Express 20(2), 1856–1861 (2012).
[Crossref] [PubMed]

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Li, M.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Lin, H. Z.

Liu, S. D.

Liu, X. N.

X. N. Liu, D. Z. Yao, H. M. Zhou, F. Chen, and G. G. Xiong, “Third-order nonlinear optical response in quantum dot-metal nanoparticle hybrid structures,” Appl. Phys. B 113(4), 603–610 (2013).
[Crossref]

Lu, Z.

Z. Lu and K. D. Zhu, “Slow light in an artificial hybrid nanocrystal complex,” J. Phys. B 42(1), 015502 (2009).
[Crossref]

Lu, Z. E.

Z. E. Lu and K. D. Zhu, “Enhancing Kerr nonlinearity of a strong coupled exciton-plasmon in hybrid nanocrystal molecules,” J. Phys. B 41(18), 185503 (2008).
[Crossref]

Lukin, M. D.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Malyshev, A. V.

A. V. Malyshev, “Condition for resonant optical bistability,” Phys. Rev. A 86(6), 065804 (2012).
[Crossref]

A. V. Malyshev and V. A. Malyshev, “Optical bistability and hysteresis of a hybrid metal-semiconductor nanodimer,” Phys. Rev. B 84(3), 035314 (2011).
[Crossref]

Malyshev, V. A.

A. V. Malyshev and V. A. Malyshev, “Optical bistability and hysteresis of a hybrid metal-semiconductor nanodimer,” Phys. Rev. B 84(3), 035314 (2011).
[Crossref]

Martín-Cano, D.

D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
[Crossref] [PubMed]

Martín-Moreno, L.

D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
[Crossref] [PubMed]

Melle, S.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

Moreno, E.

D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
[Crossref] [PubMed]

Naik, R. R.

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Narum, P.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).
[Crossref]

Ooi, C. H. R.

C. H. R. Ooi and K. S. Tan, “Controlling double quantum coherence and electromagnetic induced transparency with plasmonic metallic nanoparticle,” Plasmonics 8(2), 891–898 (2013).
[Crossref]

Pacifici, D.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photon. 1(7), 402–406 (2007).
[Crossref]

Paspalakis, E.

E. Paspalakis, S. Evangelou, S. G. Kosionis, and A. F. Terzis, “Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system,” J. Appl. Phys. 115(8), 083106 (2014).
[Crossref]

S. Evangelou, V. Yannopapas, and E. Paspalakis, “Transparency and slow light in a four-level quantum system near a plasmonic nanostructure,” Phys. Rev. A 86(5), 053811 (2012).
[Crossref]

Pelton, M.

R. A. Shah, N. F. Scherer, M. Pelton, and S. K. Gray, “Ultrafast reversal of a Fano resonance in a plasmon-exciton system,” Phys. Rev. B 88(7), 075411 (2013).
[Crossref]

Peng, X. N.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Raymer, M. G.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).
[Crossref]

Sadeghi, S. M.

S. M. Sadeghi, “Ultrafast plasmonic field oscillations and optics of molecular resonances caused by coherent exciton-plasmon coupling,” Phys. Rev. A 88(1), 013831 (2013).
[Crossref]

S. M. Sadeghi, “Plasmonic meta-resonance nanosensors: ultrasensitive sensors based on nanoparticle molecules,” IEEE Trans. NanoTechnol. 10(3), 566–571 (2011).
[Crossref]

S. M. Sadeghi, “Gain without inversion in hybrid quantum dot-metallic nanoparticle systems,” Nanotechnology 21(45), 455401 (2010).
[Crossref] [PubMed]

Scherer, N. F.

R. A. Shah, N. F. Scherer, M. Pelton, and S. K. Gray, “Ultrafast reversal of a Fano resonance in a plasmon-exciton system,” Phys. Rev. B 88(7), 075411 (2013).
[Crossref]

Schöps, O.

Y. Fedutik, V. V. Temnov, O. Schöps, U. Woggon, and M. V. Artemyev, “Exciton-plasmon-photon conversion in plasmonic nanostructures,” Phys. Rev. Lett. 99(13), 136802 (2007).
[Crossref] [PubMed]

Shah, R. A.

R. A. Shah, N. F. Scherer, M. Pelton, and S. K. Gray, “Ultrafast reversal of a Fano resonance in a plasmon-exciton system,” Phys. Rev. B 88(7), 075411 (2013).
[Crossref]

Singh, M. R.

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

M. R. Singh, “Enhancement of the second-harmonic generation in a quantum dot-metallic nanoparticle hybrid system,” Nanotechnology 24(12), 125701 (2013).
[Crossref] [PubMed]

Skeini, T.

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Slocik, J. M.

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Su, X. R.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Tan, K. S.

C. H. R. Ooi and K. S. Tan, “Controlling double quantum coherence and electromagnetic induced transparency with plasmonic metallic nanoparticle,” Plasmonics 8(2), 891–898 (2013).
[Crossref]

Temnov, V. V.

Y. Fedutik, V. V. Temnov, O. Schöps, U. Woggon, and M. V. Artemyev, “Exciton-plasmon-photon conversion in plasmonic nanostructures,” Phys. Rev. Lett. 99(13), 136802 (2007).
[Crossref] [PubMed]

Terzis, A. F.

E. Paspalakis, S. Evangelou, S. G. Kosionis, and A. F. Terzis, “Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system,” J. Appl. Phys. 115(8), 083106 (2014).
[Crossref]

Wang, Q. Q.

Woggon, U.

Y. Fedutik, V. V. Temnov, O. Schöps, U. Woggon, and M. V. Artemyev, “Exciton-plasmon-photon conversion in plasmonic nanostructures,” Phys. Rev. Lett. 99(13), 136802 (2007).
[Crossref] [PubMed]

Xiao, Z. H.

Xiong, G. G.

X. N. Liu, D. Z. Yao, H. M. Zhou, F. Chen, and G. G. Xiong, “Third-order nonlinear optical response in quantum dot-metal nanoparticle hybrid structures,” Appl. Phys. B 113(4), 603–610 (2013).
[Crossref]

Yan, J. Y.

J. Y. Yan, W. Zhang, S. Q. Duan, X. G. Zhao, and A. O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77(16), 165301 (2008).
[Crossref]

Yang, J.

H. I. Elim, W. Ji, J. Yang, and J. Y. Lee, “Intensity-dependent enhancement of saturable absorption in PbS–Au4 nanohybrid composites: evidence for resonant energy transfer by Auger recombination,” Appl. Phys. Lett. 92(25), 251106 (2008).
[Crossref]

Yang, Z. J.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Yannopapas, V.

S. Evangelou, V. Yannopapas, and E. Paspalakis, “Transparency and slow light in a four-level quantum system near a plasmonic nanostructure,” Phys. Rev. A 86(5), 053811 (2012).
[Crossref]

Yao, D. Z.

X. N. Liu, D. Z. Yao, H. M. Zhou, F. Chen, and G. G. Xiong, “Third-order nonlinear optical response in quantum dot-metal nanoparticle hybrid structures,” Appl. Phys. B 113(4), 603–610 (2013).
[Crossref]

Yu, X. F.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Zhang, W.

J. Y. Yan, W. Zhang, S. Q. Duan, X. G. Zhao, and A. O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77(16), 165301 (2008).
[Crossref]

W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006).
[Crossref] [PubMed]

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Zhang, Z. S.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Zhao, X. G.

J. Y. Yan, W. Zhang, S. Q. Duan, X. G. Zhao, and A. O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77(16), 165301 (2008).
[Crossref]

Zheng, L.

Zhou, H. J.

Zhou, H. M.

X. N. Liu, D. Z. Yao, H. M. Zhou, F. Chen, and G. G. Xiong, “Third-order nonlinear optical response in quantum dot-metal nanoparticle hybrid structures,” Appl. Phys. B 113(4), 603–610 (2013).
[Crossref]

Zhou, L.

J. B. Li, N. C. Kim, M. T. Cheng, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Optical bistability and nonlinearity of coherently coupled exciton-plasmon systems,” Opt. Express 20(2), 1856–1861 (2012).
[Crossref] [PubMed]

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Zhou, Z. K.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Zhu, K. D.

Z. Lu and K. D. Zhu, “Slow light in an artificial hybrid nanocrystal complex,” J. Phys. B 42(1), 015502 (2009).
[Crossref]

Z. E. Lu and K. D. Zhu, “Enhancing Kerr nonlinearity of a strong coupled exciton-plasmon in hybrid nanocrystal molecules,” J. Phys. B 41(18), 185503 (2008).
[Crossref]

ACS Nano (1)

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4(9), 5003–5010 (2010).
[Crossref] [PubMed]

Appl. Phys. B (1)

X. N. Liu, D. Z. Yao, H. M. Zhou, F. Chen, and G. G. Xiong, “Third-order nonlinear optical response in quantum dot-metal nanoparticle hybrid structures,” Appl. Phys. B 113(4), 603–610 (2013).
[Crossref]

Appl. Phys. Lett. (1)

H. I. Elim, W. Ji, J. Yang, and J. Y. Lee, “Intensity-dependent enhancement of saturable absorption in PbS–Au4 nanohybrid composites: evidence for resonant energy transfer by Auger recombination,” Appl. Phys. Lett. 92(25), 251106 (2008).
[Crossref]

IEEE Trans. NanoTechnol. (1)

S. M. Sadeghi, “Plasmonic meta-resonance nanosensors: ultrasensitive sensors based on nanoparticle molecules,” IEEE Trans. NanoTechnol. 10(3), 566–571 (2011).
[Crossref]

J. Appl. Phys. (2)

E. Paspalakis, S. Evangelou, S. G. Kosionis, and A. F. Terzis, “Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system,” J. Appl. Phys. 115(8), 083106 (2014).
[Crossref]

F. Carreño, M. A. Antón, S. Melle, O. G. Calderón, E. Cabrera-Granado, J. Cox, M. R. Singh, and A. Egatz-Gómez, “Plasmon-enhanced terahertz emission in self-assembled quantum dots by femtosecond pulses,” J. Appl. Phys. 115(6), 064304 (2014).
[Crossref]

J. Phys. B (2)

Z. Lu and K. D. Zhu, “Slow light in an artificial hybrid nanocrystal complex,” J. Phys. B 42(1), 015502 (2009).
[Crossref]

Z. E. Lu and K. D. Zhu, “Enhancing Kerr nonlinearity of a strong coupled exciton-plasmon in hybrid nanocrystal molecules,” J. Phys. B 41(18), 185503 (2008).
[Crossref]

Nano Lett. (3)

R. D. Artuso and G. W. Bryant, “Optical response of strongly coupled quantum dot-metal nanoparticle systems: Double peaked Fano structure and bistability,” Nano Lett. 8(7), 2106–2111 (2008).
[Crossref] [PubMed]

D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
[Crossref] [PubMed]

A. O. Govorov, G. W. Bryant, W. Zhang, T. Skeini, J. Lee, N. A. Kotov, J. M. Slocik, and R. R. Naik, “Exciton-plasmon interaction and hybrid excitons in semiconductor-metal nanoparticle assemblies,” Nano Lett. 6(5), 984–994 (2006).
[Crossref]

Nanotechnology (2)

S. M. Sadeghi, “Gain without inversion in hybrid quantum dot-metallic nanoparticle systems,” Nanotechnology 21(45), 455401 (2010).
[Crossref] [PubMed]

M. R. Singh, “Enhancement of the second-harmonic generation in a quantum dot-metallic nanoparticle hybrid system,” Nanotechnology 24(12), 125701 (2013).
[Crossref] [PubMed]

Nat. Photon. (2)

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photon. 1(7), 402–406 (2007).
[Crossref]

P. Fan, U. K. Chettiar, L. Cao, F. Afshinmanesh, N. Engheta, and M. L. Brongersma, “An invisible metal-semiconductor photodetector,” Nat. Photon. 6(6), 380–385 (2012).
[Crossref]

Nat. Phys. (1)

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3(11), 807–812 (2007).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (4)

S. Evangelou, V. Yannopapas, and E. Paspalakis, “Transparency and slow light in a four-level quantum system near a plasmonic nanostructure,” Phys. Rev. A 86(5), 053811 (2012).
[Crossref]

S. M. Sadeghi, “Ultrafast plasmonic field oscillations and optics of molecular resonances caused by coherent exciton-plasmon coupling,” Phys. Rev. A 88(1), 013831 (2013).
[Crossref]

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981).
[Crossref]

A. V. Malyshev, “Condition for resonant optical bistability,” Phys. Rev. A 86(6), 065804 (2012).
[Crossref]

Phys. Rev. B (3)

A. V. Malyshev and V. A. Malyshev, “Optical bistability and hysteresis of a hybrid metal-semiconductor nanodimer,” Phys. Rev. B 84(3), 035314 (2011).
[Crossref]

R. A. Shah, N. F. Scherer, M. Pelton, and S. K. Gray, “Ultrafast reversal of a Fano resonance in a plasmon-exciton system,” Phys. Rev. B 88(7), 075411 (2013).
[Crossref]

J. Y. Yan, W. Zhang, S. Q. Duan, X. G. Zhao, and A. O. Govorov, “Optical properties of coupled metal-semiconductor and metal-molecule nanocrystal complexes: Role of multipole effects,” Phys. Rev. B 77(16), 165301 (2008).
[Crossref]

Phys. Rev. Lett. (3)

W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006).
[Crossref] [PubMed]

Y. Fedutik, V. V. Temnov, O. Schöps, U. Woggon, and M. V. Artemyev, “Exciton-plasmon-photon conversion in plasmonic nanostructures,” Phys. Rev. Lett. 99(13), 136802 (2007).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Plasmonics (1)

C. H. R. Ooi and K. S. Tan, “Controlling double quantum coherence and electromagnetic induced transparency with plasmonic metallic nanoparticle,” Plasmonics 8(2), 891–898 (2013).
[Crossref]

Other (5)

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, 1984).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

V. V. Batygin and I. N. Toptygin, Sbornik Zadach Po Elektrodinamike 2-e izd. (M.: Nauka, 1970) [Problems in Electrodynamics, 2nd ed. (Academic, 1978)].

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Elsevier, 2008).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of a hybrid molecule composed of a SQD and a MNP interacting with a strong pump field and a weak probe field. (b) Energy-level diagram of a two-level SQD coupled to a MNP. (c) The phase matching condition for collinear propagation in this nonlinear molecular material.
Fig. 2
Fig. 2 (a) The mixing response spectrum as a function of probe-pump detuning δpr when (a) Δpu = −6, −4, −2, 0 (b) Δpu = 2.8, 4, 6. The positions of the peaks induced by three-photon resonance (TP), Rayleigh resonance (RL) and ac-Stark resonance (AC) as a function of Δpu. Other parameters are d = 15 nm and Ωpu2 = 20.
Fig. 3
Fig. 3 (a) The probe-wave gain G as a function of δpr when (a) Δpu ≤ 0 and (b) Δpu > 0. All other parameters are the same as those in Fig. 2.
Fig. 4
Fig. 4 (a) The mixing response spectrum as a function of the interparticle distance d for different values of the probe-pump detuning δpr. (b) The probe-wave gain G as a function of d. Other parameters are Δpu = −6 and Ωpu2 = 20.
Fig. 5
Fig. 5 (a) The mixing response spectrum as a function of the pump-field intensity Ωpu2 for different detuning δpr. (b) The probe-wave gain G as a function of Ωpu2. Other parameters are Δpu = −6 and d = 15 nm.

Equations (19)

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H ^ =Δ σ ^ z μ( E SQD σ ^ 01 + E SQD σ ^ 10 ),
p ˙ =( 1/ T 2 +iΔ )pi μ 10 2 E ˜ SQD w/,
w ˙ =( w+1 )/ T 1 +4Im( p E ˜ SQD )/.
χ eff ( 1 ) ( ω 0 +δ )= N p 1 ε 0 E 1 ,
χ eff ( 3 ) ( ω 0 δ )= N p 1 3 ε 0 E 0 2 E 1 ,
p 1 ( 2 ω 0 ω 1 = ω 0 δ )= 2 A 3 μ 10 4 T 2 3 w 0 3 ( i Δ pu )( 2i δ pr )[ i+( Δ pu + B pu w 0 ) ] [ i( Δ pu + B pu w 0 ) ]D( δ pr ) E 0 2 E 1 ,
p 1 ( ω 1 )= A μ 10 2 T 2 w 0 ( δ pr Δ pu B pu w 0 +i ) [ 12 A 2 Ω pu 2 ( i Δ pu )( 2i+ δ pr )( δ pr + Δ pu + B pu w 0 +i ) D ( δ pr ) ] E 1 ,
D( δ pr )=( δ pr i T 2 / T 1 )[ 1+ ( Δ pu + B pu w 0 ) 2 ][ ( δ pr i ) 2 ( Δ pu + B pu w 0 ) 2 ] +4 A 2 Ω pu 2 [ ( i δ pr )( 1+ Δ pu 2 ) B pu w 0 ( i B pu w 0 + Δ pu δ pr ) ].
P 1 =P( ω 0 +δ )= ε 0 χ eff ( 1 ) ( ω 0 +δ ) E 0 +3 ε 0 χ eff ( 3 ) ( ω 0 +δ ) E 0 2 E 1 ,
P 1 =P( ω 0 δ )= ε 0 χ eff ( 1 ) ( ω 0 δ ) E 1 +3 ε 0 χ eff ( 3 ) ( ω 0 δ ) E 0 2 E 1 .
2 E 1 + k 1 2 E 1 = ( ω 0 +δ ) 2 P 1 /( ε 0 c 2 ),
2 E 1 + k 1 2 E 1 = ( ω 0 δ ) 2 P 1 /( ε 0 c 2 ).
d A 1 /dz= α 1 A 1 + κ 1 A 1 Exp[ iΔkz ],
d A 1 /dz= α 1 A 1 + κ 1 A 1 Exp[ iΔkz ].
α ±1 = 1 2 ( ω 0 ±δ n ±1 c ) Im eff ( 1 ) ( ω 0 ±δ ),
κ ±1 =i 3 2 ( ω 0 ±δ n ±1 c ) χ eff ( 3 ) ( ω 0 ±δ ) A 0 2 .
A 1 ( z )= ( η + η ) 1 { [ κ 1 A 1 ( 0 )( η + α 1 +iΔk/2 ) A 1 ( 0 ) ] e η + z +[ κ 1 A 1 ( 0 )+( η + + α 1 +iΔk/2 ) A 1 ( 0 ) ] e η z } e iΔkz/2 ,
A 1 ( z )= ( η + η ) 1 { [ ( η + + α 1 +iΔk/2 ) A 1 ( 0 )+ κ 1 A 1 ( 0 ) ] e η + z [ ( η + α 1 +iΔk/2 ) A 1 ( 0 )+ κ 1 A 1 ( 0 ) ] e η z } e iΔkz/2 .
η ± = 1 2 ( α 1 + α 1 )± [ ( α 1 + α 1 +iΔk )+4 κ 1 κ 1 ] 1/2 .

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