Research ArticleAPPLIED OPTICS

Active quantum plasmonics

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Science Advances  18 Dec 2015:
Vol. 1, no. 11, e1501095
DOI: 10.1126/sciadv.1501095
  • Fig. 1 Schematics of the mechanism underlying the proposed bias-control strategy for active plasmonics.

    The evolution of the electron tunneling barrier across a nanoparticle junction is shown for two situations. (A) The junction width is reduced from S1 to S2. The Fermi levels EF of the left and right leads are aligned. (B) A bias U is applied to the left lead, whereas the width of the junction S is kept fixed. The shaded areas represent the tunneling barrier for the electrons at the Fermi energy before (gray) and after (red) the modification of the tunneling barrier, by changing the junction width (A) and the bias (B). The presence of the incident electromagnetic field at frequency ω induces the modulation of one-electron potentials (vertical arrow on the top left corner of the panels). Horizontal green and blue arrows show, respectively, the ac current Jω due to the optical potential and the dc current Jdc due to applied bias U.

  • Fig. 2 Optical response of the systems under study.

    The polarization of the incident light is illustrated with blue arrows. (A) The absorption cross section per unit length σ/l calculated for a cylindrical core-shell NM (R1 = 39.2 Å, R2 = 47.7 Å, R3 = 61 Å). The NM geometry is given by the radius of the core R1, the internal radius of the shell R2, and the external radius of the shell R3 [see (C)]. The core-shell gap in this case is S = R2R1 = 8.5 Å. The absorption resonances are labeled according to the underlying plasmonic modes (Embedded Image, bonding hybridized plasmon; ω+, resonance with core character; ωc+, antibonding mode with shell character). (B) The absorption cross section σ for a spherical dimer formed by two spherical nanoparticles with radius R = 21.7 Å, separated by a gap of width S = 8.5 Å. Absorption resonances correspond to the bonding dipolar mode at ωd and a bonding quadrupolar mode at ωq. (C) The near-field distribution calculated for the Embedded Image plasmon mode of the NM. (D) The near-field distribution calculated for the ωd plasmon mode of the spherical dimer. The most bias-sensitive resonances are marked with red arrows. The calculations consider an electronic density that corresponds to Na metal.

  • Fig. 3 Effects of applied bias on the plasmonic modes of the NM and the spherical dimer.

    (A and B) TDDFT results for the absorption spectra of a cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å) and a spherical dimer (R = 21.7 Å) with gap width S = 6.4 Å. (C) Absorption cross section per unit length σ/l calculated with QCM for the cylindrical NM with the same geometry as in (A). (D) Time evolution of the dipole induced in the NM of (A) by an incident pulse of light resonant with the Embedded Image plasmon mode and polarized perpendicularly to the symmetry axis. The bias is applied at time t = 2 fs. The values of the applied bias are detailed in the insets.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/11/e1501095/DC1

    Details of quantum mechanical calculations within the TDDFT

    Fig. S1. Effective one-electron potential (A) and ground-state electron density (B) calculated with density functional theory for the cylindrical NMs with different gap sizes.

    Fig. S2. Frequency-dependent absorption cross section per unit length calculated with the TDDFT for the infinite cylinder with radius R = 61 Å.

    Fig. S3. Dependence of the absorption spectra of the cylindrical NM (A) and spherical dimer (B) on the size of the plasmonic gap.

    Fig. S4. Effective one-electron potentials (A) and Hartree and exchange correlation contributions to the one-electron potentials (B) calculated with density functional theory for cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å) with a bias applied between the core and the shell.

    Fig. S5. (A to D) Electron dynamics triggered by the bias applied between the core and the shell of the cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å).

    Fig. S6. Applied bias dependence of the absorption cross section per unit length calculated for the cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å) using the TDDFT (A and B) and QCM (C) approaches within the frequency range corresponding to the bonding hybridized plasmon mode.

    Fig. S7. Applied bias dependence of the absorption cross section per unit length calculated with the TDDFT for the cylindrical NM within the frequency range corresponding to the plasmon mode with core character.

    Fig. S8. Time evolution of the effective bias triggered by the slowly varying external potential applied to the spherical dimer.

    Fig. S9. Time evolution of the induced dipole (A) and the effective bias (B) calculated with the TDDFT for the cylindrical NM in response to the illumination by the “probe” pulse and sudden change in the applied bias.

    Fig. S10. Current-voltage characteristic of the cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å).

    Additional calculations for different sizes of gap S

    Fig. S11. Applied bias dependence of the absorption cross section per unit length calculated with the TDDFT for the cylindrical NM (R1 = 40.3 Å, R2 = 47.7 Å, R3 = 61 Å).

    Fig. S12. (A and B) TDDFT calculations for the spherical dimer with a gap of S = 5 Å.

    References (4561)

  • Supplementary Materials

    This PDF file includes:

    • Details of quantum mechanical calculations within the TDDFT
    • Fig. S1. Effective one-electron potential (A) and ground-state electron density (B) calculated with density functional theory for the cylindrical NMs with different gap sizes.
    • Fig. S2. Frequency-dependent absorption cross section per unit length calculated with the TDDFT for the infinite cylinder with radius R = 61 Å.
    • Fig. S3. Dependence of the absorption spectra of the cylindrical NM (A) and spherical dimer (B) on the size of the plasmonic gap.
    • Fig. S4. Effective one-electron potentials (A) and Hartree and exchange correlation contributions to the one-electron potentials (B) calculated with density functional theory for cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å) with a bias applied between the core and the shell.
    • Fig. S5. (A to D) Electron dynamics triggered by the bias applied between the core and the shell of the cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å).
    • Fig. S6. Applied bias dependence of the absorption cross section per unit length calculated for the cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å) using the TDDFT (A and B) and QCM (C) approaches within the frequency range corresponding to the bonding hybridized plasmon mode.
    • Fig. S7. Applied bias dependence of the absorption cross section per unit length calculated with the TDDFT for the cylindrical NM within the frequency range corresponding to the plasmon mode with core character.
    • Fig. S8. Time evolution of the effective bias triggered by the slowly varying external potential applied to the spherical dimer.
    • Fig. S9. Time evolution of the induced dipole (A) and the effective bias (B) calculated with the TDDFT for the cylindrical NM in response to the illumination by the “probe” pulse and sudden change in the applied bias.
    • Fig. S10. Current-voltage characteristic of the cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å).
    • Additional calculations for different sizes of gap S
    • Fig. S11. Applied bias dependence of the absorption cross section per unit length calculated with the TDDFT for the cylindrical NM (R1 = 41.3 Å, R2 = 47.7 Å, R3 = 61 Å).
    • Fig. S12. (A and B) TDDFT calculations for the spherical dimer with a gap of S = 5 Å.
    • References (45–61)

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