4 Chirality and Antiferromagnetism in Optical Metasurfaces
77
two media with different refractive indices, where the curvature of the interface and
the index difference between two media are the main parameters to tailor the ray
of light. The disadvantage of geometry optics comes from the fact that the other
variables such as phase, polarization, coherence and diffraction of light are ignored
completely due to the model of the ray, so that its applied territory is quite limited.
When the optical elements have the feature size at the level of wavelength, the
diffraction and interference dominate its propagation of light and the light-matter
interaction due to the wave properties of light. The well-developed lithography
enables us to acquire the micro- or nano-scale elements such as optical fibers [1],
holograms [2], photonic crystals [3], plasmonic devices [4], optical metamaterials [5,
6] and metasurfaces [7–11], quantum devices, where their feature sizes range from
tens of microns to several nanometers. The diffraction effects in micro-devices is
weak, which is a good issue for optical fibers during the long-distance propagation.
But, the weak diffraction makes micro-pixelated traditional holograms with small
field-of-view, leading to the limited applications. Meanwhile, the micro-pixel pitch
in traditional holograms allows only the phase and amplitude modulation of light.
When the pixels of devices are below the subwavelength, the polarization effect is
important because the subwavelength structures have different electromagnetic resonances for transverse electric and magnetic fields. The photonic crystals with periodic subwavelength pixels could prohibit the motion of photons through confining
the electromagnetic modes within the index-contrast structures, hereby creating the
forbidden states at the designed frequencies. A well-designed photonic crystal could
support the simultaneous oscillation of multiple modes with different polarizations,
which is useful to generate the cylindrical vector beams with spatially variant states
of polarization in active nanolasers [12]. As its killer-man application, the photonic
crystal fibers offer the well-confined modes that are impossible in conventional fibers.
However, the periodic properties make photonic crystals incompetent at manipulating
the phase of light at the transvers plane vertical to the propagation direction. Such
a situation also exists at the periodic meta-materials with the pixel pitches much
smaller than one wavelength, where the effective medium theory can be used to
approximate its optical properties. For visible light with the wavelengths ranging
from 400 nm to 800 nm, the pixel pitches in metamaterials is too small for the stateof-art nanolithography to fabricate a three-dimensional structure, so that the novel
properties of metamaterials are frequently demonstrated at the micro-wave and radio
frequencies [13].
Fortunately, we can realize two-dimensional meta-materials made of highrefraction-index dielectric or metal-based plasmonic nano-structures with the pixel
pitches around a half of wavelength [14], facilitating the fabrication issue by using
electron-beam or focused ion lithography. Instead of effective-medium approach in
three-dimensional metamaterials, two-dimensional metamaterials have the distinct
working principle of controlling the polarization, amplitude, phase and wavelength
of light through the electromagnetic responses of the confined nanomodes, which
oscillate between two lower-refraction-index media (i.e., substrate and surrounding
medium) [15]. Due to its planarity and ultrathin thickness of smaller than one
wavelength, two-dimensional meta-materials are usually phrased as “metasurfaces”,
77
two media with different refractive indices, where the curvature of the interface and
the index difference between two media are the main parameters to tailor the ray
of light. The disadvantage of geometry optics comes from the fact that the other
variables such as phase, polarization, coherence and diffraction of light are ignored
completely due to the model of the ray, so that its applied territory is quite limited.
When the optical elements have the feature size at the level of wavelength, the
diffraction and interference dominate its propagation of light and the light-matter
interaction due to the wave properties of light. The well-developed lithography
enables us to acquire the micro- or nano-scale elements such as optical fibers [1],
holograms [2], photonic crystals [3], plasmonic devices [4], optical metamaterials [5,
6] and metasurfaces [7–11], quantum devices, where their feature sizes range from
tens of microns to several nanometers. The diffraction effects in micro-devices is
weak, which is a good issue for optical fibers during the long-distance propagation.
But, the weak diffraction makes micro-pixelated traditional holograms with small
field-of-view, leading to the limited applications. Meanwhile, the micro-pixel pitch
in traditional holograms allows only the phase and amplitude modulation of light.
When the pixels of devices are below the subwavelength, the polarization effect is
important because the subwavelength structures have different electromagnetic resonances for transverse electric and magnetic fields. The photonic crystals with periodic subwavelength pixels could prohibit the motion of photons through confining
the electromagnetic modes within the index-contrast structures, hereby creating the
forbidden states at the designed frequencies. A well-designed photonic crystal could
support the simultaneous oscillation of multiple modes with different polarizations,
which is useful to generate the cylindrical vector beams with spatially variant states
of polarization in active nanolasers [12]. As its killer-man application, the photonic
crystal fibers offer the well-confined modes that are impossible in conventional fibers.
However, the periodic properties make photonic crystals incompetent at manipulating
the phase of light at the transvers plane vertical to the propagation direction. Such
a situation also exists at the periodic meta-materials with the pixel pitches much
smaller than one wavelength, where the effective medium theory can be used to
approximate its optical properties. For visible light with the wavelengths ranging
from 400 nm to 800 nm, the pixel pitches in metamaterials is too small for the stateof-art nanolithography to fabricate a three-dimensional structure, so that the novel
properties of metamaterials are frequently demonstrated at the micro-wave and radio
frequencies [13].
Fortunately, we can realize two-dimensional meta-materials made of highrefraction-index dielectric or metal-based plasmonic nano-structures with the pixel
pitches around a half of wavelength [14], facilitating the fabrication issue by using
electron-beam or focused ion lithography. Instead of effective-medium approach in
three-dimensional metamaterials, two-dimensional metamaterials have the distinct
working principle of controlling the polarization, amplitude, phase and wavelength
of light through the electromagnetic responses of the confined nanomodes, which
oscillate between two lower-refraction-index media (i.e., substrate and surrounding
medium) [15]. Due to its planarity and ultrathin thickness of smaller than one
wavelength, two-dimensional meta-materials are usually phrased as “metasurfaces”,