Plasmon-polariton modes

As another example, we mention the hybrid plasmon-polariton modes in chains of noncontacting noble metal nanoparticles where the interaction of a photon and nanoparticles leads toe delocalized plasmon-polaritons (see (35) and... 

Extinction spectra for nanoparticles represented as a silver core covered by a carbon sheath in an insulating matrix (PMMA) will be analyzed in terms of the Mie relationships for sheathed cores [53, 54]. Here, an additional interface for which electrodynamic boundary conditions must be set up arises. Plasmon-polariton modes may be excited in both the core and the sheath. These modes, interacting through the inner interface, are responsible for the resulting extinction spectrum. 

S. A. Maier, P. G. Kik and H. A. Atwater, Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths Estimation of waveguide loss, Appl. Phys. Lett. 81(9), 1714-1716(2002). 

Equation (1.163) represents the dispersion relation of the surface plasmon polariton mode (SPP-mode), i.e. the relationship between the frequency co and the in-plane wavevector for SPPs propagating along the interface between a metal and a dielectric. 

Surface plasmon-polaritons (SPP), also referred as to surface plasma waves, are special modes of electromagnetic field which can exist at the interface between a dielectric and a metal that behaves like a nearly-iree electron plasma. A surface plasmon is a transverse-magnetic mode (magnetic vector is perpendicular to the direction of propagation of the wave and parallel to the plane of interface) and is characterized by its propagation constant and field distribution. The propagation constant, P can be expressed as follows ... 

TMM handles thin metallic films as well, as they are used in lO-sensors based on surface-plasmon-polaritons (SPP). SPPs appear at the dielectric-metal interface for TM polarization, exclusively. The sensor principle is to have a waveguide mode and the SPP close to resonance, and screen the resonance vs. angle or vs. wavelength to detect refractive index changes of the cladding. Figure 4 shows the resonance of the absorption vs. the... 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

No doubt, the present author has his own private consensus which, in spite of his efforts, may inject itself into the review. In order to offset such an undesirable bias, as much as possible, and perhaps putting the cart before the horse, the author will state here his own conclusions and beliefs I am convinced that electric field amplification and enhanced emission near SERS-active surfaces due to resonating metal excitations (surface-plasmon polaritons, plasmonlike modes, shape resonances, or electron-hole pairs) is an active mechanism in most of the systems studied. However, in most systems, this contribution, though an important one, is minor compared to the total enhancement possible in SERS. The major mechanism, in my opinion, must be a resonance mechanism, in the sense of a resonance Raman process, i.e., a mechanism by which a part of the system (molecule, molecule-metal atoms, metal surface) becomes a strong scatterer by virtue of its large resonance polarizability and not as a result of strong fields exerted by the other parts of the system . 

The considerable distinctions between optical spectra of a metal nanostmcture and corresponding bulk metal appear due to surface modes (plasmon-polariton resonances) in nanoparticles and size dependence of their optical constants. In the case of partially-ordered nanoparticle arrays these effects are of the collective nature because of strong electrodynamic coupling. The theoretical approach for regarding... 

We examined the effect of coupling between surface plasmon polariton (SPP) modes on the optical activity of metal nanostructures. By measuring the in-plane wave vector dependence on transmission and polarization azimuth rotation, we show that coupling of the SPP modes with orthogonal polarization localized at different interfaces is responsible for the optical activity in metal nanostructures. 

Instrumentation. In order to employ local enhancement of infrared absorption by surface plasmon polaritons that cause locally enhanced surface electromagnetic fields, a suitable optical arrangement is needed [295]. Surface enhanced infrared absorption spectroscopy can also be observed in the transmission mode [285, 296]. However, since no application of this approach in spectroelectrochemistry has been reported so far, it is not discussed further. 

Figure 1.16 Imaginary part of the complex polarizability a o)) for an Na cluster with N = 198 in units of Effective single-pair excitations, as well as the surface plasmon and the volume plasmon, are clearly resolved. For comparison the result of the local Drude theory is also given. In this case there is only one mode of excitation, the classical surface-plasmon polariton or Mie-resonance at coply/3. Because the frequency is scaled with this frequency the Drude curve peaks trivially at 1. For more explanation see text. Reproduced with permission from Reference [5]. Copyright 1985 by the American Physical Society...

No condition is found for they component of the field which can be set to zero. A solution with a non zero y component of the field will correspond to a TE (s-polarized) electromagnetic wave. However it can be easily shown from boundary conditions that such solution cannot exist [7]. Thus surface plasmon polaritons localized at the interfaces exist only in the TM (p-polarized) mode. 

From the surface plasmon-polariton wavevector (Eq. (1.163)) we can then obtain the wavelength of the surface plasmon-polariton A-spp which represents the period of the surface charge density oscillation and of the associated field distribution of the mode (see Fig. 1.6). In particular, the SPP wavelength can be found from the complex dispersion relation Eq. (1.163) by taking the real part. Writing the complex relative permittivity of the metal as m(ft>) = —1 I-pie" we can write the complex SPP wavevector as kx =... 

For higher order modes, the resonance condition for the multipolar polarizability in Eq. (3.4) approaches to p(o>) = -Sout, which is indeed the resonance condition of the planar surface plasmon polaritons of Sec. 1.3, i.e. plasmon resonance for a flat metal surface. This is because in multipolar modes fast charge oscillations practically cancel out the interaction between distant charges, therefore each small region on the surface of the metal behaves as in a planar bulk metal. These considerations however need to be taken with care, since at the large sizes at which... 

It has been shown that localized plasmon polaritons inthe region of sharp metal tips act in an analogous fashion, giving rise to TERS. In the usual mode of operation, TERS employs a sharp metal tip, which is illuminated from the outside to create a localized light source [42]. Alternatively, silver nanoparticles have been deposited on silica or titania surfaces and a silicon tip is used [43, 44]. TERS is rapidly becoming an important technique for microspectroscopy and is described in some detail in Chapter 11 of this book. 

Kovacs G (1982) Optical excitation of surface plasmon-polaritons in layered media. In Broadman AD (ed) Electromagnetic Surface Modes, pp 143-200. New York Wiley. 

Depending on the substrate excitations which are coupled with light into the SP mode, one distinguishes surface plasmon polaritons, surface phonon polaritons, surface exciton polaritons, etc. In this section we shall consider surface plasmon polaritons in some detail. This type of electromagnetic wave was first discussed by Sommerfeld in connection with the propagation of radiowaves along the Earth s surface (Sommerfeld 1909). 

In addition to the localized SP modes, metal/dielectric interfaces support surface plasmon polaritons (SPP), which propagate according to the dielectric properties of the interface at the local speed of light. The complex dispersion relationship for SPP propagation at a metal/dielectric interface is given by ... 

Therefore the dispersion of the LO plasmon-phonon states is formally equivalent to the dispersion of the TO photon-phonon states, with 4irne2/m replacing k2 c2. When the plasmon-phonon frequency to is plotted against fn instead of k, dispersion curves for the LO modes are obtained which are similar to the polariton dispersion curves, the TO phonons showing no dispersion with /n. 

Figure 1(a) shows the Kretschmann configuration [9] for the excitation of plasmon surface polaritons (surface plasmons for short) [10] in the attenuated total reflection (ATR) mode. When a p-polarized laser beam is irradiated at the (internal) incident angle 9t from the prism of a refractive index np above 6c, a strong nonradiative electromagnetic wave, i.e. a surface plasmon is excited at the resonant angle which propagates at the metal /electrolyte interface. 

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