Abstract

We revisit the electrodynamics of resonant high-Q interactions in atomic systems with a view to gaining insights into the design of meta-atoms and hence bulk metamaterials with profoundly different electromagnetic responses. The relevance of phase coherence and nonlinearity in charged systems is emphasized, as is the need to take care over defining how one specifies effective boundaries and cavities that ultimately determine light–matter interactions. Radically new material properties become apparent once one designs organized clusters of small numbers of atoms or meta-atoms for which the usually applied random phase approximation (RPA) does not apply. The RPA relies on averages in sufficiently large volumes consisting of large numbers of interacting systems, while our model assumes a small volume with averages in time, i.e., ergodicity. New meaning is given to the concept of effective and practically useful constitutive parameters, based on this very fundamental point of view, which is important to metamaterials.

© 2013 Chinese Laser Press

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References

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  1. H. Ehrenreich and M. H. Cohen, “Self consistent field approach to the many electron problem,” Phys. Rev. 115, 786–790 (1959).
    [CrossRef]
  2. L. Solymar, Lectures on Electromagnetic Theory (Oxford University, 1984), p. 166.
  3. H. R. Stuart and A. Pidwebetsky, “Electrically small antenna elements using negative permittivity resonator,” IEEE Trans. Antennas Propag. 54, 1644–1653 (2006).
    [CrossRef]
  4. R. Tsu, Superlattice to Nanoelectronics, 2nd ed. (Elsevier, 2011), Chaps. 2 and 7.
  5. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, 1963).
  6. M. Wegener, Extreme Nonlinear Optics (Springer, 2004).
  7. D. Bohm, Quantum Theory (Dover, 1989).
  8. C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” arXiv.org, arXiv:1206.3527v1 (2012).
  9. S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
    [CrossRef]
  10. W. E. Lamb and M. O. Scully, “The photoelectric effect without photons,” Center for Theoretical Studies Report (University of Miami, Coral Gables, February 1968).
  11. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [CrossRef]
  12. N. Bloembergen, Nonlinear Optics (W. A. Benjamin, 1965).
  13. C. R. Schwarze, D. A. Pommet, G. Flynn, and M. A. Fiddy, “Enhancement of χ3 in nanoparticle composite media exhibiting electrostriction and quantum confinement,” Waves Random Media 10, 43–52 (2000).
    [CrossRef]
  14. R. Tsu and M. A. Fiddy, “Single atom trapping of light,” in Proceedings of 2012 Progress in Electromagnetics Research Symposium (Electromagnetics Academy, 2012), pp. 1152–1155.
  15. R. Fitzpatrick, “Quantum mechanics,” lecture notes, http://farside.ph.utexas.edu/teaching/qmech/lectures/lectures.html .
  16. L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys. 19, 1163–1175 (1948).
    [CrossRef]
  17. J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antennas Propag. 44, 672–675 (1996).
    [CrossRef]
  18. G. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Philos. Mag. 15, 752–761 (1933).
  19. G. Gbur, “Invisibility physics: past, present, and future,” in Progress in Optics, E. Wolf, ed. (to be published).
  20. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. 49, 9838–9852 (2010).
    [CrossRef]
  21. M. Kafesaki, N.-H. Shen, S. Tzortzakis, and C. M. Soukoulis, “Optically switchable and tunable terahertz metamaterials through photoconductivity,” J. Opt. 14, 114008 (2012).
    [CrossRef]
  22. K. Y. Jung and F. L. Texeira, “Photonic crystals with a degenerate band edge: field enhancement effects and sensitivity analysis,” Phys. Rev. B 77, 125108 (2008).
    [CrossRef]
  23. A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).
  24. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
    [CrossRef]
  25. R. Tsu, Superlattice to Nanoelectronics, 2nd ed. (Elsevier, 2011), pp. 286–291.
  26. R. Tsu and L. Esaki, “Nonlinear optical response of conduction electrons in a superlattice,” Appl. Phys. Lett. 19, 246–248 (1971).
    [CrossRef]
  27. E. T. Jaynes, “The maser as a parametric amplifier,” in Quantum Electronics: A Symposium, C. H. Townes, ed. (Columbia University, 1960), pp. 287–292.
  28. A. Alu, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83, 081102(R) (2011).
    [CrossRef]
  29. D. R. Chowdhury, R. Singh, M. Reiten, J. Zhou, and A. J. Taylor, “Tailored resonator coupling for modifying the terahertz metamaterial response,” Opt. Express 19, 10679–10685 (2011).
    [CrossRef]

2012 (2)

M. Kafesaki, N.-H. Shen, S. Tzortzakis, and C. M. Soukoulis, “Optically switchable and tunable terahertz metamaterials through photoconductivity,” J. Opt. 14, 114008 (2012).
[CrossRef]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

2011 (3)

A. Alu, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83, 081102(R) (2011).
[CrossRef]

D. R. Chowdhury, R. Singh, M. Reiten, J. Zhou, and A. J. Taylor, “Tailored resonator coupling for modifying the terahertz metamaterial response,” Opt. Express 19, 10679–10685 (2011).
[CrossRef]

S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
[CrossRef]

2010 (1)

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. 49, 9838–9852 (2010).
[CrossRef]

2008 (1)

K. Y. Jung and F. L. Texeira, “Photonic crystals with a degenerate band edge: field enhancement effects and sensitivity analysis,” Phys. Rev. B 77, 125108 (2008).
[CrossRef]

2006 (1)

H. R. Stuart and A. Pidwebetsky, “Electrically small antenna elements using negative permittivity resonator,” IEEE Trans. Antennas Propag. 54, 1644–1653 (2006).
[CrossRef]

2000 (1)

C. R. Schwarze, D. A. Pommet, G. Flynn, and M. A. Fiddy, “Enhancement of χ3 in nanoparticle composite media exhibiting electrostriction and quantum confinement,” Waves Random Media 10, 43–52 (2000).
[CrossRef]

1996 (1)

J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antennas Propag. 44, 672–675 (1996).
[CrossRef]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

1971 (1)

R. Tsu and L. Esaki, “Nonlinear optical response of conduction electrons in a superlattice,” Appl. Phys. Lett. 19, 246–248 (1971).
[CrossRef]

1959 (1)

H. Ehrenreich and M. H. Cohen, “Self consistent field approach to the many electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

1948 (1)

L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys. 19, 1163–1175 (1948).
[CrossRef]

1933 (1)

G. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Philos. Mag. 15, 752–761 (1933).

Abrikosov, A. A.

A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, 1963).

Alu, A.

A. Alu, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83, 081102(R) (2011).
[CrossRef]

Baker-Jarvis, J.

S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
[CrossRef]

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (W. A. Benjamin, 1965).

Boardman, A. D.

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

Bohm, D.

D. Bohm, Quantum Theory (Dover, 1989).

Chikoti, A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Chowdhury, D. R.

Chu, L. J.

L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys. 19, 1163–1175 (1948).
[CrossRef]

Ciracì, C.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Cohen, M. H.

H. Ehrenreich and M. H. Cohen, “Self consistent field approach to the many electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

Dzyaloshinski, I. E.

A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, 1963).

Ehrenreich, H.

H. Ehrenreich and M. H. Cohen, “Self consistent field approach to the many electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

Esaki, L.

R. Tsu and L. Esaki, “Nonlinear optical response of conduction electrons in a superlattice,” Appl. Phys. Lett. 19, 246–248 (1971).
[CrossRef]

Fernandez-Dominguez, A. I.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Fiddy, M. A.

C. R. Schwarze, D. A. Pommet, G. Flynn, and M. A. Fiddy, “Enhancement of χ3 in nanoparticle composite media exhibiting electrostriction and quantum confinement,” Waves Random Media 10, 43–52 (2000).
[CrossRef]

R. Tsu and M. A. Fiddy, “Single atom trapping of light,” in Proceedings of 2012 Progress in Electromagnetics Research Symposium (Electromagnetics Academy, 2012), pp. 1152–1155.

Fietz, C.

C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” arXiv.org, arXiv:1206.3527v1 (2012).

Flynn, G.

C. R. Schwarze, D. A. Pommet, G. Flynn, and M. A. Fiddy, “Enhancement of χ3 in nanoparticle composite media exhibiting electrostriction and quantum confinement,” Waves Random Media 10, 43–52 (2000).
[CrossRef]

Gbur, G.

G. Gbur, “Invisibility physics: past, present, and future,” in Progress in Optics, E. Wolf, ed. (to be published).

Giessen, H.

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. 49, 9838–9852 (2010).
[CrossRef]

Gorkov, L. P.

A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, 1963).

Hill, R. T.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Holloway, C. L.

S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Jaynes, E. T.

E. T. Jaynes, “The maser as a parametric amplifier,” in Quantum Electronics: A Symposium, C. H. Townes, ed. (Columbia University, 1960), pp. 287–292.

Jung, K. Y.

K. Y. Jung and F. L. Texeira, “Photonic crystals with a degenerate band edge: field enhancement effects and sensitivity analysis,” Phys. Rev. B 77, 125108 (2008).
[CrossRef]

Kafesaki, M.

M. Kafesaki, N.-H. Shen, S. Tzortzakis, and C. M. Soukoulis, “Optically switchable and tunable terahertz metamaterials through photoconductivity,” J. Opt. 14, 114008 (2012).
[CrossRef]

Kim, S.

S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
[CrossRef]

Kuester, E. F.

S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
[CrossRef]

Lamb, W. E.

W. E. Lamb and M. O. Scully, “The photoelectric effect without photons,” Center for Theoretical Studies Report (University of Miami, Coral Gables, February 1968).

Liu, N.

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. 49, 9838–9852 (2010).
[CrossRef]

Maier, S. A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

McLean, J. S.

J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antennas Propag. 44, 672–675 (1996).
[CrossRef]

Mock, J. J.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Pendry, J. B.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Pidwebetsky, A.

H. R. Stuart and A. Pidwebetsky, “Electrically small antenna elements using negative permittivity resonator,” IEEE Trans. Antennas Propag. 54, 1644–1653 (2006).
[CrossRef]

Pommet, D. A.

C. R. Schwarze, D. A. Pommet, G. Flynn, and M. A. Fiddy, “Enhancement of χ3 in nanoparticle composite media exhibiting electrostriction and quantum confinement,” Waves Random Media 10, 43–52 (2000).
[CrossRef]

Reiten, M.

Scher, A. D.

S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
[CrossRef]

Schott, G.

G. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Philos. Mag. 15, 752–761 (1933).

Schwarze, C. R.

C. R. Schwarze, D. A. Pommet, G. Flynn, and M. A. Fiddy, “Enhancement of χ3 in nanoparticle composite media exhibiting electrostriction and quantum confinement,” Waves Random Media 10, 43–52 (2000).
[CrossRef]

Scully, M. O.

W. E. Lamb and M. O. Scully, “The photoelectric effect without photons,” Center for Theoretical Studies Report (University of Miami, Coral Gables, February 1968).

Shen, N.-H.

M. Kafesaki, N.-H. Shen, S. Tzortzakis, and C. M. Soukoulis, “Optically switchable and tunable terahertz metamaterials through photoconductivity,” J. Opt. 14, 114008 (2012).
[CrossRef]

Singh, R.

Smith, D. R.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Solymar, L.

L. Solymar, Lectures on Electromagnetic Theory (Oxford University, 1984), p. 166.

Soukoulis, C. M.

M. Kafesaki, N.-H. Shen, S. Tzortzakis, and C. M. Soukoulis, “Optically switchable and tunable terahertz metamaterials through photoconductivity,” J. Opt. 14, 114008 (2012).
[CrossRef]

C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” arXiv.org, arXiv:1206.3527v1 (2012).

Stuart, H. R.

H. R. Stuart and A. Pidwebetsky, “Electrically small antenna elements using negative permittivity resonator,” IEEE Trans. Antennas Propag. 54, 1644–1653 (2006).
[CrossRef]

Taylor, A. J.

Texeira, F. L.

K. Y. Jung and F. L. Texeira, “Photonic crystals with a degenerate band edge: field enhancement effects and sensitivity analysis,” Phys. Rev. B 77, 125108 (2008).
[CrossRef]

Tsu, R.

R. Tsu and L. Esaki, “Nonlinear optical response of conduction electrons in a superlattice,” Appl. Phys. Lett. 19, 246–248 (1971).
[CrossRef]

R. Tsu, Superlattice to Nanoelectronics, 2nd ed. (Elsevier, 2011), Chaps. 2 and 7.

R. Tsu, Superlattice to Nanoelectronics, 2nd ed. (Elsevier, 2011), pp. 286–291.

R. Tsu and M. A. Fiddy, “Single atom trapping of light,” in Proceedings of 2012 Progress in Electromagnetics Research Symposium (Electromagnetics Academy, 2012), pp. 1152–1155.

Tzortzakis, S.

M. Kafesaki, N.-H. Shen, S. Tzortzakis, and C. M. Soukoulis, “Optically switchable and tunable terahertz metamaterials through photoconductivity,” J. Opt. 14, 114008 (2012).
[CrossRef]

Urzhumov, Y.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Wegener, M.

M. Wegener, Extreme Nonlinear Optics (Springer, 2004).

Zhou, J.

Angew. Chem. Int. Ed. (1)

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. 49, 9838–9852 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

R. Tsu and L. Esaki, “Nonlinear optical response of conduction electrons in a superlattice,” Appl. Phys. Lett. 19, 246–248 (1971).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antennas Propag. 44, 672–675 (1996).
[CrossRef]

H. R. Stuart and A. Pidwebetsky, “Electrically small antenna elements using negative permittivity resonator,” IEEE Trans. Antennas Propag. 54, 1644–1653 (2006).
[CrossRef]

S. Kim, E. F. Kuester, C. L. Holloway, A. D. Scher, and J. Baker-Jarvis, “Boundary effects on the determination of metamaterial parameters from normal incidence reflection and transmission measurements,” IEEE Trans. Antennas Propag. 59, 2226–2240 (2011).
[CrossRef]

J. Appl. Phys. (1)

L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys. 19, 1163–1175 (1948).
[CrossRef]

J. Opt. (1)

M. Kafesaki, N.-H. Shen, S. Tzortzakis, and C. M. Soukoulis, “Optically switchable and tunable terahertz metamaterials through photoconductivity,” J. Opt. 14, 114008 (2012).
[CrossRef]

Opt. Express (1)

Philos. Mag. (1)

G. Schott, “The electromagnetic field of a moving uniformly and rigidly electrified sphere and its radiationless orbits,” Philos. Mag. 15, 752–761 (1933).

Phys. Rev. (1)

H. Ehrenreich and M. H. Cohen, “Self consistent field approach to the many electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

Phys. Rev. B (2)

K. Y. Jung and F. L. Texeira, “Photonic crystals with a degenerate band edge: field enhancement effects and sensitivity analysis,” Phys. Rev. B 77, 125108 (2008).
[CrossRef]

A. Alu, “Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83, 081102(R) (2011).
[CrossRef]

Phys. Rev. Lett. (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef]

Science (1)

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chikoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Waves Random Media (1)

C. R. Schwarze, D. A. Pommet, G. Flynn, and M. A. Fiddy, “Enhancement of χ3 in nanoparticle composite media exhibiting electrostriction and quantum confinement,” Waves Random Media 10, 43–52 (2000).
[CrossRef]

Other (14)

R. Tsu and M. A. Fiddy, “Single atom trapping of light,” in Proceedings of 2012 Progress in Electromagnetics Research Symposium (Electromagnetics Academy, 2012), pp. 1152–1155.

R. Fitzpatrick, “Quantum mechanics,” lecture notes, http://farside.ph.utexas.edu/teaching/qmech/lectures/lectures.html .

N. Bloembergen, Nonlinear Optics (W. A. Benjamin, 1965).

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

L. Solymar, Lectures on Electromagnetic Theory (Oxford University, 1984), p. 166.

W. E. Lamb and M. O. Scully, “The photoelectric effect without photons,” Center for Theoretical Studies Report (University of Miami, Coral Gables, February 1968).

R. Tsu, Superlattice to Nanoelectronics, 2nd ed. (Elsevier, 2011), Chaps. 2 and 7.

A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, 1963).

M. Wegener, Extreme Nonlinear Optics (Springer, 2004).

D. Bohm, Quantum Theory (Dover, 1989).

C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” arXiv.org, arXiv:1206.3527v1 (2012).

R. Tsu, Superlattice to Nanoelectronics, 2nd ed. (Elsevier, 2011), pp. 286–291.

G. Gbur, “Invisibility physics: past, present, and future,” in Progress in Optics, E. Wolf, ed. (to be published).

E. T. Jaynes, “The maser as a parametric amplifier,” in Quantum Electronics: A Symposium, C. H. Townes, ed. (Columbia University, 1960), pp. 287–292.

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Figures (1)

Fig. 1.
Fig. 1.

(a) m=1 spherical harmonic, (b) m=4, and (c) m=12.

Equations (18)

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

E(x)=E0exp(ikx)=m=m=imJm(kr)exp(imφ).
kθ2+kr2=εω2c2,
dv/dt+γv=emE
dv/dt+(·)v+γv=em(E+v×B)β2·n,
x ¨+γx˙+ω02x=eE/m
P=Nex=(Ne2/mϵ0)E/[ω02ω2iγω].
ϵ(ω)=1+(ωes2)/[ω02ω2iγω].
ϵ1(ω)=1+(ωes2){(ω02ω2)/[(ω02ω2)2+(γω)2]},
ϵ2(ω)=(ωes2){γω/[(ω02ω2)2+(γω)2]}.
ω2p1sspon=ω2p1s3d2p1s2/3πϵ0c3=γ=(2/3)8α5(mc2/)=6.3×108s1
100|x|2,1,±1=±(27/35)a0,
100|y|2,1,±1=i(27/35)a0,
100|z|2,1,0=2(27/35)a0,
E(r,ω)=E0(r,ω)+iωμ0μr(ω)VG(r,r,ω)js(r)d3r,
js(r)=iωqδ(rr).
β2(·J)+(ω2+iγω)J=iωωp2ε0E,
ε(ω)=1[ωp2/(ω2+iγω)],
εL(k,ω)=1ωp2ω2+iγωβ2|k|2,

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