380
P. Lalanne and H. Liu
and physics, and nowadays with the progress of nanofabrication, metallic surfaces
patterned with subwavelength indentations are studied for a variety of interesting
properties, with applications ranging from sensing, new photonic and metamaterial
devices, to integrated circuits mixing photonics and electronics [9]. It is the purpose
of this chapter to examine the concepts, to elucidate the underlying physics and to
discuss recent results and current problems in relation with resonance of metallic
gratings. Particular emphasis will be placed on work carried out in the last decade,
in anticipating future directions and in assessing the relevance of the subject to other
areas of science.
Section 10.2 provides a historical background on the waves that are launched on a
conducting surface by a subwavelength indentation, recalling the pioneer works at the
beginning of last century by Marconi, Sommerfeld, Norton … in relation with longdistance radio-wave communications. Note that the field radiated by a dipole source
in the vicinity of an interface has been considerably studied in the context of molecule
fluorescence and other optical processes, such as surface-enhance Raman scattering,
energy transfer … An interface may alter the way an excited molecule loses energy
through fluorescence in several ways. It may absorb part of the spontaneous decay,
and may alter both the radiative decay rate and the spatial distribution of the emitted
radiation. Such situations are completely out of the scope of the present survey. The
interested reader may refer to the review article [3] and to other reviews quoted there.
At optical frequency, the field scattered by subwavelength indentations on metal
surface has been first considered for understanding the spectacular Wood’s anomalies. Well before the establishment of modern theories of gratings (Floquet-Bloch
expansions, phenomenological models with the zeros and poles of scattering operators …) and before the discovery of surface plasmon polaritons (SPP) by Ritchie
[27], microscopic theories of metallic gratings considered the SPP launched by the
individual grating indentations as responsible for Wood anomalies. Section 10.3 summarizes the Fano’s seminal ideas that, since 1941, have durably impacted the field
of periodic metallic surfaces.
Section 10.4 describes what is presently known on the waves launched on metal
surfaces by subwavelength indentations, which include the SPP mode and another
contribution called the quasi-cylindrical wave (quasi-CW). A good knowledge of the
properties of these waves is essential for understanding the rich physics of subwavelength metallic surfaces. Particular emphasis is put on 1D indentations such as ridges
or grooves, 0D point defects such as holes being rapidly visited.
In Sects 10.5 and 10.6, we examine the scattering of SPPs and quasi-cylindrical
waves by tiny indentations, emphasizing cross-conversion processes that convert
quasi-CWs into SPPs and vice versa. Under the assumption that the indentations
have subwavelength dimensions, scattering coefficients for the SPPs, quasi-CWs,
and for a combination of theses waves can be consistently defined. The objective is
to settle the foundation of a “microscopic” treatment of the electromagnetic properties of metallic subwavelength surfaces, which is accurate and intuitive. For that,
the microscopic treatment should fit our current understanding and design recipes
that all rely on a wavy description, which assume that surface waves are first generated by some illuminated indentations, then propagate on the metal surface and
P. Lalanne and H. Liu
and physics, and nowadays with the progress of nanofabrication, metallic surfaces
patterned with subwavelength indentations are studied for a variety of interesting
properties, with applications ranging from sensing, new photonic and metamaterial
devices, to integrated circuits mixing photonics and electronics [9]. It is the purpose
of this chapter to examine the concepts, to elucidate the underlying physics and to
discuss recent results and current problems in relation with resonance of metallic
gratings. Particular emphasis will be placed on work carried out in the last decade,
in anticipating future directions and in assessing the relevance of the subject to other
areas of science.
Section 10.2 provides a historical background on the waves that are launched on a
conducting surface by a subwavelength indentation, recalling the pioneer works at the
beginning of last century by Marconi, Sommerfeld, Norton … in relation with longdistance radio-wave communications. Note that the field radiated by a dipole source
in the vicinity of an interface has been considerably studied in the context of molecule
fluorescence and other optical processes, such as surface-enhance Raman scattering,
energy transfer … An interface may alter the way an excited molecule loses energy
through fluorescence in several ways. It may absorb part of the spontaneous decay,
and may alter both the radiative decay rate and the spatial distribution of the emitted
radiation. Such situations are completely out of the scope of the present survey. The
interested reader may refer to the review article [3] and to other reviews quoted there.
At optical frequency, the field scattered by subwavelength indentations on metal
surface has been first considered for understanding the spectacular Wood’s anomalies. Well before the establishment of modern theories of gratings (Floquet-Bloch
expansions, phenomenological models with the zeros and poles of scattering operators …) and before the discovery of surface plasmon polaritons (SPP) by Ritchie
[27], microscopic theories of metallic gratings considered the SPP launched by the
individual grating indentations as responsible for Wood anomalies. Section 10.3 summarizes the Fano’s seminal ideas that, since 1941, have durably impacted the field
of periodic metallic surfaces.
Section 10.4 describes what is presently known on the waves launched on metal
surfaces by subwavelength indentations, which include the SPP mode and another
contribution called the quasi-cylindrical wave (quasi-CW). A good knowledge of the
properties of these waves is essential for understanding the rich physics of subwavelength metallic surfaces. Particular emphasis is put on 1D indentations such as ridges
or grooves, 0D point defects such as holes being rapidly visited.
In Sects 10.5 and 10.6, we examine the scattering of SPPs and quasi-cylindrical
waves by tiny indentations, emphasizing cross-conversion processes that convert
quasi-CWs into SPPs and vice versa. Under the assumption that the indentations
have subwavelength dimensions, scattering coefficients for the SPPs, quasi-CWs,
and for a combination of theses waves can be consistently defined. The objective is
to settle the foundation of a “microscopic” treatment of the electromagnetic properties of metallic subwavelength surfaces, which is accurate and intuitive. For that,
the microscopic treatment should fit our current understanding and design recipes
that all rely on a wavy description, which assume that surface waves are first generated by some illuminated indentations, then propagate on the metal surface and