4 Chirality and Antiferromagnetism in Optical Metasurfaces
87
For optical chiral metasurfaces, the total scattering E s can be tuned by controlling
the parameters s x and s y , which are determined by the geometry of nanostructures,
materials and working mode. In (4.8), the item |s x −s y |/2 is related with the efficiency
of metasurfaces. For the passive nanostructures without gain, we have |s x |≤1 and
|s y |≤1. To achieve high efficiency, one should maximize |s x -s y |/2 and minimize the
co-polarization part |s x +s y |/2. Mathematically, the highest conversion efficiency is 1
by setting s x = −s y =1, which means that the nanostructures have the equal amplitude
of 1 and the phase delay of π between two orthogonal components of the scattering
light. Correspondingly, the conversion efficiency is 0 when s x = s y , implying that
the nanostructures have the isotropic responses for the E x and E y polarized light.
The zero-efficiency case usually appears in the circular and square nanostructures.
Therefore, most of the demonstrated geometric metasurfaces adopt the nanostructures with anisotropic geometry, such as rectangle shape. On the basis of working
principles, they are classified into plasmonic chiral metasurfaces, helical nanosieves,
and dielectric chiral metasurfaces, where the nano-structures work as miniaturized
half-waveplates that holds the physical origins of electric dipole resonances, birefringent transmission and antiferromagnetic resonances, respectively. In practical design
of nanostructures, one tune the parameters s x and s y that are controlled by the geometry of nanostructure for a give material platform and numerically simulated with
the help of electromagnetic numerical calculation methods such as finite-element
method (FEM) and finite-difference time-domain (FDTD) methods. Both electromagnetic simulation methods are important in designing optical metasurfaces and
the relative sources can be found easily, so that we will not introduce them here.
4.3.1 Plasmonic Chiral Metasurfaces
Figure 4.4 sketches plasmonic chiral metasurfaces in a transmission and reflective
mode. The working principle is the anisotropic resonances of the electric dipoles
induced by the circularly polarized incident light. With the illumination by the circular
polarized light, the metal nanorodes have the plasmonic resonances at the designed
wavelengths. Considering that the feature size of nanorode is smaller than one wavelength, the plasmonic resonances induced by E x and E y components could be approximated theoretically as optical responses of two electric dipoles orientated along x
and y directions, respectively. For the transmission mode as shown in Fig. 4.4a, the
single-layer nanostructures can excite the transversely located electric dipoles that
have both the forward and backward radiation. But, only the forward radiation is
useful for controlling the s x and s y parameters, which refer to the transmittance r x
and r y in the transmission mode. In addition, due to small filling factor of nanostructures, most of the incident light has no any interaction with nano-structures and
directly passed through the substrate, leaving the background with co-polarization
in the transmitted light. Therefore, the transmissive plasmonic chiral metasurfaces
have the low conversion efficiency. The rigorous electromagnetic theory predicts that
the highest conversion efficiency is 25% for metasurfaces that support only electric
87
For optical chiral metasurfaces, the total scattering E s can be tuned by controlling
the parameters s x and s y , which are determined by the geometry of nanostructures,
materials and working mode. In (4.8), the item |s x −s y |/2 is related with the efficiency
of metasurfaces. For the passive nanostructures without gain, we have |s x |≤1 and
|s y |≤1. To achieve high efficiency, one should maximize |s x -s y |/2 and minimize the
co-polarization part |s x +s y |/2. Mathematically, the highest conversion efficiency is 1
by setting s x = −s y =1, which means that the nanostructures have the equal amplitude
of 1 and the phase delay of π between two orthogonal components of the scattering
light. Correspondingly, the conversion efficiency is 0 when s x = s y , implying that
the nanostructures have the isotropic responses for the E x and E y polarized light.
The zero-efficiency case usually appears in the circular and square nanostructures.
Therefore, most of the demonstrated geometric metasurfaces adopt the nanostructures with anisotropic geometry, such as rectangle shape. On the basis of working
principles, they are classified into plasmonic chiral metasurfaces, helical nanosieves,
and dielectric chiral metasurfaces, where the nano-structures work as miniaturized
half-waveplates that holds the physical origins of electric dipole resonances, birefringent transmission and antiferromagnetic resonances, respectively. In practical design
of nanostructures, one tune the parameters s x and s y that are controlled by the geometry of nanostructure for a give material platform and numerically simulated with
the help of electromagnetic numerical calculation methods such as finite-element
method (FEM) and finite-difference time-domain (FDTD) methods. Both electromagnetic simulation methods are important in designing optical metasurfaces and
the relative sources can be found easily, so that we will not introduce them here.
4.3.1 Plasmonic Chiral Metasurfaces
Figure 4.4 sketches plasmonic chiral metasurfaces in a transmission and reflective
mode. The working principle is the anisotropic resonances of the electric dipoles
induced by the circularly polarized incident light. With the illumination by the circular
polarized light, the metal nanorodes have the plasmonic resonances at the designed
wavelengths. Considering that the feature size of nanorode is smaller than one wavelength, the plasmonic resonances induced by E x and E y components could be approximated theoretically as optical responses of two electric dipoles orientated along x
and y directions, respectively. For the transmission mode as shown in Fig. 4.4a, the
single-layer nanostructures can excite the transversely located electric dipoles that
have both the forward and backward radiation. But, only the forward radiation is
useful for controlling the s x and s y parameters, which refer to the transmittance r x
and r y in the transmission mode. In addition, due to small filling factor of nanostructures, most of the incident light has no any interaction with nano-structures and
directly passed through the substrate, leaving the background with co-polarization
in the transmitted light. Therefore, the transmissive plasmonic chiral metasurfaces
have the low conversion efficiency. The rigorous electromagnetic theory predicts that
the highest conversion efficiency is 25% for metasurfaces that support only electric