Tikalon Blog by Dev Gualtieri

Metamaterial Lenses

November 18, 2019

One measure of the importance of a technology is how many instances you have in your home. By that measure, the transistor easily takes first place, since the integrated circuits in your cellphones, computers, and other devices contain many billions of transistors. If we come up from the nanoscale to something about the size of common fruits, overlooking the many instances of advanced material items made of glass, metal, and plastic, the electric motor is a likely second to the transistor. Electric motors are a part of your refrigerator, hair dryer, home appliances, and even the device that vibrates your cellphone.

Your household likely contains at least as many optical lenses as electric motors. My eyeglasses have two lenses that allow me to more easily write this article, and there are lenses in cellphone cameras, tablet computer cameras, and laptop computer cameras. If a household member uses disposable contact lenses, the number of contact lenses in a single box will alone outnumber the electric motors.

The Glasses Apostle, a 1403 painting by Conrad von Soest

Optical lenses have been known from antiquity, but the apparent first mention of their use as a corrective lens is in Pliny the Elder's description of the Roman emperor Nero's use of an emerald as a vision aid.[1]

Roger Bacon discussed the scientific principles behind the use of corrective lenses in Part V of his c.1266 Opus Majus.[2]

(The Glasses Apostle, a 1403 painting by Conrad von Soest (c. 1730 - c. 1422), considered to be the oldest depiction of eyeglasses north of the alps, via Wikimedia Commons.)

Early lenses were made from glass by the protracted process of grinding and polishing flat, or near-net-shape, pieces into the required shape and high surface finish. The lenses of in the devices of today are cast from high refractive index epoxy gels in precision molds with a subsequent thermal reflow process. However, one effective lens from antiquity, the pinhole lens didn't need a refractive material to function. If light rays are constrained to pass through a small opening, they will project an inverted image on a wall or screen.

Such a room having a small opening to admit light, called a camera obscura, was supposedly known to the Greek philosopher Aristotle (384 BC-322 BC). This pinhole lensing is described in Book XV, chapter 6, of his "Problems." In the Problems, Aristotle writes how the image of the Sun, projected through the rectangular holes of a wicker basket, still maintains its circular shape in the image projected onto the ground.[3]

"Why does the Sun penetrating through quadrilaterals form not rectilinear shapes but circles, as for instance when it passes through wicker-work? Is it because the projection of the vision is in the form of a cone, and the base of a cone is a circle, so that the rays of the sun always appear circular on whatever object they fall? For the figure also formed by the sun must be contained by straight lines, if the rays are straight; for when they fall in a straight line on to a straight line, they form a figure contained by straight lines. And this is what happens with the rays."[3]

Just slightly more complex than a hole in a wall is a lens formed by water in a spherical glass vessel. This type of lens, used as a burning glass in antiquity, was described by Pliny the Elder (23-79) in his Naturalis Historia (Natural History):

"Est autem caloris inpatiens, ni praecedat frigidus liquor, cum addita aqua vitreae pilae sole adverso in tantum candescant, ut vestes exurant."[4]

"And yet, we find that globular glass vessels, filled with water, when brought in contact with the rays of the sun, become heated to such a degree as to cause articles of clothing to ignite."[5]

The magnifying effect of water droplets were possibly the inspiration for the spherical glass lenses made by Antonie van Leeuwenhoek (1632-1723) in construction of the first microscopes. Van Leeuwenhoek created these lenses by first forming slender fibers of soda-lime glass in a hot flame, then reinserting one end of such fibers into the flame to form a small sphere at the end. Since he could only make small glass spheres of high quality by this method, his microscopes were likewise small.

Spherical lenses distort their images, a phenomenon called spherical aberration. This is how a square grid looks when a spherical lens is placed on it.

Central objects are reasonably free of distortion, but overall distortion is minimized in the aptly named aspheric lenses.

(Illustration by the author, using Inkscape.)

Lenses are used to focus things other than light. Electron microscopes focus their electron beams with electrostatic and electromagnetic lenses. As I discussed in an earlier article (Focusing X-Rays, July 20, 2015), a far more difficult task is the creation of lenses for X-rays, which easily pass through most objects, with their passage somewhat impeded by a material-dependent attenuation coefficient. This attenuation allows the X-ray imaging of tooth and bone in dental and medical radiography. The zone plate, as shown in the figure, is one effective lens for X-rays.

A Zone plate uses the interference of waves to focus X-rays and other forms of electromagnetic radiation. Zone plates can be designed to focus sound waves.

Zone plates are formed as a set of radially symmetric rings that alternate between opaque and transparent. X-rays will diffract around the edges of the opaque zones, and the spacing of the zones is arranged such that Constructive interference produces an image at a focus point.

(Wikimedia Commons image by Tom Murphy VII.)

Reflection can also be used as a lensing principle for X-rays. If X-rays impinge on a metal surface, they will obey Snell's law, so there's an angle for which total internal reflection is obtained. For X-rays, this grazing angle is very small, and it ranges from a few arc-minutes to about a degree, depending on X-ray wavelength. This principle is used to focus X-rays in a Wolter telescope, named after German physicist, Hans Wolter (1911-1978), who published the idea in 1952.[6] Two NASA satellite observatories, the Neil Gehrels Swift Observatory and the Chandra X-ray Observatory, both use Wolter telescopes.

There's an old adage that "Many hands make light work." This was true of the Multiple Mirror Telescope in which the traditional, huge mirror of reflecting telescopes was replaced by an arrangement of multiple mirrors of the same aperture. Such was also true for an innovative lens developed at Harvard University in 2016. This extremely thin optical lens was built from an array of smaller optical elements.[7-8] The array elements were high refractive index titanium dioxide (Ti O₂) pillars on a silica glass (SiO₂) substrate (see figure).[8] These pillars act as phase-shifting elements for light. I described this metamaterial lens in a previous article (Harvard Metamaterial Flat lens, July 4, 2016).

Titanium dioxide pillar metamaterial lens

The Harvard metamaterial lens. Left image, the process parameters for titanium dioxide pillars on silica. The phase shift of light through the lens at each point can be adjusted through rotation of the pillars. Right image, a scanning electron micrograph of the metamaterial lens. The titanium dioxide pillars are formed by atomic layer deposition on a silica glass substrate. (Left image, created using Inkscape. Right image, Capasso Lab image via Harvard University.)

The metamaterial lens is just 2 millimeters in dimension, it has a numerical aperture of 0.8, and it focuses light with efficiencies as high as 86%.[8] The focusing was excellent, being diffraction-limited, but the lens operates at just a particular wavelength of light, and it is out-of-focus at other wavelengths.[8] However, a new metamaterial lens from researchers at the University of Utah electrical and computer engineering department operates over a wide bandwidth, albeit in the infrared.[9-10]. This lens is described in an open access article in a recent issue of the Proceedings of the National Academy of Sciences.[9]

This long-wave infrared (LWIR) lens has a thickness of just 10 micrometers, and a weight that's two orders of magnitude less than that of the equivalent refractive optics.[9-10] Like other metamaterial lenses, this lens is built from many microstructures, each of which bend light to a focus. Says Rajesh Menon, an associate professor at the University of Utah and an author of the paper, "You can think of these microstructures as very small pixels of a lens... They're not a lens by themselves but all working together to act as a lens."[10] The research team calls this lens a multilevel diffractive lens (MDL), and it's designed to correct for optical aberrations, including chromatic aberrations, in the LWIR band.[9] Its thickness can be of the order of the infrared wavelength.[9]

$University of Utah Multilevel Diffractive Lens$

University of Utah multilevel diffractive lens with an 8 mm focal length. Left image, an optical micrograph of the lens from ref. 9, distributed under a Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). Left image, a photograph of the lens by Dan Hixson/University of Utah College of Engineering.

The lens functions in a spectral band from 8 μm to 12 μm, with chromatic aberrations corrected over that entire LWIR band.[9] At this time, no other broadband LWIR metamaterial lens has been demonstrated.[9] The first prototypes exhibited 25% absorption losses,but good imaging was obtained with a field of view of 35° and angular resolution better than 0.013°.[9] These MDLs are polarization-insensitive, and they can be improved by substitution of lossless, higher-refractive-index materials like silicon for the polymers of the prototypes.[9]

Since these lenses are so thin, they can be fabricated from materials with high absorption in the LWIR, such as they polymers used in the prototypes. This would allow inexpensive manufacturing using nanoimprint lithography.[9] Since these lenses are so light and have a short focal length, they can be incorporated in cameras on drones to allow them to fly longer, and soldiers could have much lighter night vision equipment.[10] This research was funded by the National Science Foundation and the U.S. Office of Naval Research.[10]

Metamaterial Lenses

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