Plasmon penetration depth

As follows from Fig. 5, the electromagnetic field of a surface plasmon reaches its maximum at the metal-dielectric interface and decays into both media. The field decay in the direction perpendicular to the metal-dielectric interface is characterized by the penetration depth Lp, which is defined as the distance from the interface at which the amplitude of the field decreases by a factor of 1/e ... 

The spectral dependence of the penetration depth of a surface plasmon at the interface between gold and a non-dispersive medium with a refractive index of 1.32 is shown in Fig. 6. As follows from Fig. 6, with an increasing wavelength, the portion of the electromagnetic field carried in the dielectric increases and the field of the surface plasmon extends farther into the dielectric. 

Fig. 6 Penetration depth of a surface plasm on into the metal upper plot) and dielectric (lower plot) as a fimction of wavelength for a surface plasmon propagating along the interface of gold and a dielectric (refractive index 1.32)...

Another example of a planar waveguide supporting surface plasmons is a thin metal film sandwiched between two semi-infinite dielectric media (Fig. 7). If the metal film is much thicker than the penetration depth of a surface plasmon at each metal-dielectric interface, this waveguide supports two TM modes, which correspond to two surface plasmons at the opposite boundaries of the metal film. When the metal thickness decreases, coupling between the two surface plasmons occurs, giving rise to mixed modes of electromagnetic field. 

The second type of perturbation is a homogenous change in the refractive index that occurs within a limited distance h from the surface of the metal film which is smaller than the penetration depth of a surface plasmon. Fig. 14, (herein referred as to surface refractive index change). Such a refractive index perturbation is characterized by a permittivity profile change e(x) s(x), where ... 

The perturbation of the effective index of a surface plasmon depends exponentially on the thickness of the layer within which the refractive index change occurs. For a thicknesses much larger than the penetration depth of the surface plasmon (h Ipd = 1/ Re /d )> the exponential term can be neglected and Eq. 60 simplifies to Eq. 57. For refractive index changes occurring within a layer thinner than the penetration depth of the field of fhe surface plasmon (h Ipd = 1/ Re /d ). the expressions for the perturbations in the propagation constant and the effective refractive index can be reduced to ... 

Figure 16 shows the sensitivity of the propagation constant Re 8fS)/8n)s and effective index (8ne /8n)s to a surface refractive index change calculated for a surface plasmon supported on gold and a refractive index change occurring within a 5 nm thick layer at the surface of the metal supporting a surface plasmon. As the layer thickness is much smaller than the penetration depth of the field of the surface plasmon on the considered structure, the sensitivity is a linear function of the thickness of the layer h. 

As noted above, previous reports of the SEIRA effect had attributed the enhancement to a similar mechanism similar to the one leading to the SERS effect, namely the excitation of surface plasmon polaritons. " Because the effect was observed with Ni, Pt and Pd as well as Ag, Nakao and Yamada recognized that the effect that they observed was caused by some mechanism other than the effect of excitation of surface plasmon polar-itons. Nakao and Yamada postulated that the effect of multiple reflection in the metal film, of the decrease in penetration depth of the IRE caused by the metal layer and/or the effect of local (chemical) interaction at the metal-sample interface might contribute to the enhancement. However, as will be discussed later in this chapter, none of these putative causes fully explains the enhancement. 

The metal NPs which have both size and optical penetration-depth smaller than wavelength of light, all atoms in those particles can be collectively excited. Hence, collective electronic oscillations are known as Mie plasmon. For Mie Plasmon, prominent optical resonance is observed in UV-Vis range. The resonance frequency of the oscillation depends on dielectric properties of the metal, surrounding medium. 

The penetration depth of the electromagnetic field due to surface plasmons has been extensively studied for planar SPR. The electromagnetic field in planar SPR decays exponentially from the surface, and the SPR sensor responds to the refractive index change upto 200 nm from the surface. In contrast to planar SPR, there is less information available on the sensing depth of metal nanoparticles. The electromagnetic field due to SPR in nanoparticles depends on the metal composition, size and shape of the nanoparticles. A few experimental results available for 14 and 15 nm diameter gold nanoparticles indicate that the sensing distance is 20-25 nm from the surface of the nanoparticles. Theoretical studies by Schatz and co-workers have shown that the... 

Problem 3.7. Neglecting relaxation, find the penetration depths of surface plasmon polaritons into both metal and vacuum for wavelengths A much longer than the plasma wavelength, Ap. Calculate them for a surface plasmon polariton at an A1 surface (Ap 800 A) with A = 5890 A. 

Thus the value of the dielectric constant at the sample/metal interface determines the shift of the resonance. When adsorption of molecules at the metal surface results in the change of the refractive index or of the local value of the dielectric constant, the change of reflectivity is observed. This phenomenon has been used as the mechanism for detection of gases (Fig. 9.18a) and of adsorbed biomolecules (Fig. 9.18b). The depth of penetration of the surface plasmon is comparable to that of the evanescent field, that is, 100-500 nm for the visible-near infrared range. 

---