Abstract

The inclusion of atomic inversion in Raman scattering can significantly alter field dynamics in plasmonic settings. Our calculations show that large local fields and femtosecond pulses combine to yield (i) population inversion within hot spots, (ii) gain saturation, and (iii) conversion efficiencies characterized by a switch-like transition to the stimulated regime that spans 12 orders of magnitude. While in Raman scattering atomic inversion is usually neglected, we demonstrate that in some circumstances full accounting of the dynamics of the Bloch vector is required.

© 2013 Optical Society of America

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References

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  1. M. Scalora, M. A. Vincenti, D. de Ceglia, M. Grande, and J. W. Haus, “Raman scattering near metal nanostructures,” J. Opt. Soc. Am. B 29, 2035–2045 (2012).
    [CrossRef]
  2. D. Bhandari, “Surface-enhanced Raman scattering: substrate development and applications in analytical detection,” Ph.D. dissertation (University of Tennessee, 2011).
  3. S. Franzen, “Intrinsic limitations on the |E|4 dependence of the enhancement factor for surface enhanced Raman scattering,” J. Phys. Chem. C 113, 5912–5919 (2009).
    [CrossRef]
  4. 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, 411–423 (1981).
    [CrossRef]
  5. M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
    [CrossRef]
  6. M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
    [CrossRef]
  7. R. W. Boyd, Nonlinear Optics (Academic, 2003), Chap. 10.
  8. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).
  9. M. Raymer, K. Rzazewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
    [CrossRef]
  10. J. R. Ackerholt and P. W. Milonni, “Solitons in four-wave mixing,” Phys. Rev. A 33, 3185–3198 (1986).
    [CrossRef]
  11. J. C. Englund and C. M. Bowden, “Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman soliton generation,” Phys. Rev. A 46, 578–591 (1992).
    [CrossRef]
  12. H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
    [CrossRef]
  13. R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21B, 510–516 (1978).
    [CrossRef]
  14. C. M. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: generalized Maxwell–Bloch equations,” Phys. Rev. A 47, 1247–1251 (1993).
    [CrossRef]
  15. M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
    [CrossRef]

2013 (1)

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

2012 (3)

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, M. Grande, and J. W. Haus, “Raman scattering near metal nanostructures,” J. Opt. Soc. Am. B 29, 2035–2045 (2012).
[CrossRef]

2009 (1)

S. Franzen, “Intrinsic limitations on the |E|4 dependence of the enhancement factor for surface enhanced Raman scattering,” J. Phys. Chem. C 113, 5912–5919 (2009).
[CrossRef]

1993 (1)

C. M. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: generalized Maxwell–Bloch equations,” Phys. Rev. A 47, 1247–1251 (1993).
[CrossRef]

1992 (2)

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef]

J. C. Englund and C. M. Bowden, “Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman soliton generation,” Phys. Rev. A 46, 578–591 (1992).
[CrossRef]

1986 (1)

J. R. Ackerholt and P. W. Milonni, “Solitons in four-wave mixing,” Phys. Rev. A 33, 3185–3198 (1986).
[CrossRef]

1982 (1)

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, 411–423 (1981).
[CrossRef]

1978 (1)

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21B, 510–516 (1978).
[CrossRef]

Ackerholt, J. R.

J. R. Ackerholt and P. W. Milonni, “Solitons in four-wave mixing,” Phys. Rev. A 33, 3185–3198 (1986).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Bhandari, D.

D. Bhandari, “Surface-enhanced Raman scattering: substrate development and applications in analytical detection,” Ph.D. dissertation (University of Tennessee, 2011).

Bianco, G. V.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21B, 510–516 (1978).
[CrossRef]

Bowden, C. M.

C. M. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: generalized Maxwell–Bloch equations,” Phys. Rev. A 47, 1247–1251 (1993).
[CrossRef]

J. C. Englund and C. M. Bowden, “Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman soliton generation,” Phys. Rev. A 46, 578–591 (1992).
[CrossRef]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[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, 411–423 (1981).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 2003), Chap. 10.

Bruno, G.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Chiang, H.-C.

H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
[CrossRef]

Crenshaw, M. E.

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef]

D’Orazio, A.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

de Ceglia, D.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, M. Grande, and J. W. Haus, “Raman scattering near metal nanostructures,” J. Opt. Soc. Am. B 29, 2035–2045 (2012).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

De Vittorio, M.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Dowling, J. P.

C. M. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: generalized Maxwell–Bloch equations,” Phys. Rev. A 47, 1247–1251 (1993).
[CrossRef]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Englund, J. C.

J. C. Englund and C. M. Bowden, “Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman soliton generation,” Phys. Rev. A 46, 578–591 (1992).
[CrossRef]

Franzen, S.

S. Franzen, “Intrinsic limitations on the |E|4 dependence of the enhancement factor for surface enhanced Raman scattering,” J. Phys. Chem. C 113, 5912–5919 (2009).
[CrossRef]

Grande, M.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, M. Grande, and J. W. Haus, “Raman scattering near metal nanostructures,” J. Opt. Soc. Am. B 29, 2035–2045 (2012).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

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, 411–423 (1981).
[CrossRef]

Haus, J. W.

Limori, T.

H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
[CrossRef]

Lugiato, L. A.

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21B, 510–516 (1978).
[CrossRef]

Milonni, P. W.

J. R. Ackerholt and P. W. Milonni, “Solitons in four-wave mixing,” Phys. Rev. A 33, 3185–3198 (1986).
[CrossRef]

Mostowski, J.

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, 411–423 (1981).
[CrossRef]

Ohta, N.

H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
[CrossRef]

Oikawa, H.

H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
[CrossRef]

Onedora, T.

H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
[CrossRef]

Petruzzelli, V.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Raymer, M.

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, 411–423 (1981).
[CrossRef]

Rzazewski, K.

Scalora, M.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, M. Grande, and J. W. Haus, “Raman scattering near metal nanostructures,” J. Opt. Soc. Am. B 29, 2035–2045 (2012).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef]

Stomeo, T.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Vincenti, M. A.

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, M. Grande, and J. W. Haus, “Raman scattering near metal nanostructures,” J. Opt. Soc. Am. B 29, 2035–2045 (2012).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

J. Appl. Phys. (1)

M. A. Vincenti, M. Grande, G. V. Bianco, D. de Ceglia, T. Stomeo, M. De Vittorio, V. Petruzzelli, G. Bruno, A. D’Orazio, and M. Scalora, “Surface-enhanced Raman scattering from finite arrays of gold nano-patches,” J. Appl. Phys. 113, 013103 (2013).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (2)

H.-C. Chiang, T. Limori, T. Onedora, H. Oikawa, and N. Ohta, “Gigantic electric dipole moment of organic microcrystals in dispersion liquid with polarized electroabsorption spectra,” J. Phys. Chem. C 116, 8230–8235 (2012).
[CrossRef]

S. Franzen, “Intrinsic limitations on the |E|4 dependence of the enhancement factor for surface enhanced Raman scattering,” J. Phys. Chem. C 113, 5912–5919 (2009).
[CrossRef]

Lett. Nuovo Cimento (1)

R. Bonifacio and L. A. Lugiato, “Instabilities for a coherently driven absorber in a ring cavity,” Lett. Nuovo Cimento 21B, 510–516 (1978).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

C. M. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: generalized Maxwell–Bloch equations,” Phys. Rev. A 47, 1247–1251 (1993).
[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, 411–423 (1981).
[CrossRef]

J. R. Ackerholt and P. W. Milonni, “Solitons in four-wave mixing,” Phys. Rev. A 33, 3185–3198 (1986).
[CrossRef]

J. C. Englund and C. M. Bowden, “Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman soliton generation,” Phys. Rev. A 46, 578–591 (1992).
[CrossRef]

Phys. Rev. Lett. (1)

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef]

Other (3)

R. W. Boyd, Nonlinear Optics (Academic, 2003), Chap. 10.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

D. Bhandari, “Surface-enhanced Raman scattering: substrate development and applications in analytical detection,” Ph.D. dissertation (University of Tennessee, 2011).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Unit cell of a generic 1D periodic array composed of metal nanowires placed near a metal substrate. (b) Illustration of extreme environment for the geometry of Fig. 1(a): aluminum nanowire of radius r=20nm attached to an aluminum substrate. Incident wavelength is λ=220nm. The local field is amplified by a factor of 2×104. Incident fields with peak powers in the W/cm2 range can achieve local field intensities of order 1GW/cm2. In this example we use aluminum because silver does not perform as well in the wavelength range of interest.

Fig. 2.
Fig. 2.

(a) Normalized linear reflection (R) and absorption (A) spectra for the structure in Fig. 1(a) with r=36nm, t=50nm, and p=180nm, with (solid) and without (markers) nonlocal effects, obtained by integrating Eqs. (1)–(3) together with Maxwell’s equations, using an incident pulse a few femtoseconds in duration. (b) First Stokes and first anti-Stokes transitions exemplified on a four-level scheme that reduces to an effective two-level atom, with coherence between levels |0 and |2.

Fig. 3.
Fig. 3.

(a) Reflected Stokes efficiency versus incident peak power for pulse durations as shown. The comparison is made relative to a Raman layer 5 nm thick standing in free space (curve labeled “without metal”). Removing the nanowire and leaving only the metal substrate voids field localization phenomena near the surface, and does not guarantee any improvements in conversion efficiency beyond the dashed curve, as a field node tends to form at the metal surface. (b) Spatial distribution of the inversion associated with the longitudinal component of the field. The dark blue regions represent a Raman medium in the ground state. The medium is inverted in the yellow and red spots, where the local field is largest.

Fig. 4.
Fig. 4.

Reflected Stokes efficiencies versus incident peak power for 1 ps pulses, with (long dashes, empty circles) and without (short dashes, empty squares) inversion. Inversion inhibits efficiency as the medium stores energy and saturation occurs.

Fig. 5.
Fig. 5.

Reflected Stokes efficiency versus incident peak power for 1 ps pulses, without (long dashes, empty circles) and with (short dashes, empty squares) anti-Stokes channel. The anti-Stokes field interferes with Stokes sources, modifies the evolution of the atomic variable, and changes the dynamics of the fields themselves. If the anti-Stokes field is absent, more photons are available to drive the Stokes process, lowering nonlinear thresholds by approximately one order of magnitude.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

P¨f+γ˜fP˙f=n0,fe2mf*(λ0c)2E+53EFmf*c2(·Pf),
P¨1+γ˜01P˙1+ω˜0,12P1=n0,1e2mb*E,
P¨2+γ˜02P˙2+ω˜0,22P2=n0,2e2mb*E,
E=Eyj+Ezk=l(El,y(r,t)ei(kz,lzωlt)+c.c.)j+l(El,z(r,t)ei(kz,lzωlt)+c.c.)k,H=Hix=l(Hl,x(r,t)ei(kz,lzωlt)+c.c.)i,
W˙k=μ02λ02ω01c(Qk*l=12El,k(r,τ)El+1,k*(r,τ)+c.c.),
Q˙k=μ02λ022ω01c(l=12El,k(r,τ)El+1,k*(r,τ))Wk+Fk(r,τ).
Pk=χLEk+iχL(QkEkeiδtQk*Ekeiδt).
Pωp,kNL=iχL[QkES,kQk*EAS,k],PωS,kNL=iχLQk*EP,k,PωAS,kNL=iχLQkEP,k,
W˙k=μ02λ02ω01c[Qk*(EA,kEP,k*+EP,kES,k*)+Qk(EA,k*EP,k+EP,k*ES,k)],Q˙k=μ02λ022ω01c(EA,kEP,k*+EP,kES,k*)Wk.
Wk(r0,t+δt)Wk(r0,t)+μ02λ02ω01c(Qk*(r0,t)Tk(r0,t)+Qk(r0,t)Tk*(r0,t))δt,Qk(r0,t+δt)Qk(r0,t)μ02λ022ω01cTk(r0,t)Wk(r0,t)δt,

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