A flat lens is a lens whose flat shape allows it to provide distortion-free imaging, potentially with arbitrarily-large

aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An opt ...

s. The term is also used to refer to other

lenses A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...

that provide a negative

index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...

. 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.

History

Russian mathematician

Victor Veselago Victor Georgievich Veselago (13 June 1929, Ukraine – 15 September 2018) The first, near-infrared, flat lens was announced in 2012 using nanostructured antennas. It was followed in 2013 by an ultraviolet flat lens that used a bi-metallic sandwich. In 2014 a flat lens was announced that combined composite metamaterials and

transformation optics Transformation optics is a branch of optics which applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction ...

. The lens works over a broad frequency range.

Traditional lenses

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 Petzval field curvature, named for Joseph Petzval, describes the optical aberration in which a flat object normal to the optical axis (or a non-flat object past the hyperfocal distance) cannot be brought properly into focus on a flat image pl ...

and other aberrations.) To correct this, lenses use extra pieces of glass, adding bulk, complexity, and mass.

Metamaterials

Flat lenses employ

metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...

s, that is, electromagnetic structures engineered on subwavelength scales to elicit tailored polarization responses. 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 Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...

in two and three dimensions at

microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...

frequencies have been achieved in resonant metamaterials with centimetre-scale features. Metamaterials can image infrared, visible, and, most recently,

ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nanometer, nm (with a corresponding frequency around 30 Hertz, PHz) to 400 nm (750 Hertz, THz), shorter than that of visible light, but longer than ...

wavelengths.

Types

Graphene oxide

With the advances in micro- and

nanofabrication Nanolithography (NL) is a growing field of techniques within nanotechnology dealing with the engineering (patterning e.g. etching, depositing, writing, printing etc) of nanometer-scale structures on various materials. The modern term reflects on a ...

techniques, continued miniaturization of conventional optical lenses has been requested for applications such as communications, sensors, and data storage. Specifically, smaller and thinner micro lenses are needed for subwavelength optics or nano-optics with small structures, for visible and near-IR applications. As the distance scale for optical communications shrinks, the required feature sizes of micro lenses shrink.

Graphene oxide An oxide () is a chemical compound that contains at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of −2. Most of the ...

provides solutions to advance planar focusing devices. Giant

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...

modification (as large as 10^-1 or one order of magnitude larger than earlier materials), between graphene oxide (GO) and reduced graphene oxide (rGO) were demonstrated by manipulating its oxygen content using

direct laser writing Multiphoton lithography (also known as direct laser lithography or direct laser writing) of polymer templates has been known for years by the photonic crystal community. Similar to standard photolithography techniques, structuring is accomplished ...

(DLW) method. The overall lens thickness potentially can be reduced by more than ten times. Also, the linear optical absorption of GO increases as the reduction of GO deepens, which results in transmission contrast between GO and rGO and therefore provides an

amplitude modulation Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the amplitude (signal strength) of the wave is varied in proportion to ...

mechanism. Moreover, both the

and optical absorption are dispersionless over a

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

range from visible to near infrared. GO film offers flexible patterning capability by using the maskless DLW method, which reduces manufacturing complexity. A novel ultrathin planar lens on a GO thin film used the DLW method. Its advantage 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 subwavelength scale (~200 nm), which is thinner than dielectric lenses (~ µm scale). The focusing intensities and the

focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...

can be controlled effectively by varying laser power and lens size, respectively. By using oil immersion high

numerical aperture In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the proper ...

(NA) objective during DLW process, 300 nm fabrication feature size on GO film has been realized, and therefore the minimum lens size reached 4.6 µm in diameter, the smallest planar micro lens. This 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 NA and the focusing resolution. The full-width at half-maximum (FWHM) of 320 nm at the minimum focal spot using a 650 nm input beam has been demonstrated experimentally, which corresponds to an effective NA of 1.24 (n=1.5). Furthermore, ultra-broadband focusing capability from 500 nm to as far as 2 µm have been realized with this planar lens.

Nanoantennas

The first flat lens used a thin wafer of

silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...

60 nanometers thick coated with concentric rings of v-shaped gold nanoantennas to produce photographic images. The antennas 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 refraction angle — more at the edges than in the middle — is controlled by the antennas' shape, size, and orientation. It could focus only a single near-infrared wavelength. Nanoantennas introduce a radial distribution of phase discontinuities, thereby generating respectively spherical

wavefronts In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal freque ...

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 In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...

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. This lens does not suffer from the chromatic aberrations, or color fringing, that plague refractive lenses. As such, it does not require the additional lens elements traditionally used to compensate for this chromatic dispersion.

Bi-metallic sandwich

A bi-metallic flat lens is made of a sandwich of alternating nanometer-thick layers of silver and

titanium dioxide Titanium dioxide, also known as titanium(IV) oxide or titania , is the inorganic compound with the chemical formula . When used as a pigment, it is called titanium white, Pigment White 6 (PW6), or CI 77891. It is a white solid that is insolubl ...

. It consists of a stack of strongly-coupled

plasmonic In physics, a plasmon is a quantum of plasma oscillation. Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. The plasmon can be considered as a quasiparticle since it arises from the quan ...

waveguides sustaining backward waves. It exhibits a negative

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.

Membrane

Membrane optics employ plastic in place of glass to

diffract Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...

rather than

refract In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...

or reflect light. Concentric microscopic grooves etched into the plastic provide the

diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...

. 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

Holographic lenses are made from a

hologram Holography is a technique that enables a wavefront to be recorded and later re-constructed. Holography is best known as a method of generating real three-dimensional images, but it also has a wide range of other Holography#Applications, applic ...

of a conventional lens. It is flat, and present any drawbacks of the original lens (aberrations), plus the drawbacks of the hologram (diffraction). The hologram of a mathematical lens is flat, and it has the properties of the mathematical lens, but it has the drawbacks of the hologram (diffraction).

Geometric-phase lenses

Geometric phase lenses, also known as polarization-directed flat lenses are made by depositing

liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. T ...

polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

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.

References

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External links

Aberration-Free Ultrathin Flat Lenses and Axicons at Telecom Wavelengths Based on Plasmonic Metasurfaces (full text)
Metamaterials Photographic lens designs