Abstract

We study the propagation and momentum transport of the inhomogeneous component of second and third harmonic pulses in dielectrics and semiconductors, at visible and UV wavelengths, focusing on materials like GaP. In these spectral regions GaP is characterized by large absorption, metallic behavior or a combination of both. We show that phase locking causes the generated inhomogeneous signals to propagate through a bulk metallic medium without being absorbed. This means that it occurs even in centrosymmetric materials thanks to the magnetic Lorentz force. We show that the transport of energy and momentum is quite peculiar and it can appear as anomalous, and that the direction of the Poynting vector of some of the harmonic pulses does not follow Snell’s law after crossing the interface. These results make it clear that there are new opportunities in ultrafast nonlinear optics and nanoplasmonics in new wavelength ranges.

© 2011 Optical Society of America

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  1. J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
    [CrossRef]
  2. V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98, 111105 (2011).
    [CrossRef]
  3. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  4. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
    [CrossRef]
  5. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
    [CrossRef]
  6. E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
    [CrossRef] [PubMed]
  7. M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
    [CrossRef]
  10. V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
    [CrossRef] [PubMed]
  11. V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, “Cavity behaviour of second and third harmonic inhomogeneous solutions of Maxwell’s equations,” Waves Random Complex Media 20, 319–331 (2010).
    [CrossRef]
  12. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
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    [CrossRef]
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    [CrossRef]
  15. M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
    [CrossRef]
  16. M. A. Vincenti, D. de Ceglia, V. Roppo, and M. Scalora, “Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths,” Opt. Express 19, 2064–2078 (2011).
    [CrossRef] [PubMed]
  17. A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
    [CrossRef] [PubMed]
  18. R. Soref, R. E. Peale, and W. Buchwald, “Longwave plasmonics on doped silicon and silicides,” Opt. Express 16, 6507–6514 (2008).
    [CrossRef] [PubMed]
  19. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
    [CrossRef] [PubMed]
  20. E. D. Palik, “Handbook of Optical Constants of Solids,” (Academic, 1985).
  21. R. W. Boyd, “Nonlinear Optics,” (Academic, 2008).
  22. M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
    [CrossRef]
  23. V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
    [CrossRef]
  24. M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
    [CrossRef]
  25. S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
    [CrossRef]
  26. O. Voskoboynikov, G. Dyankov, and C. M. J. Wijers, “Left handed composite materials in the optical range,” Microelectron. J. 36, 564–566 (2005).
    [CrossRef]
  27. Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
    [CrossRef] [PubMed]

2011 (3)

2010 (2)

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, “Cavity behaviour of second and third harmonic inhomogeneous solutions of Maxwell’s equations,” Waves Random Complex Media 20, 319–331 (2010).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

2009 (3)

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
[CrossRef]

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

2008 (4)

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

R. Soref, R. E. Peale, and W. Buchwald, “Longwave plasmonics on doped silicon and silicides,” Opt. Express 16, 6507–6514 (2008).
[CrossRef] [PubMed]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

2007 (3)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high transparency in the visible range,” Appl. Phys. Lett. 90, 174113 (2007).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

2006 (3)

J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
[CrossRef]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

2005 (2)

O. Voskoboynikov, G. Dyankov, and C. M. J. Wijers, “Left handed composite materials in the optical range,” Microelectron. J. 36, 564–566 (2005).
[CrossRef]

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

1987 (1)

S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
[CrossRef]

1962 (3)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Akozbek, N.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high transparency in the visible range,” Appl. Phys. Lett. 90, 174113 (2007).
[CrossRef]

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Alonzo, M.

Anderson, E. H.

J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Attwood, D. T.

J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
[CrossRef]

Belardini, A.

Bertolotti, M.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
[CrossRef] [PubMed]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Bloemer, M.

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high transparency in the visible range,” Appl. Phys. Lett. 90, 174113 (2007).
[CrossRef]

Bloemer, M. J.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
[CrossRef]

Boyd, R. W.

R. W. Boyd, “Nonlinear Optics,” (Academic, 2008).

Buchwald, W.

Cappeddu, M. G.

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

Centini, M.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Chauvet, M.

Chemla, D. S.

S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
[CrossRef]

Cojocaru, C.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, “Cavity behaviour of second and third harmonic inhomogeneous solutions of Maxwell’s equations,” Waves Random Complex Media 20, 319–331 (2010).
[CrossRef]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

D’Aguanno, G.

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high transparency in the visible range,” Appl. Phys. Lett. 90, 174113 (2007).
[CrossRef]

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
[CrossRef]

D’Orazio, A.

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

de Ceglia, D.

M. A. Vincenti, D. de Ceglia, V. Roppo, and M. Scalora, “Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths,” Opt. Express 19, 2064–2078 (2011).
[CrossRef] [PubMed]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dyankov, G.

O. Voskoboynikov, G. Dyankov, and C. M. J. Wijers, “Left handed composite materials in the optical range,” Microelectron. J. 36, 564–566 (2005).
[CrossRef]

Fazio, E.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

Foreman, J. V.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Halioua, Y.

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

Haus, J. W.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
[CrossRef]

Hillenbrand, R.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Kandidov, V. P.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Kapteyn, H. C.

J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
[CrossRef]

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

Kosareva, O. G.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Mandel, P.

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

Mattiucci, N.

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high transparency in the visible range,” Appl. Phys. Lett. 90, 174113 (2007).
[CrossRef]

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
[CrossRef]

Menoni, C. S.

J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
[CrossRef]

Miller, D. A. B.

S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
[CrossRef]

Murnane, M. M.

J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
[CrossRef]

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Palik, E. D.

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

Peale, R. E.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interaction between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Pettazzi, F.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

Podolskiy, V. A.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Raineri, F.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

Raj, R.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

Rocca, J. J.

J. J. Rocca, H. C. Kapteyn, D. T. Attwood, M. M. Murnane, C. S. Menoni, and E. H. Anderson, “Tabletop lasers in the extreme ultraviolet,” Opt. Photon. News 17, 30–38 (2006).
[CrossRef]

Roppo, V.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

M. A. Vincenti, D. de Ceglia, V. Roppo, and M. Scalora, “Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths,” Opt. Express 19, 2064–2078 (2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, “Cavity behaviour of second and third harmonic inhomogeneous solutions of Maxwell’s equations,” Waves Random Complex Media 20, 319–331 (2010).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Sagnes, I.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Scalora, M.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

M. A. Vincenti, D. de Ceglia, V. Roppo, and M. Scalora, “Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths,” Opt. Express 19, 2064–2078 (2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, “Cavity behaviour of second and third harmonic inhomogeneous solutions of Maxwell’s equations,” Waves Random Complex Media 20, 319–331 (2010).
[CrossRef]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
[CrossRef]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high transparency in the visible range,” Appl. Phys. Lett. 90, 174113 (2007).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
[CrossRef]

Schmitt-Rink, S.

S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
[CrossRef]

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

Sibilia, C.

E. Fazio, F. Pettazzi, M. Centini, M. Chauvet, A. Belardini, M. Alonzo, C. Sibilia, M. Bertolotti, and M. Scalora, “Complete spatial and temporal locking in phase- mismatched second-harmonic generation,” Opt. Express 17, 3141–3147 (2009).
[CrossRef] [PubMed]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Sivco, D. L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
[CrossRef] [PubMed]

Soref, R.

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[CrossRef]

Thommen, Q.

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

Trull, J.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, “Cavity behaviour of second and third harmonic inhomogeneous solutions of Maxwell’s equations,” Waves Random Complex Media 20, 319–331 (2010).
[CrossRef]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313, 1595 (2006).
[CrossRef] [PubMed]

Vilaseca, R.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Generation efficiency of the second harmonic inhomogeneous component,” Opt. Lett. 36, 1809–1811(2011).
[CrossRef] [PubMed]

V. Roppo, C. Cojocaru, J. Trull, R. Vilaseca, and M. Scalora, “Cavity behaviour of second and third harmonic inhomogeneous solutions of Maxwell’s equations,” Waves Random Complex Media 20, 319–331 (2010).
[CrossRef]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80, 043834 (2009).
[CrossRef]

Vincenti, M. A.

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98, 111105 (2011).
[CrossRef]

M. A. Vincenti, D. de Ceglia, V. Roppo, and M. Scalora, “Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths,” Opt. Express 19, 2064–2078 (2011).
[CrossRef] [PubMed]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second and third harmonic generation in metal-based structures,” Phys. Rev. A 82, 043828(2010).
[CrossRef]

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-IR ranges,” Phys. Rev. A 77, 033848 (2008).
[CrossRef]

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

Voskoboynikov, O.

O. Voskoboynikov, G. Dyankov, and C. M. J. Wijers, “Left handed composite materials in the optical range,” Microelectron. J. 36, 564–566 (2005).
[CrossRef]

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
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O. Voskoboynikov, G. Dyankov, and C. M. J. Wijers, “Left handed composite materials in the optical range,” Microelectron. J. 36, 564–566 (2005).
[CrossRef]

Zheltikov, A. M.

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
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Appl. Phys. (1)

M. A. Vincenti, A. D’Orazio, M. G. Cappeddu, N. Akozbek, M. J. Bloemer, and M. Scalora, “Semiconductor-based superlens for subwavelength resolution below the diffraction limit at extreme ultraviolet frequencies,” Appl. Phys. 105, 103103–103108 (2009).
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Appl. Phys. B (1)

M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, J. W. Haus, and A. M. Zheltikov, “Negative refraction of ultra-short electromagnetic pulses,” Appl. Phys. B 81, 393–402(2005).
[CrossRef]

Appl. Phys. Lett. (2)

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high transparency in the visible range,” Appl. Phys. Lett. 90, 174113 (2007).
[CrossRef]

V. Roppo, J. V. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98, 111105 (2011).
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Metamaterials (1)

V. Roppo, M. Centini, D. de Ceglia, M. A. Vincenti, J. W. Haus, N. Akozbek, M. J. Bloemer, and M. Scalora, “Anomalous momentum states, non-specular reflections and negative refraction of phase-locked, second harmonic pulses,” Metamaterials 2, 135–144 (2008).
[CrossRef]

Microelectron. J. (1)

O. Voskoboynikov, G. Dyankov, and C. M. J. Wijers, “Left handed composite materials in the optical range,” Microelectron. J. 36, 564–566 (2005).
[CrossRef]

Nat. Mater. (1)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007).
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Phys. Rev. A (4)

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second harmonic generation: walk-off and phase-locked twin pulses in negative index media,” Phys. Rev. A 76, 033829 (2007).
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Supplementary Material (1)

» Media 1: MOV (217 KB)     

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Figures (5)

Fig. 1
Fig. 1

Dielectric constant of GaP (left) and GaAs (right), taken from [22]. The regions of negative dielectric constant ( 100 nm 250 nm ) are denoted by the shaded areas.

Fig. 2
Fig. 2

Generic scheme of the interaction. The incident fields need not necessarily be collinear.

Fig. 3
Fig. 3

(Media 1) Snapshot of a TM-polarized pump pulse propagation 30 fs in duration tuned to 670 nm after it crosses the interface into GaP and generates SH and TH fields. The material is denoted by white boundaries and it is surrounded by air on both sides. (Top row) TM-polarized fields. (Bottom row) TE-polarized fields. Part of the signals are specularly reflected and part is transmitted with similar results for all generated fields. Only the pump refracts into the medium proceeds as predicted by Snell’s law. The SH and TH fields are locked to the pump.”

Fig. 4
Fig. 4

Pump (red), SH (blue), and TH (magenta) momentum refraction angles. The pump’s momentum refraction angles coincide well with predictions made using Snell’s law. Pump tuning at 670 nm (a) and 1200 nm (b). The angles shown for the momenta of SH and TH beams refer only to the inhomogeneous portions of the signals, especially in (b) where both homogeneous and inhomogeneous SH signals are allowed in the absence of absorption.

Fig. 5
Fig. 5

Phase-locked fundamental (red shell), SH (blue shell), and TH (magenta shell) TM-polarized pulses. Pump momentum and energy nearly always overwhelm corresponding SH and TH values, so that the total momentum of the system (in green) is always approximately equal to the pump’s momentum.

Equations (14)

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E = ( E x E y E z ) = ( i ( E TE x ω e i ω t + ( E TE x ω ) * e i ω t + E TE x 2 ω e 2 i ω t + ( E TE x 2 ω ) * e 2 i ω t + E TE x 3 ω e 3 i ω t + ( E TE x 3 ω ) * e 3 i ω t ) + j ( E TM y ω e i ω t + ( E TM y ω ) * e i ω t + E TM y 2 ω e 2 i ω t + ( E TM y 2 ω ) * e 2 i ω t + E TM y 3 ω e 3 i ω t + ( E TM y 3 ω ) * e 3 i ω t ) + k ( E TM z ω e i ω t + ( E TM z ω ) * e i ω t + E TM z 2 ω e 2 i ω t + ( E TM z 2 ω ) * e 2 i ω t + E TM z 3 ω e 3 i ω t + ( E TM z 3 ω ) * e 3 i ω t ) )
H = ( H x H y H z ) = ( i ( H TM x ω e i ω t + ( H TM x ω ) * e i ω t + H TM x 2 ω e 2 i ω t + ( H TM x 2 ω ) * e 2 i ω t + H TM x 3 ω e 3 i ω t + ( H TM x 3 ω ) * e 3 i ω t ) + j ( H TE y ω e i ω t + ( H TE y ω ) * e i ω t + H TE y 2 ω e 2 i ω t + ( H TE y 2 ω ) * e 2 i ω t + H TE y 3 ω e 3 i ω t + ( H TE y 3 ω ) * e 3 i ω t ) + k ( H TE z ω e i ω t + ( H TE z ω ) * e i ω t + H TE z 2 ω e 2 i ω t + ( H TE z 2 ω ) * e 2 i ω t + H TE z 3 ω e 3 i ω t + ( H TE z 3 ω ) * e 3 i ω t ) ) .
( P NL , x ( 2 ) P NL , y ( 2 ) P NL , z ( 2 ) ) = 2 d 14 ( E y E z E x E z E x E y ) ,
P NL , x ( 2 ) = 2 d 14 ( ( E TM y 2 ω ( E TM z ω ) * + ( E TM y ω ) * E TM z 2 ω + E TM y 3 ω ( E TM z 2 ω ) * + ( E TM y 2 ω ) * E TM z 3 ω ) e i ω t + + ( E TM y ω E TM z ω + E TM y 3 ω ( E TM z ω ) * + ( E TM y ω ) * E TM z 3 ω ) e 2 i ω t + + ( E TM y 2 ω E TM z ω + E TM y ω E TM z 2 ω ) e 3 i ω t )
P NL , y ( 2 ) = 2 d 14 ( ( E TE x 2 ω ( E TM z ω ) * + ( E TE x ω ) * E TM z 2 ω + E TE x 3 ω ( E TM z 2 ω ) * + ( E TE x 2 ω ) * E TM z 3 ω ) e i ω t + + ( E TE x ω E TM z ω + E TE x 3 ω ( E TM z ω ) * + ( E TE x ω ) * E TM z 3 ω ) e 2 i ω t + + ( E TE x 2 ω E TM z ω + E TE x ω E TM z 2 ω ) e 3 i ω t )
P NL , z ( 2 ) = 2 d 14 ( ( E TE x 2 ω ( E TM y ω ) * + ( E TE x ω ) * E TM y 2 ω + E TE x 3 ω ( E TM y 2 ω ) * + ( E TE x 2 ω ) * E TM y 3 ω ) e i ω t + + ( E TE x ω E TM y ω + E TE x 3 ω ( E TM y ω ) * + ( E TE x ω ) * E TM y 3 ω ) e 2 i ω t + + ( E TE x 2 ω E TM y ω + E TE x ω E TM y 2 ω ) e 3 i ω t ) .
P ¨ b , ω + γ ˜ b , ω P ˙ b , ω + ω ˜ 0 , b , ω 2 P b , ω n 0 , b e 2 λ 0 2 m b * c 2 E ω + e λ 0 m b * c 2 ( 1 2 E ω * · P b , 2 ω + + 2 E 2 ω · P b , ω * + 2 3 E 2 ω * · P b , 3 ω + 3 2 E 3 ω · P b , 2 ω * ) + e λ 0 m b * c 2 ( ( P ˙ b , ω * + i ω P b , ω * ) × H 2 ω + + ( P ˙ b , 2 ω 2 i ω P b , 2 ω ) × H ω * + + ( P ˙ b , 2 ω * + 2 i ω P b , 2 ω * ) × H 3 ω + + ( P ˙ b , 3 ω 3 i ω P b , 3 ω ) × H 2 ω * ) ,
P ¨ b , 2 ω + γ ˜ b , 2 ω P ˙ b , 2 ω + ω ˜ 0 , b , 2 ω 2 P b , 2 ω n 0 , b e 2 λ 0 2 m b * c 2 E 2 ω + e λ 0 m b * c 2 ( E ω · P b , ω + 1 3 E ω * · P b , 3 ω + 3 E 3 ω · P b , ω * ) + e λ 0 m b * c 2 ( ( P ˙ b , ω i ω P b , ω ) × H ω + + ( P ˙ b , ω * + i ω P b , ω * ) × H 3 ω + + ( P ˙ b , 3 ω 3 i ω P b , 3 ω ) × H ω * ) ,
P ¨ b , 3 ω + γ ˜ b , 3 ω P ˙ b , 3 ω + ω ˜ 0 , b , 3 ω 2 P b , 3 ω n 0 , b e 2 λ 0 2 m b * c 2 E 3 ω + e λ 0 m b * c 2 ( 1 2 E ω · P b , 2 ω + + 2 E 2 ω · P b , ω ) + e λ 0 m b * c 2 ( ( P ˙ b , 2 ω 2 i ω P b , 2 ω ) × H ω + + ( P ˙ b , ω i ω P b , ω ) × H 2 ω ) .
P NL , i ( 3 ) = j = 1 , 3 k = 1 , 3 l = 1 , 3 χ i , j , k , l ( 3 ) E j E k E l j , k , l = x , y , z .
P NL , x ( 3 ) = χ x x x x ( 3 ) E x 3 + 3 χ x x y y ( 3 ) E y 2 E x + 3 χ x x z z ( 3 ) E z 2 E x P NL , y ( 3 ) = χ y y y y ( 3 ) E y 3 + 3 χ x x y y ( 3 ) E x 2 E y + 3 χ y y z z ( 3 ) E z 2 E y P NL , z ( 3 ) = χ z z z z ( 3 ) E z 3 + 3 χ z z x x ( 3 ) E x 2 E z + 3 χ z z y y ( 3 ) E y 2 E z .
P ξ , y ˜ ( τ ) = 1 c 2 ξ = 0 ξ = L y ˜ = y ˜ = S ξ ( y ˜ , ξ , τ ) d y ˜ d ξ ,
S ξ , y ˜ ( y ˜ , ξ , τ ) = c 4 π E × H
θ r , ω ( τ ) = tan 1 [ P y ˜ , ω ( τ ) / P ξ , ω ( τ ) ] .

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