Plasmonic Fano resonance and dip of Au-SiO2-Au nanomatryoshka
© Liaw et al.; licensee Springer. 2013
Received: 15 September 2013
Accepted: 22 October 2013
Published: 8 November 2013
This study theoretically investigates Fano resonances and dips of an Au-SiO2-Au nanomatryoshka that is excited by a nearby electric dipole. An analytical solution of dyadic Green's functions is used to analyze the radiative and nonradiative power spectra of a radial dipole in the proximity of a nanomatryoshka. From these spectra, the plasmon modes and Fano resonances that accompany the Fano dips are identified. In addition, the scattering and absorption spectra of a nanomatryoshka that is illuminated by a plane wave are investigated to confirm these modes and Fano dips. Our results reveal that a Fano dip splits each of the dipole and quadrupole modes into bonding and anti-bonding modes. The Fano dip and resonance result from the destructive interference of the plasmon modes of the Au shell and the Au core. The Fano factors that are obtained from the nonradiative power spectra of the Au shell and the Au core of a nanomatryoshka are in accordance with those obtained from the absorption cross section spectra. Moreover, these Fano factors increase as the plasmonic coupling of the Au shell with the core increases for both dipole and quadrupole modes.
KeywordsNanomatryoshka Au-SiO2-Au Fano resonance Fano dip Fano factor Dyadic Green’s function Radiative power Nonradiative power Scattering efficiency Absorption efficiency
The interaction of an emitter with a nearby plasmonic nanostructure is an important topic in nanophotonics and nanooptics [1–7]. The effects of the surface-enhanced fluorescence of a plasmonic nanostructure on the photoluminescence of a molecule or quantum dot in its proximity have recently become more important [5–9]. Owing to the localized surface plasmon resonances (LSPR), the photoluminescence of an emitter can be modified - either enhanced or quenched . More recently, the Fano resonance and dip of the external interference of two or more coupled plasmonic nanostructures, such as a dimer of two nanorods, have been studied [10–16]. Luk'yanchuk et al. provided a detailed review of Fano resonance, particularly that associated with external interference . In the past decade, various plasmonic nanocomposites have been synthesized and proposed to exhibit Fano resonance, such as the Au-SiO2-Au nanomatryoshka [18–21]. In addition, the symmetry breaking of a nanomatryoshka due to the offset of the core from the shell can induce significant Fano resonance . This paper studies the Fano resonance and dip of the internal interference in a nanomatryoshka, which is the electromagnetic (EM) coupling between Au shell and Au core. In particular, the effects of the Fano resonance and dip on the dipole and quadrupole modes are discussed. The Fano resonances and dips of an Au-SiO2-Au nanomatryoshka that are induced by a nearby dipole or an incident plane wave are investigated theoretically. The former phenomenon is analyzed using the dyadic Green's function in terms of spherical harmonic wave functions , and the latter is analyzed using the Mie theory . The plasmon modes of this multi-layered structure are discussed. The Fano factors of the Au core and the Au shell of a nanomatryoshka that are obtained from the nonradiative power spectrum of an electric dipole and the absorption spectrum of a plane wave are analyzed and quantitatively compared. We have calculated the responses of a tangential dipole as well as a radial dipole interacting with the Ag nanoshell . Both results at these plasmon modes are in accordance. However, the features of the plasmon modes of nanoshell excited by the radial dipole are more pronounced than those by the tangential dipole. Therefore, we are only dedicated to studying the responses of a radial dipole interacting with nanomatryoshka in this paper.
where [10–12]. In Equation 4, q, λ0, and δ f are the Fano factor, the central wavelength, and the bandwidth, respectively. Here, A is a constant for amplitude. Below, this profile will be used to fit the spectra of the nonradiative powers or absorption efficiencies of the Au shell and the Au core at the Fano resonance.
Results and discussion
Fano dips and resonances of the dipole and quadrupole modes of nanomatryoshka in water
Dipole mode (nm)
Quadrupole mode (nm)
Fano dip/ resonance
Fano dip/ resonance
Parameters of Fano line-shape function for Au core and shell of nanomatryoshka at dipole and quadrupole modes
Dipole (d = 25 nm)
Dipole (d = 30 nm)
Dipole (d = 25 nm)
For the quadrupole mode, another Fano dip is observed in the radiative power spectrum (n = 2) in Figure 2a at 568 nm between the bonding mode and the anti-bonding mode for d = 25 nm. The corresponding Fano resonance is observed at 590 nm in the nonradiative power spectrum of Figure 2b. Notice that the peak at 530 nm in Figure 2b is associated with the interband transition (absorption band), rather than any plasmon mode. Accordingly, the absorption band at 520 to 530 nm is observed for each order (n = 1, 2, 3,…) component of the nonradiative power. Similarly, the Fano dip at 571 nm in the SCS spectrum (n = 2) for a plane wave and the Fano resonance at 587 nm in the ACS spectrum are observed in Figure 3. In contrast to the dipole mode, the quadrupolar bonding and anti-bonding modes and the Fano dip are not pronounced in the radiative power or SCS spectra; only an indication of a shoulder next to the dipolar anti-bonding mode is observed. However, using the order mode analysis, we can identify these features of the quadrupole mode from the component of n = 2.
Subsequently, the components of the Au shell and core are decomposed from the nonradiative power spectrum of the nanomatryoshka, and then fitted by the Fano line-shape function in the region of 550 to 650 nm. The Fano factors for t2 = 15 nm that are extracted from and are q1 = -11.63 and q2 = 2.97, respectively, where d = 25 nm. The Fano factors that are obtained from the absorption efficiency spectra of the Au core and the Au shell are q1 = - 14.06 and q2 = 1.89 (Table 2). In contrast, the Fano factors of a nanomatryoshka with a thinner silica layer of t2 = 13 nm are q1 = -12.74, q2 = 4.34 (nonradiative power) and q1 = -15.04 and q2 = 2.85 (ACS), respectively. Comparing the results of t2 = 13 nm and t2 = 15 nm, we find that stronger internal interferences between two coupled nanostructures (Au shell and core) correspond to larger Fano factors, again. In summary, as the silica layer becomes thinner, the internal coupling between the Au shell and the Au core increases, as revealed by the increase in the Fano factors for both dipole and quadrupole modes.
The Fano resonances and dips of an Au-SiO2-Au nanomatryoshka induced by an electric dipole or a plane wave were investigated theoretically. A Fano dip is the local minimum in the radiative power spectrum (electric dipole) or the scattering efficiency spectrum (plane wave), which is caused by the coupling of destructive interference between the plasmon modes of the Au core and the Au shell. The corresponding Fano resonance is the local maximum of the nonradiative power spectrum (electric dipole) or absorption efficiency spectrum (plane wave), which is very close to the Fano dip. Numerical results herein reveal that a Fano dip divides each of the dipole and the quadrupole modes into bonding and anti-bonding modes. This is to say that the Fano dip (resonance), which is a dark mode, is a phenomenon that arises from the maximum coupling between the Au shell and the core, which induces the strongest internal dissipation and the least radiation. Moreover, the Fano factors of the Au core and the Au shell of a nanomatryoshka quantify coupling around the Fano resonance. These Fano factors that are obtained from the nonradiative power spectrum of an electric dipole are in accordance with those obtained from the absorption spectrum of a plane wave. Additionally, these Fano factors were found to increase with plasmonic coupling.
Localized surface plasmon resonances
Absorption cross section
Extinction cross section
Scattering cross section.
This work was carried out as part of a research sponsored by the National Science Council, Taiwan (NSC 99-2221-E-182-030-MY3, NSC 100-2221-E-002-041-MY2) and Chang Gung Memorial Hospital (CMRPD290042).
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