422
A. Pors et al.
indexes that result in a phase difference between orthogonally polarized waves traveling through the crystal, thereby permitting the construction of wave retarders, e.g.,
half- and quarter-wave plates. An alternative method for obtaining birefringence is
to introduce a periodic anisotropy in the (nonbirefringent) material so that transverse
electric and transverse magnetic waves experience different effective refractive indexes. Their difference, πn, is known as form birefringence [50–52]. Generally, a
high πn is desired as it can lead to more compact optical components that can be used
in on-chip photonics [53]. Although difficult to achieve at optical wavelengths (typically, πn ∼ 0.1 − 0.2 [54]), it has recently been shown that the waveguide dispersion
of surface plasmon polaritons (SPPs) in gold nanoslits can be used to create giant
form birefringence πn ∼ 2.7 at ϕ = 632.8 nm [55], facilitating sub-wavelength-thin
wave plates. In a different approach [56], a subwavelength circular aperture in a gold
film surrounded by an elliptical grating was used to introduce a phase shift between
SPPs traveling along the ellipse axes, influencing the polarization of transmitted
light.
Based on our DED concept, we demonstrate theoretically and experimentally
a new method to construct a nanometer-thin quarter-wave plate that in contrast to
previous studies [55, 56] works in reflection mode. Also, the quarter-wave plate
relies on anisotropic detuned electric resonant scattering and not form birefringence
as in grating-based circular polarizers (see, e.g., [51, 57]). Furthermore, the proposed
nanostructures, constituting a unit cell in the metamaterial wave retarders, are not
related to the optically active extrinsic chiral metamaterials [30] as they only display
an electric response (no magnetic response), eliminating the possibility of extrinsic
chirality.
Our approach can be illustrated by considering two perpendicular noninteracting
electric dipolar scatterers centered at the origin of the coordinate system with electric
dipole moments in the x- and y-direction, respectively, and the observation region
being in the far field close to the z-axis (z ≈ x, y). Assuming that the resonances of
the noninteracting dipole scatterers are equally detuned from the central frequency
ε 0 , their dipole polarizabilities can be represented by Eq. (11.1), and for weak detuning (ε 0 ≈ π) their polarizability phase difference, πΦ, is equivalent to Eq. (11.10)
implying that for π = ω /2 the scattered light close to the z-axis will be circularly
polarized (πΦ = η/2). Consequently, a metamaterial consisting of subwavelength
noninteracting DED unit cells will work as a circular polarizer as the polarizability of each cell, λ 1 + λ 2 , adds coherently in this limit [58] [see Eq.(11.3)]. The
above condition for circular polarized light is strictly valid only for noninteracting
scatterers with the same strength and damping factor, but, as we will see below, the
simplified description is still valid as a guideline for more realistic cases due to very
weak dipole-dipole interaction for orthogonal dipoles [59]. Note that even though
we focus on the quarter-wave plate structure, the same idea can be used to construct
a wave plate with arbitrary retardation by adjusting the detuning π and/or slightly
displacing two scatterers along the propagation direction. Furthermore, based on a
similar concept, recent studies have shown that orthogonally oriented nanoslits of
different lengths in a metal surface, i.e. complementary structures to the perpendic-
A. Pors et al.
indexes that result in a phase difference between orthogonally polarized waves traveling through the crystal, thereby permitting the construction of wave retarders, e.g.,
half- and quarter-wave plates. An alternative method for obtaining birefringence is
to introduce a periodic anisotropy in the (nonbirefringent) material so that transverse
electric and transverse magnetic waves experience different effective refractive indexes. Their difference, πn, is known as form birefringence [50–52]. Generally, a
high πn is desired as it can lead to more compact optical components that can be used
in on-chip photonics [53]. Although difficult to achieve at optical wavelengths (typically, πn ∼ 0.1 − 0.2 [54]), it has recently been shown that the waveguide dispersion
of surface plasmon polaritons (SPPs) in gold nanoslits can be used to create giant
form birefringence πn ∼ 2.7 at ϕ = 632.8 nm [55], facilitating sub-wavelength-thin
wave plates. In a different approach [56], a subwavelength circular aperture in a gold
film surrounded by an elliptical grating was used to introduce a phase shift between
SPPs traveling along the ellipse axes, influencing the polarization of transmitted
light.
Based on our DED concept, we demonstrate theoretically and experimentally
a new method to construct a nanometer-thin quarter-wave plate that in contrast to
previous studies [55, 56] works in reflection mode. Also, the quarter-wave plate
relies on anisotropic detuned electric resonant scattering and not form birefringence
as in grating-based circular polarizers (see, e.g., [51, 57]). Furthermore, the proposed
nanostructures, constituting a unit cell in the metamaterial wave retarders, are not
related to the optically active extrinsic chiral metamaterials [30] as they only display
an electric response (no magnetic response), eliminating the possibility of extrinsic
chirality.
Our approach can be illustrated by considering two perpendicular noninteracting
electric dipolar scatterers centered at the origin of the coordinate system with electric
dipole moments in the x- and y-direction, respectively, and the observation region
being in the far field close to the z-axis (z ≈ x, y). Assuming that the resonances of
the noninteracting dipole scatterers are equally detuned from the central frequency
ε 0 , their dipole polarizabilities can be represented by Eq. (11.1), and for weak detuning (ε 0 ≈ π) their polarizability phase difference, πΦ, is equivalent to Eq. (11.10)
implying that for π = ω /2 the scattered light close to the z-axis will be circularly
polarized (πΦ = η/2). Consequently, a metamaterial consisting of subwavelength
noninteracting DED unit cells will work as a circular polarizer as the polarizability of each cell, λ 1 + λ 2 , adds coherently in this limit [58] [see Eq.(11.3)]. The
above condition for circular polarized light is strictly valid only for noninteracting
scatterers with the same strength and damping factor, but, as we will see below, the
simplified description is still valid as a guideline for more realistic cases due to very
weak dipole-dipole interaction for orthogonal dipoles [59]. Note that even though
we focus on the quarter-wave plate structure, the same idea can be used to construct
a wave plate with arbitrary retardation by adjusting the detuning π and/or slightly
displacing two scatterers along the propagation direction. Furthermore, based on a
similar concept, recent studies have shown that orthogonally oriented nanoslits of
different lengths in a metal surface, i.e. complementary structures to the perpendic-