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P. Lalanne and H. Liu
of the order of λ and rarely exceeds 10λ. The second important difference concerns
the fact that the dipole orientation cannot be chosen in nanophotonics. For instance,
for a subwavelength 1D indentation under illumination of transverse-magnetic (TM)
polarization, two coherent equivalent electrical dipoles of different polarizations are
generally excited with different strengths.
Despite its importance for understanding the rich optics of subwavelength metallic surfaces, the field scattered by subwavelength indentations on a metal surface has
been studied only recently. Lezec and his co-workers [11] were the first to recognize the importance of a “direct” wave other than the SPP. This initial finding has
been followed by theoretical [5, 13, 20, 33] and experimental [1] works aiming at
determining the main characteristics of this wave. It turns out that for intermediate
distances of interest (x < 10λ), the direct wave is very different from the Norton
wave; it looks like a cylindrical wave.
10.3 Fano’s Microscopic Model of Wood Anomaly
In 1902, R.W. Wood, when observing the spectrum of a continuous light source
reflected by an optical metallic diffraction grating when the incident wave is polarized
with its magnetic vector parallel to the grooves (TM polarization), noticed a surprising
phenomenon: “I was astounded to find that under certain conditions, the drop from
maximum illumination to minimum, a drop certainly of from 10 to 1, occurred within
a range of wavelengths not greater than the distance between the sodium lines” [35].
Wood’s discovery drew immediately a considerable attention and the fascination of
many specialists of optics for the so-called Wood’s anomalies that never died.
By considering the metal as perfectly conducting and using a complicated mathematical derivation, Lord Rayleigh proposed the first explanation to the existence
of the anomalies [26]: an anomaly in a given spectrum occurs at a wavelength corresponding to the passing-off of a spectrum of higher order, in other words, at the
wavelength given by the grating equation for which a scattered wave emerges tangentially to the grating surface. Considering the imprecise knowledge of the grating period in Wood’s experiment, the agreement between the grating equation and
Wood’s experimental results was considered as rather fair, and the Rayleigh conjecture remained unquestioned during almost two decades. However, the conclusions
radically changed in 1936, with Strong’s study of Wood’s anomalies for various
metallic gratings having the same period [32]. Strong evidenced that the anomalies
occur at a wavelength systematically larger than that predicted by the grating equation.
To explain the red shift from the Rayleigh condition, U. Fano introduced a microscopic model of Wood’s anomalies in his seminal article published in 1941 [10]
(40 years after Wood’s observation). Fano’s model is much less mathematically
involved than the theoretical work by Lord Rayleigh. It rather relied on a Huygenstype very intuitive interpretation, and importantly, it suggested that a surface mode
with a parallel momentum greater than the free space momentum be involved in
P. Lalanne and H. Liu
of the order of λ and rarely exceeds 10λ. The second important difference concerns
the fact that the dipole orientation cannot be chosen in nanophotonics. For instance,
for a subwavelength 1D indentation under illumination of transverse-magnetic (TM)
polarization, two coherent equivalent electrical dipoles of different polarizations are
generally excited with different strengths.
Despite its importance for understanding the rich optics of subwavelength metallic surfaces, the field scattered by subwavelength indentations on a metal surface has
been studied only recently. Lezec and his co-workers [11] were the first to recognize the importance of a “direct” wave other than the SPP. This initial finding has
been followed by theoretical [5, 13, 20, 33] and experimental [1] works aiming at
determining the main characteristics of this wave. It turns out that for intermediate
distances of interest (x < 10λ), the direct wave is very different from the Norton
wave; it looks like a cylindrical wave.
10.3 Fano’s Microscopic Model of Wood Anomaly
In 1902, R.W. Wood, when observing the spectrum of a continuous light source
reflected by an optical metallic diffraction grating when the incident wave is polarized
with its magnetic vector parallel to the grooves (TM polarization), noticed a surprising
phenomenon: “I was astounded to find that under certain conditions, the drop from
maximum illumination to minimum, a drop certainly of from 10 to 1, occurred within
a range of wavelengths not greater than the distance between the sodium lines” [35].
Wood’s discovery drew immediately a considerable attention and the fascination of
many specialists of optics for the so-called Wood’s anomalies that never died.
By considering the metal as perfectly conducting and using a complicated mathematical derivation, Lord Rayleigh proposed the first explanation to the existence
of the anomalies [26]: an anomaly in a given spectrum occurs at a wavelength corresponding to the passing-off of a spectrum of higher order, in other words, at the
wavelength given by the grating equation for which a scattered wave emerges tangentially to the grating surface. Considering the imprecise knowledge of the grating period in Wood’s experiment, the agreement between the grating equation and
Wood’s experimental results was considered as rather fair, and the Rayleigh conjecture remained unquestioned during almost two decades. However, the conclusions
radically changed in 1936, with Strong’s study of Wood’s anomalies for various
metallic gratings having the same period [32]. Strong evidenced that the anomalies
occur at a wavelength systematically larger than that predicted by the grating equation.
To explain the red shift from the Rayleigh condition, U. Fano introduced a microscopic model of Wood’s anomalies in his seminal article published in 1941 [10]
(40 years after Wood’s observation). Fano’s model is much less mathematically
involved than the theoretical work by Lord Rayleigh. It rather relied on a Huygenstype very intuitive interpretation, and importantly, it suggested that a surface mode
with a parallel momentum greater than the free space momentum be involved in