A flat lens is a lens whose flat shape allows it to provide distortion-free imaging, potentially with arbitrarily-large apertures. The term is also used to refer to other lenses that provide a negative index of refraction. Flat lenses require a refractive index close to −1 over a broad angular range. In recent years, flat lenses based on metasurfaces were also demonstrated.
Russian mathematician Victor Veselago predicted that a material with simultaneously negative electric and magnetic polarization responses would yield a negative refractive index (an isotropic refractive index of −1), a "left-handed" medium in which light propagates with opposite phase and energy velocities.
Traditional curved glass lenses can bend light coming from many angles to end up at the same focal point on a piece of photographic film or an electronic sensor. Light captured at the very edges of a curved glass lens does not line up correctly with the rest of the light, creating a fuzzy image at the edge of the frame. (Petzval field curvature and other aberrations.) To correct this, lenses use extra pieces of glass, adding bulk, complexity, and mass.
Left-handed responses typically are implemented using resonant metamaterials composed of periodic arrays of unit cells containing inductive–capacitive resonators and conductive wires. Negative refractive indices that are isotropic in two and three dimensions at microwave frequencies have been achieved in resonant metamaterials with centimetre-scale features.
Graphene oxide lens
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With the advances in micro- and nanofabrication techniques, continued miniaturization of the conventional optical lenses has always been requested for various applications such as communications, sensors, data storage, and a wide range of other technology-driven and consumer-driven industries. Specifically, ever smaller sizes as well as thinner thicknesses of micro lenses are highly needed for subwavelength optics or nano-optics with extremely small structures, particularly for visible and near-IR applications. Also, as the distance scale for optical communications shrinks, the required feature sizes of micro lenses are rapidly pushed down.
Recently, the excellent properties of newly discovered graphene oxide provide novel solutions to overcome the challenges of current planar focusing devices. Specifically, giant refractive index modification (as large as 10^-1), which is one order of magnitude larger than the current materials, between graphene oxide (GO) and reduced graphene oxide (rGO) have been demonstrated by dynamically manipulating its oxygen content using direct laser writing (DLW) method. As a result, the overall lens thickness can be potentially reduced by more than ten times. Also, the linear optical absorption of GO is found to increase as the reduction of GO deepens, which results in transmission contrast between GO and rGO and therefore provides amplitude modulation mechanism. Moreover, both the refractive index and the optical absorption are found to be dispersionless over a broad wavelength range from visible to near infrared. Finally, GO film offers flexible patterning capability by using the maskless DLW method, which reduces the manufacturing complexity and requirement.
As a result, a novel ultrathin planar lens on a GO thin film has been realized recently using the DLW method. The distinct advantage of the GO flat lens is that phase modulation and amplitude modulation can be achieved simultaneously, which are attributed to the giant refractive index modulation and the variable linear optical absorption of GO during its reduction process, respectively. Due to the enhanced wavefront shaping capability, the lens thickness is pushed down to subwavelength scale (~200 nm), which is thinner than all current dielectric lenses (~ µm scale). The focusing intensities and the focal length can be controlled effectively by varying the laser powers and the lens sizes, respectively. By using oil immersion high NA objective during DLW process, 300 nm fabrication feature size on GO film has been realized, and therefore the minimum lens size has been shrink down to 4.6 µm in diameter, which is the smallest planar micro lens and can only be realized with metasurface by FIB. Thereafter, the focal length can be reduced to as small as 0.8 µm, which would potentially increase the numerical aperture (NA) and the focusing resolution.
The full-width at half-maximum (FWHM) of 320 nm at the minimum focal spot using 650 nm input beam has been demonstrated experimentally, which corresponding to the effective numerical aperture (NA) of 1.24 (n=1.5), the largest NA of current micro lenses. Furthermore, ultra-broadband focusing capability from 500 nm to as far as 2 µm have been realized with the same planar lens, which is still a major challenge of focusing in infrared range due to limited availability of suitable materials and fabrication technology. Most importantly, the synthesized high quality GO thin films can be flexibly integrated on various substrates and easily manufactured by using the one-step DLW method over a large area at a comparable low cost and power (~nJ/pulse), which eventually makes the GO flat lenses promising for various practical applications.
The first flat lens used a thin wafer of silicon 60 nanometers thick coated with concentric rings of v-shaped gold nanoantennas to produce photographic images. The antennas were systematically arranged on the silicon wafer and refract the light so that it all ends up on a single focal plane, a so-called artificial refraction process. The antennas were surrounded by an opaque silver/titanium mask that reflected all light that did not strike the antennas. Varying the arm lengths and angle provided the required range of amplitudes and phases. The distribution of the rings controls focal length.
The nanoantennas introduce a radial distribution of phase discontinuities, thereby generating respectively spherical wavefronts and nondiffracting Bessel beams. Simulations show that such aberration-free designs are applicable to high-numerical aperture lenses such as flat microscope objectives.
In 2015 a refined version used an achromatic metasurface to focus different wavelengths of light at the same point, employing a dielectric material rather than a metal. This improves efficiency and can produce a consistent effect by focusing red, blue and green wavelengths at the same point to achieve instant color correction, yielding a color image. The new flat lens does not suffer from the chromatic aberrations, or color fringing, that plague refractive lenses. As such, it will not require the additional bulky lens elements traditionally used to compensate for this chromatic dispersion.
A later flat lens is made of a sandwich of alternating nanometer-thick layers of silver and titanium dioxide. It consists of a stack of strongly-coupled plasmonic waveguides sustaining backward waves and exhibits a negative index of refraction regardless of the incoming light's angle of travel. The waveguides yield an omnidirectional left-handed response for transverse magnetic polarization. Transmission through the metamaterial can be turned on and off using higher frequency light as a switch, allowing the lens to act as a shutter with no moving parts.
Glass transmits light with 90% efficiency, while membrane efficiencies range from 30-55%. Membrane thickness is on the order of that of plastic wrap.
Holographic lenses have been made. A hologram of a [real] lens can be used as a lens. It is flat, but it has all the drawbacks of the original lens (aberrations), plus the drawbacks of the hologram (diffraction).
The hologram of a mathematical lens can be generated. It is flat, and it has the properties of the mathematical lens, but it has the drawbacks of the hologram (diffraction).
Geometric phase lenses, also known as Polarization-Directed Flat lenses, are being made by depositing liquid-crystal polymer in a pattern to make a "holographically recorded wavefront profile". They exhibit a positive focal length for circularly polarized light of one direction, and a negative focal length for circularly polarized light of one direction. 
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