10 Waves on Subwalength Metallic Surfaces: A Microscopic View Point
393
10.6 Generalized Microscopic Model with Surface Plasmon
Polaritons and Quasi-Cylindrical Waves
The pure-SPP microscopic model captures most of the important features of the
EOT at visible frequencies, but it is largely inaccurate at longer wavelengths. In this
Section, we keep on elaborating on an intuitive microscopic description of multiple
scattering phenomena occurring on metallic subwavelength surfaces. By incorporating the quasi-CW into the pure SPP model, we obtain a more accurate model
that provides quantitative predictions well above the visible wavelengths. In the first
Sect. 10.6.1, a key scattering process of surface waves, the cross conversion from
quasi-CWs to the SPPs is investigated. In the second Sect. 10.6.2, the quasi-CW contribution is incorporated into the pure-SPP model, and a generalized wavy model,
similar to the pure-SPP model (actually it is much more accurate as shown by the
black dash-dot curves in Fig. 10.8), is presented.
10.6.1 Cross Conversion from Quasi-Cylindrical Wave to Surface
Plasmon Polariton
For a metal surface patterned with a set of 1D indentations under external illumination
by TM-polarized light, several scattering processes of surface waves may exist: the
SPP-to-SPP scattering that has been considered in the pure-SPP description, the
possible CW-to-SPP or SPP-to-CW cross conversions, and the CW-to-CW scattering.
The cross conversion between different surface waves plays a key role in the physical
multiple-scattering picture. Demonstration of its existence along with a quantitative
description of its scattering coefficient appear to be a heuristic step in incorporating
quasi-CWs to build up an accurate microscopic description of subwavelength metallic
surfaces.
The importance of the cross conversion has been demonstrated in [36], by considering a groove doublet and by calculating its SPP excitation efficiency on the
outer sides as a function of the groove separation-distance. The interpretation of
the computational results has led the authors to conclude that the SPP excitation
efficiency dependence on the separation distance cannot be explained if one does
not consider a CW-to-SPP cross conversion. Additionally, the authors have proposed a method to directly extract, from the SPP excitation efficiency, the scattering
coefficients associated to the cross-conversion process and have argued and verified
that the cross-conversion scattering coefficients are simply related to SPP scattering
coefficients,
ρ c ≈ ρ SP ,
(10.3a)
τ c ≈ τ SP −1,
(10.3b)
where τ c and ρ c are the cross-conversion coefficients from an incident CW to a
transmitted and a reflected SPP (Fig. 10.9a), and τ SP and ρ SP are the elastic transmis-
393
10.6 Generalized Microscopic Model with Surface Plasmon
Polaritons and Quasi-Cylindrical Waves
The pure-SPP microscopic model captures most of the important features of the
EOT at visible frequencies, but it is largely inaccurate at longer wavelengths. In this
Section, we keep on elaborating on an intuitive microscopic description of multiple
scattering phenomena occurring on metallic subwavelength surfaces. By incorporating the quasi-CW into the pure SPP model, we obtain a more accurate model
that provides quantitative predictions well above the visible wavelengths. In the first
Sect. 10.6.1, a key scattering process of surface waves, the cross conversion from
quasi-CWs to the SPPs is investigated. In the second Sect. 10.6.2, the quasi-CW contribution is incorporated into the pure-SPP model, and a generalized wavy model,
similar to the pure-SPP model (actually it is much more accurate as shown by the
black dash-dot curves in Fig. 10.8), is presented.
10.6.1 Cross Conversion from Quasi-Cylindrical Wave to Surface
Plasmon Polariton
For a metal surface patterned with a set of 1D indentations under external illumination
by TM-polarized light, several scattering processes of surface waves may exist: the
SPP-to-SPP scattering that has been considered in the pure-SPP description, the
possible CW-to-SPP or SPP-to-CW cross conversions, and the CW-to-CW scattering.
The cross conversion between different surface waves plays a key role in the physical
multiple-scattering picture. Demonstration of its existence along with a quantitative
description of its scattering coefficient appear to be a heuristic step in incorporating
quasi-CWs to build up an accurate microscopic description of subwavelength metallic
surfaces.
The importance of the cross conversion has been demonstrated in [36], by considering a groove doublet and by calculating its SPP excitation efficiency on the
outer sides as a function of the groove separation-distance. The interpretation of
the computational results has led the authors to conclude that the SPP excitation
efficiency dependence on the separation distance cannot be explained if one does
not consider a CW-to-SPP cross conversion. Additionally, the authors have proposed a method to directly extract, from the SPP excitation efficiency, the scattering
coefficients associated to the cross-conversion process and have argued and verified
that the cross-conversion scattering coefficients are simply related to SPP scattering
coefficients,
ρ c ≈ ρ SP ,
(10.3a)
τ c ≈ τ SP −1,
(10.3b)
where τ c and ρ c are the cross-conversion coefficients from an incident CW to a
transmitted and a reflected SPP (Fig. 10.9a), and τ SP and ρ SP are the elastic transmis-