10 Waves on Subwalength Metallic Surfaces: A Microscopic View Point
381
interact with nearby indentations before being recovered as freely propagating light
or detected. Note the large gap existing between such an intuitive wavy picture
and state-of-the-art numerical tools (some are purely numerical like finite-element
and finite-difference methods, some are more physically oriented like modal- or
multipole-expansion methods …), that rarely consider the waves launched on the
surface and that never directly calculate how those waves are scattered by the subwavelength indentations. The main physical ingredients of our understanding of
subwavelength surfaces (the launching, absorption, propagation and scattering of
surface waves) are only implicitly taken into account in standard modelisation by
matching the continuous electromagnetic field components at the interface.
Section 10.7 concludes the chapter.
10.2 Waves on Metal Surfaces: Historical Background
The field scattered by subwavelength indentations or emitted by subwavelength emitters in the vicinity of interfaces has been of longstanding interest in electromagnetism.
In the 1900s, the rapid development of radio-wave technology prompted theoretical studies to explain why very long-distance (over-ocean transmission have been
achieved in 1907 by Marconi) transmission could be achieved with radio waves above
the earth. The solution is indeed linked to guiding by the ionosphere layers, but at
the beginning of the twentieth century, the explanation was thought to be due to the
nature of the surface waves launched on the flat earth by the emitting antennas acting
as a dipole. Sommerfeld was the first to determine the complete electromagnetic field
radiated by a subwavelength antenna (a 0D vertical dipole) at the interface between
two semi-infinite half spaces. He verified that his complicated solution [30] is composed of a “direct contribution” and of a bounded Zenneck mode [37], the analogue
of the surface plasmon polariton (SPP) [25] for metals at optical frequencies, with an
exponential damping. On the other hand, the amplitude of the direct contribution does
not decay exponentially, but algebraically as 1/r 2 at asymptotically long-distance
from the antenna [21–23]. The direct contribution, known as the Norton wave [2, 6],
was therefore believed to be responsible for long-distance radio transmission.
In nanophotonics, the field scattered on metallic surfaces by subwavelength
indentations is also essential, since it is responsible for the electromagnetic interaction between nearby indentations on the surfaces. Since the initial milestone interpretation of Wood’s anomalies [35] by U. Fano [10] who introduced the concept of
bounded SPP modes, SPPs have been central in modern history of the research on
the optical properties of metallic surfaces, which have recently enabled researchers
to overcome the diffraction limit for applications in microscopy [31], nano-optical
tweezing [28], integrated optics [8] and lasers [38]. From a mathematical point of
view, the solution of this photonic problem is identical to that of the radio-wave
problem [14, 19]. However, there are also differences. We are mainly concerned
by short-distance (rather than long-distance) electromagnetic interactions, since the
distance between two neighboring indentations on subwavelength optical surfaces is
381
interact with nearby indentations before being recovered as freely propagating light
or detected. Note the large gap existing between such an intuitive wavy picture
and state-of-the-art numerical tools (some are purely numerical like finite-element
and finite-difference methods, some are more physically oriented like modal- or
multipole-expansion methods …), that rarely consider the waves launched on the
surface and that never directly calculate how those waves are scattered by the subwavelength indentations. The main physical ingredients of our understanding of
subwavelength surfaces (the launching, absorption, propagation and scattering of
surface waves) are only implicitly taken into account in standard modelisation by
matching the continuous electromagnetic field components at the interface.
Section 10.7 concludes the chapter.
10.2 Waves on Metal Surfaces: Historical Background
The field scattered by subwavelength indentations or emitted by subwavelength emitters in the vicinity of interfaces has been of longstanding interest in electromagnetism.
In the 1900s, the rapid development of radio-wave technology prompted theoretical studies to explain why very long-distance (over-ocean transmission have been
achieved in 1907 by Marconi) transmission could be achieved with radio waves above
the earth. The solution is indeed linked to guiding by the ionosphere layers, but at
the beginning of the twentieth century, the explanation was thought to be due to the
nature of the surface waves launched on the flat earth by the emitting antennas acting
as a dipole. Sommerfeld was the first to determine the complete electromagnetic field
radiated by a subwavelength antenna (a 0D vertical dipole) at the interface between
two semi-infinite half spaces. He verified that his complicated solution [30] is composed of a “direct contribution” and of a bounded Zenneck mode [37], the analogue
of the surface plasmon polariton (SPP) [25] for metals at optical frequencies, with an
exponential damping. On the other hand, the amplitude of the direct contribution does
not decay exponentially, but algebraically as 1/r 2 at asymptotically long-distance
from the antenna [21–23]. The direct contribution, known as the Norton wave [2, 6],
was therefore believed to be responsible for long-distance radio transmission.
In nanophotonics, the field scattered on metallic surfaces by subwavelength
indentations is also essential, since it is responsible for the electromagnetic interaction between nearby indentations on the surfaces. Since the initial milestone interpretation of Wood’s anomalies [35] by U. Fano [10] who introduced the concept of
bounded SPP modes, SPPs have been central in modern history of the research on
the optical properties of metallic surfaces, which have recently enabled researchers
to overcome the diffraction limit for applications in microscopy [31], nano-optical
tweezing [28], integrated optics [8] and lasers [38]. From a mathematical point of
view, the solution of this photonic problem is identical to that of the radio-wave
problem [14, 19]. However, there are also differences. We are mainly concerned
by short-distance (rather than long-distance) electromagnetic interactions, since the
distance between two neighboring indentations on subwavelength optical surfaces is