Photonic metasurfaces are surfaces which contain nano-scale (sub-wavelength) structures which lead to special and sometimes highly remarkable optical properties. Usually (but not always), they are also required to have a sub-wavelength thickness. Basic operation principles of such metasurfaces are similar as for photonic metamaterials, but here the sub-wavelength structuring is applied only in a thin layer at the surface of some substrate. While the fabrication of photonic metasurfaces is generally much less demanding than that of 3D metamaterials, a large number of interesting optical functions can be realized with that approach of metaoptics, which is thus overall considered to have a substantially larger potential for widespread practical use in a new kind of flat optics [7, 21].
Types of Metasurfaces
Metasurfaces can contain different types of nanostructures:
- Some of them have metallic features such as tiny antennas, which can be straight or bent, or exhibit sharp angles (see Figure 1). (A pronounced anisotropic behavior is often obtained.) Due to the conductive properties of metals, the electron charge distribution can move under the influence of an electromagnetic field and can radiate a scattered field, apart from absorbing part of the incident optical power. This field is called plasmonics, alluding to the plasma formed by the conduction electrons.
- One may also use patterns of tiny openings (e.g. nanoslits) in metallic films or in graphene.
- Other metasurfaces are made with dielectric structures only, or similarly with semiconductors. They need to have a high refractive index contrast, and they often contain nanopillars (nanorods) surrounded by air. These pillars can have a cylindrical shape or a less symmetric cross section, such that the interaction with the electromagnetic field depends on the relative orientation between the pillars and the propagation direction and the polarization direction of the incident wave. Instead of pillars, nanoparticles with other shapes may also be used. In some cases with small enough spacing, the nano-elements are coupled to each other, which can give rise to additional phenomena. A substantial advantage of purely dielectric or semiconductor structures is that they typically exhibit substantially lower absorption losses than plasmonic structures.
- Tunable metasurfaces may be realized with liquid crystal devices, where the orientation of large molecules can be controlled with an applied electric field. Note that the thickness of liquid crystal devices will in general not be small compared with the optical wavelength, as usually expected for metasurfaces. However, there are also attempts to use liquid crystal materials into thin nanostructured devices in order to obtain tunability .
A single layer of plasmonic or dielectric structures is often used, but there are also cases where one uses several such layers, for example with the goal of impedance matching. Still, the overall thickness is typically well below one wavelength.
In many cases, the optical effects depend on the orientation of structural features (“meta-atoms”) such as antennas or dielectric pillars with respect to the direction of the incident electric field. That phenomenon is called geometrical phase change or Pancharatnam–Berry phase . That effect is frequently exploited.
Purely reflective devices can be obtained by covering a metasurface with a sufficiently thick metallic layer.
For both plasmonic and dielectric structures, resonances may occur for certain optical frequencies – not necessarily at the frequency of operation. If the interaction is sufficiently strong, such resonances can provide substantial phase changes even in a very thin layer.
In the simplest cases, the nanostructure is periodic in the transverse dimensions, effectively leading to uniform optical properties of the surface. In many cases, however, structural details such as the diameter of dielectric nanopillars or the orientation of antennas is varied on the surface such as to obtain variable changes of optical phase, for example.
Photonic metasurfaces are more easily made for operation at long wavelengths, e.g. in the mid-infrared, where the required structure size is not that small. Note, however, that already well before the year 2000 semiconductor fabrication technology routinely reached the capability to produce structures with sizes well below an optical wavelength in the visible spectral region. Even structure sizes well below 10 nm are now routinely produced with optimized techniques of lithography based on short-wavelength radiation. Even smaller structures become possible with extreme-UV lithography. Generally, nanotechnology has shown enormous advances in recent years.
Description of Optical Effects of Metasurfaces
The optical function of a photonic metasurface basically arises from scattering and possibly also from the absorption of light at nanostructures. Frequently, the interaction depends on the polarization of the light. The scattering may lead to reflection, or only to the modification of the properties of transmitted light.
In principle, one can investigate the optical function in full detail, i.e., considering the interaction of the light field with the nanostructures on a nanometer scale. For example, one could apply a numerical model which solves Maxwell's equations. Such an approach, however, would be realistic at most for rather small regions; otherwise, the requirements in terms of computer memory and computation time would be excessive Also, it is not realistic to find analytic solutions to such equations for structures with considerable complexity. Note also that a purely scalar treatment of the light field is usually not sufficient, also for purely dielectric structures, because these usually have a higher refractive index contrast; full vectorial models are thus required.
Usually, one develops physical models for a “homogenized” material, i.e., treating the nanometer-scale details only through effective properties on longer length scales. That leads to a much simplified description of the optical effects in terms of changes of optical phase and/or amplitude for transmitted or reflected light, e.g. with transmission or reflection factors for complex phasors, which may be spatially dependent, but not on a sub-wavelength scale. (In contrast to that, 3D photonic metamaterials are often described with a refractive index which can vary on a similar length scale.) Considering the optical phase only, the obtained factors describe the change of the wavefronts, which themselves influence the further propagation of light in homogeneous material, e.g. the convergence due to a focus. The condition for such a simplified description to be realistic is essentially that the nanostructure features are fine enough not to be “seen” by the light. That condition may be well fulfilled in practice, even if the nanostructures have dimensions only a few times below the wavelength.
In some situations, it is not sufficient to consider the phase changes only. With suitably designed metasurfaces, one can control both the electric and magnetic polarizability. These in combination do not only determine phase delays, but also the impedance η = (μeff / εeff)1/2. Impedance matching over some wavelength range can be achieved with certain structures .
Different methods have been developed for calculating the spatially dependent transmission and reflection factors. For example, they can be based on numerical solutions, obtained for rather small volumes of material with periodic boundary conditions in the transverse directions. Once such complex factors have been obtained, the further calculation of the optical effects can be a relatively simple, based on the principles of Huygens' wave theory or Fourier optics. For example, a metalens (see below) is obtained when the phase changes for transmitted light are approximately proportional to the square of the transverse distance from the lens center.
Optical Functions of Photonic Metasurfaces
In the following sub-sections, some typical optical functions are explained which can be realized with photonic metasurfaces and may find interesting applications. Actually, a much wider range of functions may be realized, some of which could not be possible with conventional optical elements.
Some metasurfaces are designed such that they provide a phase change for transmitted light which varies linearly in one transverse direction. That can be achieved by systematically varying some nanostructure properties such as the orientation or size of features. Since only the phase change modulo 2π is relevant, the arrangement can be periodic, but obviously it is necessary to use a kind of structure where phase control is possible over a range of 2π. That is not possible for a single resonance, but for example for the combination of two resonances (e.g. associated with two plasmonic eigenmodes) above and below the operation frequency.
It is also possible to utilize the idea of digital metamaterials : one may combine (on a sub-wavelength scale) two different elemental materials, having oppositely-signed real parts of their permittivities, such as to obtain different effective permittivities.
For an ordinary optical surface, such as the interface between some optical glass and air, the laws of refraction hold, described by Fresnel equations. For a metasurface as described above, these laws can be modified in a relatively simple way, taking into account the additional spatially varying phase shift [1, 2]. With such equations, it can be seen quite easily, for example, that refraction angles can be completely modified, giving rise to curious phenomena such as negative refraction: the outgoing beam is on the same side of the surface normal as the incoming beam (see Figure 2).
There is great freedom to realize other structures with interesting properties. For example, one can design metasurfaces which essentially act as blazed diffraction gratings. Here, the transmitted light is largely concentrated into a single diffraction order. Highly compact spectrometers could be realized that way. There are also other ideas how to realize ultra-compact spectrometers with metasurfaces .
The essential function of a lens is to provide a radially varying change of optical phase of transmitted light – typically, with an approximate square dependence on the transverse distance to the lens center. That leads to an approximately spherical curvature of wavefronts for incident plane waves, for example. In an ordinary lens, this is achieved with a substantial variation of the thickness, leading to the typical geometrical shape of a lens. Alternatively, one may realize a gradient-index lens, where the thickness is constant, but the refractive index is varied in the transverse directions. Another possibility is now to employ a suitably designed metasurface, where the required phase change is achieved within a very thin layer on a substrate which only has the purposes of providing mechanical stability and an opportunity for mounting.
A frequently encountered problem with lenses are the introduced optical aberrations. For example, spherical aberrations result of from spherical lens shapes, which are advantageous for easy fabrication, and can in principle be avoided by using aspheric lenses, requiring more sophisticated fabrication technology. Photonic metasurfaces now provide the opportunity to achieve basically arbitrary phase profiles without making the fabrication significantly more difficult. Once it is understood what nanostructure is required for each value of required phase change, the overall structure can be easily designed for any phase profile. One can then design relatively simple optics, possibly using only a single lens, with optical aberrations being so weak as achieved only with complex multi-lens arrangements (objectives) in traditional optics.
Simple metalens designs may work only in a narrow wavelength region due to strong chromatic aberrations. In some cases, those are intentionally used, e.g. for purposes of optical filtering. It is also possible, however, to optimize metalens designs for much weaker chromatic aberrations [19, 27], or for a wanted increase or decrease of focal length for increasing wavelength. Note also that there are plenty of potential applications for essentially monochromatic light, where even strong chromatic aberrations do not matter.
Under certain circumstances, even sub-diffraction focusing and imaging is possible with metasurfaces .
Tunable meta-lenses are also possible. They may be based on liquid crystal devices, but also an ultra-thin metasurfaces combined with elastomer actuators . In contrast to conventional zoom optics, here one uses actuators which operate in transverse directions.
Complex wavefront shaping can also be achieved was suitably designed photonic metasurfaces. For example, vortex beams (having an orbital angular momentum, OAM) can be generated by sending a simple plane wave beam to a plasmonic structure which causes a phase change which depends on the azimuthal angle .
The chromatic properties of photonic metasurfaces can be utilized in many ways to obtain wavelength-dependent optical filters. For example, a bandpass filter for the mid-infrared has been demonstrated based on a fishnet nanostructure .
Polarizing Optical Elements
As mentioned above, the interaction of metasurfaces can easily be made polarization-dependent. Together with the possibility to achieve basically arbitrary spatial dependence of polarization changes, this leads to a very wide range of possibilities. One can obtain the functions of classical elements of polarization optics such as waveplates and polarizers, including circular polarizers. A wide range of optical devices could profit from that; for example, one could realize ultra-compact polarimeters . Also, one can obtain more sophisticated functions, e.g. where the polarization changes also have a spatial and/or spectral dependence.
For sufficiently high incident optical intensities, nonlinearities of the involved materials may come into play. That allows one to realize various nonlinear functions such as intensity-dependent polarization, phase and amplitude changes, as well as nonlinear frequency conversion , e.g. in the form of four-wave mixing, frequency doubling and frequency tripling, albeit usually with quite low conversion efficiencies. An interesting aspect of nonlinear frequency conversion processes in photonic metasurfaces is the possibility of anomalous phase matching situations, such as backward phase matching in plasmonic devices. Generally, phase matching becomes less critical due to the very small propagation distances in metasurfaces.
Attractions of “Flat Optics”
Photonic metasurfaces are the basis of a new kind of “flat optics” – using only optical components which essentially have flat parallel surfaces and are fairly thin, in contrast to traditional optics with partially curved surfaces e.g. of mirrors and lenses. That approach has certain substantial attractions:
- At least as long as such flat optical components can be operated in close proximity, precise mechanical mounting becomes easy, and optical setups can become extremely compact.
- Well established technology from the area of CMOS microelectronics, which has been used for decades for mass-producing mostly quite cheap integrated electronic circuits, could be adapted for new uses in the area of optics. It works with semiconductors and metals, both of which can be suitable for photonic metasurfaces, and the readily achieved small structure sizes are fully sufficient for that.
- The relatively expensive traditional optics technology, involving the fabrication of precisely curved optical surfaces (with precision milling, polishing, coating etc.) and the precise mounting of components in considerable distances, may in some areas be fully replaced with such flat optics. That would be particularly interesting in areas where both electronics and optics are needed – for example, for cameras in smartphones.
Cost savings may particularly be achieved in application areas where quite small optical setups are sufficient, because many devices could then be produced together on one wafer, just as in microelectronics. Also, the easy integration with electronic functions can be attractive. It is thus well conceivable that new types of highly compact and cheap optoelectronics can be developed for use in areas like imaging, printing, optical fiber communications, optical sensors and spectroscopy.
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