Physics: Optics

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Physics: Optics

Introduction

Optics is the branch of physics concerned with the nature and uses of light. Especially through systems made of lenses—pieces of glass or plastic shaped to alter the light passing through them—optics have made possible photography; the discovery of microorganisms through microscopes; the correction of some vision disorders by eyeglasses and contact lenses; the study of the distant universe through telescopes; movie and slide projection; and thousands of industrial processes, including the manufacture of computer microchips using optics to outline billions of transistors on tiny tiles of silicon. Lenses, mirrors, lasers, and optical fibers are used in data transmission, storage, and retrieval; in surgery; weapons targeting; document scanning and printing; and for many other purposes. Optical systems have been essential to scientific and technological progress.

Historical Background and Scientific Foundations

The earliest known theories about the nature of light were made by the ancient Greeks. Greek philosophers reasoned from the casting of shadows by solid objects that light must travel in straight lines. They also knew that light rays are reflected from a surface at the same angle that they strike it. The followers of Democritus (c.460–370 BC), who taught that the world was made of atoms and void (emptiness), speculated that light consisted of streams of particles and that visual sensation is caused when these particles strike the eye. Pythagoras (c.575–500 BC) explained that light is not the cause of visual sensation, but that “seeing rays” are emitted from the eye, rays which interact with light somehow at the surface of the object being viewed or in some other way. Aristotle (384–322 BC) denied Democritus's theory of atoms and void, and proposed a quite different theory of light, namely, that light is an alteration of the materials between the source of illumination and the eye.

Greeks of the fifth century BC were able to make glass and understood the ability of lenses to concentrate sunlight to burning intensity. Later, the Romans also used lenses as burning-glasses, though they do not seem to have understood their full potential.

Growth in optics was slow throughout the Middle Ages (AD 900–1400). Arab scientists such as Ibn Sahl (c.940–1000) and Ibn al Haitham (963–1039) published treatises on mirrors and lenses that would eventually influence European students of optics. Various properties of lenses and prisms were observed by Arab and European scientists in the Middle Ages—English scientist and Franciscan monk Roger Bacon (1215–1294) was the first person to write down observations on the magnifying properties of lenses and also wrote a book attempting to explain the nature of rainbows—but no general agreement was reached on the nature of light itself, and, apart from the use of lenses as burning-glasses to start fires, few practical uses were found for optics. This changed with the invention of eyeglasses in Italy around 1280. Although expensive, eyeglasses gradually became common in some places. In the 1400s, the ability of concave lenses to correct nearsightedness was discovered by German churchman and scientist Nicholas of Cusa (1401–1464). The making and wearing of eyeglasses spread awareness of lenses and the ability to craft them over all Europe, preparing the way for other advances in optics.

In the 1400s, the device known as the camera obscura, Latin for “dark chamber” and origin of the English word “camera,” became popular in Europe. A camera obscura is a darkened room pierced by a pinhole or a larger hole in which a convex lens is inserted. The lens or pinhole projects an image of the outer world on the opposite interior wall of the dark room, where it can be traced on paper or simply viewed. Modern cameras are miniature camera obscura, where instead of the image being traced by hand, it is recorded by an array of electronic components or a sheet of film coated with light-sensitive chemicals.

The rise of modern, scientific optics occurred gradually during the late 1500s and early 1600s, a period when all areas of physical science were undergoing revolutionary changes. In 1600, a Dutch maker of eyeglasses, probably Zacharias Janssen (1580–1638), invented the compound microscope, a combination of two or more magnifying lenses that allow the inspection of details smaller than the unaided human eye can see. Microscopes were steadily improved during the 1600s, achieving higher and higher magnifications and revealing the existence of a hitherto unknown micro-world. In 1675, Dutch scientist Antoni van Leeuwenhoek (1632–1723) discovered the existence of microorganisms.

The refracting telescope was invented in 1608, also by Dutch makers of eyeglasses. New scientific discoveries followed rapidly. The first person to turn the telescope on the heavens was Italian scientist Galileo Galilei (1564–1642), who had heard about the new invention and in 1609 built one of his own. On the basis of his observations, Galileo advocated the Copernican view that Earth moves around the sun. The official view of the church at that time was that Earth is stationary, and Galileo was forced to officially retract his support of Copernicanism.

The seventeenth century also was the time of many discoveries of optical phenomena. Dutch scientist Willebrord Snell (1580–1626) discovered the law of refraction, today known as Snell's law. This mathematical law relates the angle through which a light ray is bent when

passing from one medium into another (for example, from air into glass) to the index of refraction of each material. A transparent material's index of refraction is its tendency to slow light down.

With Snell's law in hand, scientists could make fast progress in geometrical optics, the mathematical description of the paths that light rays take through systems of lenses and mirrors. Geometrical optics are needed for the scientific design of microscopes, telescopes, eyeglasses, and other optical devices. Double refraction and polarization were discovered in the late 1600s, and in 1676 Danish astronomer Olaus (or Ole) Romer (1644–1710) made observations of the moons of Jupiter that allowed the first realistic estimates of the velocity of light. Romer's view that light travels from point to point at a finite velocity, rather than instantaneously, remained controversial for another 40 years but was verified by other scientists in the early 1700s.

Knowledge of how light behaved grew quickly in the seventeenth and eighteenth centuries, but the nature of light itself was still a mystery. Aristotle's views were still influential in many universities, and the atomistic view of Democritus (light consists of “corpuscles,” or particles) was revived. An influential theory of light was put forward by French philosopher and mathematician René Descartes (1596–1650). Descartes theorized that all space is filled with subtle (hard to detect) material of several types, and that some of this material swirls in tiny vortices or whirlpools. Descartes' theory was influential but was soon eclipsed by the work of English physicist Isaac Newton (1643–1724), who not only revolutionized physics with his laws of motion and gravitation but also did important work in optics.

Newton was a champion of the corpuscular, or particle, theory. He examined the properties of colors and prisms, proving that white light consists of a variety of colored lights that can be separated, whose colors cannot be altered, and which can be recombined into white light. So influential was Newton that the wave theory of light, championed by English scientist Robert Hooke (1635–1703) and Dutch astronomer Christiaan Huygens (1629–1695), was not widely accepted by scientists until the nineteenth century, even though it could describe a wider range of optical phenomena than Newton's particle theory.

In the nineteenth century rapid progress was made in all fields of physics, including optics. In 1801, English scientist Thomas Young (1773–1829) discovered the phenomenon of interference. This occurs when the peaks and troughs of waves, including light waves, add to or subtract from each other, causing areas of heightened brightness or darkness. Electricity and magnetism were unified optics in the work of Scottish physicist James Clerk Maxwell (1831–1879), who showed that light can

be explained as a transverse electromagnetic wave. That is, a ray of light can be viewed as an electrical field paired with a magnetic field, both fields pointing crosswise (transverse) to the direction of the ray. Each field produces the other by changing constantly in strength.

Not only did Maxwell explain the nature of light, he predicted that other types of electromagnetic waves would be discovered. His prediction came true in 1887, when radio waves were first studied by German physicist Heinrich Hertz (1857–1894). From that time onward, visible light was understood as only one narrow band of the electromagnetic spectrum, that is, all possible electromagnetic waves ordered by frequency (speed of vibration) from lowest to highest.

Hertz did not foresee any use for the phenomenon of invisible electromagnetic waves: “It's of no use whatsoever,” he told his students. But in 1896, Italian physicist Guglielmo Marconi (1874–1937) set up in England the world's first radio broadcasting station. Marconi's primitive station did not transmit voice or music, but bursts of radio energy that could be used to telegraph messages one coded letter at a time.

The camera was invented in the 1820s. The camera obscura of studio art, miniaturized and mounted on a tripod, was united with light-sensitive chemicals layered on glass plates to produce permanent photographs. Although for several decades cameras were used by only of a few hobbyists, they were mass-marketed starting with Kodak's one-dollar Brownie in 1900. (One dollar in 1900 was the equivalent of about $24 in 2007.) In the 1990s, the mass-marketed digital camera appeared, further expanding the ubiquity of the optically formed and technologically captured image. Today, imaging systems are built into cellular phones, personal digital organizers, and other multipurpose digital devices, and millions of people never leave home without one.

In the late nineteenth century, the triumph of the wave theory of light seemed complete. But German physicist Max Planck (1858–1947) showed in 1901 that the spectrum (mixture of intensities and frequencies) of electromagnetic radiation emitted by a perfectly black object (black body) can be best explained by assuming that energy is transferred only in chunks or fixed quantities (quanta). A few years later, German-American physicist Albert Einstein (1879–1955) showed that Planck's energy quanta, combined with the assumption that light is composed of tiny particles called photons, can explain certain features of the photoelectric effect, which occurs when light knocks electrons out of metal surfaces.

In the early twentieth century, light drove the discovery of new physics in two ways. First, through the theories of Planck and Einstein just described and through the work of many other people, light was basic to the development of quantum mechanics—the new theory of matter's properties at very small size scales. Today, light and all material particles are known to have the property of wave-particle duality. That is, a light wave is neither a wave nor a particle, but shows the characteristics of one or the other, depending on circumstances.

Secondly, through Einstein's theories of special relativity (1905) and general relativity (1915), light became essential to our understanding of the nature of time, space, matter, and energy, and thus of the size, shape, and history of the universe. The speed of light in a vacuum is the fundamental limiting velocity of the universe; no material object can be made to move as fast as or faster than light.

Science's fundamental understanding of light has not changed much over the last century, but the physics and technology of light have been intensely studied. A few notable developments are as follows:

IN CONTEXT: THE IMPOSSIBLE PERFECT LENS

For almost two centuries, it was taught that there was a fundamental limit to the amount of detail that a magnifying lens could bring out: no detail smaller than the wavelength of the light being magnified could be seen.

But in 1968, Russian physicist Victor Veselago (1929–) predicted that materials with a negative refractive index might exist—materials that bend light in the reverse direction compared to ordinary lens materials such as glass. And in 2000, English physicist John Pendry (1944–) predicted that by using a material with a negative refractive index of -1, a “perfect lens” might be constructed—a lens that could focus an image with perfect resolution. Lenses with lesser negative refractive indices wouldn't produce perfect images but would still surpass the wavelength limit on clarity.

Scientists set out to build a material having a negative refractive index for microwaves, a type of radio wave. (Radio waves differ from visible light only in having fewer vibrations per second.) In 2001, a team of physicists at the University of California, San Diego, claimed to have built a metamaterial—a screen of tiny electronic components—that acted on microwaves with a negative refractive index.

Some physicists disputed this claim. They argued that Pendry and Veselago had done their math wrong. Negative refraction was impossible: it would violate Special Relativity and even causality, the rule that causes must follow effects, not precede them. They said that the wavelength barrier on resolution would never be broken.

In 2003 and 2004, microwave lenses were built that actually demonstrated negative refraction and surpassed the wavelength limit. Perfect lenses for microwaves or light are still a long way off, but we now know that they are theoretically possible.

  • The laser was invented by 1958. The laser (short for “light amplification by stimulated emission of radiation”) produces a beam of extraordinarily pure light. Laser light is pure in the sense that it is nearly coherent (all its waves march together) and monochromatic (all its energy is at a single wavelength or color). Laser light travels in tight beams that can be made extremely powerful. Among the hundreds of areas in which laser optics are used are eye surgery, optical-disc writing and readback, holograms, welding, nuclear fusion, distance measurement, entertainment, microscopy, weaponry, and spectroscopy.

  • The first true optical fibers, invented in 1950, were thin rods or fibers of glass used in medicine

to allow doctors to peer inside the body. In 1956 the term “fiber optics” was coined and research began on the use of optical fibers to transmit information. After the perfection of low-loss (highly transparent) optical fibers in the 1970s, the modern system of high-speed digital data transmission through optical fibers began to come into being. Optical fiber was first deployed widely in the telephone system in the 1980s and today is the backbone of the long-distance data transmission network through which most telephone and Internet traffic passes.

The Science

Contemporary optics is usually divided into two general fields: geometrical optics and physical optics. Physical optics, in turn, includes the study of wave optics, light as an electromagnetic phenomenon, color, the interactions of light with matter, quantum optics, and relativistic optics.

Geometrical optics deals with the behavior of light when its wave nature and quantum nature can be ignored. Wherever the wavelength of light is much smaller than the objects it is interacting with, the light can be treated as an affair of raylike lines traveling from one point to another. Telescopes, microscopes, and cameras are all designed using geometrical optics.

Wave optics is concerned with light as a wave phenomenon. Interference is a wave phenomenon, and is used in holography to make three-dimensional images recorded and projected using laser light. In astronomy, the wave-optical technique known as interferometry is used to add information about light or radio waves recorded at two or more widely separated points in order to craft higher-resolution images.

Physical optics is also concerned with the light phenomena of scattering, polarization, and spectra. Material objects both emit and absorb light in different patterns: each substance, in fact, absorbs or emits some colors (wavelengths) more strongly than others, producing a spectrum as telltale as a fingerprint. By comparing these telltale spectra with light received from distant stars and other objects, scientists can study the chemical composition of objects much too far away to ever sample directly. Spectra can also be used at closer range to examine the composition of objects small or large.

Quantum optics, in which the properties of individual photons (light particles) are significant, is a particularly active field in modern physics. Lasers are used in most quantum optics work because researchers can so precisely control the properties of the light they produce.

Impact on Science

Starting in the seventeenth century, optics enabled the range of scientific observation to explode outward from the realm of everyday experience, down into the microscopic and outward into the cosmic. Since the late nineteenth century, specialized optical systems for making images of many types have become essential in almost all scientific fields.

Not only has light been of use in research and practical technology, it has been an important challenge to scientific understanding. The question of light's nature also prompted development of both relativity and quantum mechanics at the beginning of the twentieth century, revolutionizing physics.

Impact on Society

The impact of optics on art, ideas, and human relations has been profound. During the Renaissance, many books on the uses of geometry and geometrical optics in art were written by learned people. Artists reconceived the task of painting as recording how things looked, guided by perspective, an aspect of geometric optics.

Optics has had great influence on daily life through technology. The billions of components that are built on a silicon chip to make a microprocessor are projected onto the raw chip's surface using techniques ultimately derived from the printing of photographs. The discovery of microorganisms using microscopes has made possible our modern knowledge of infectious diseases. Optical systems for examining the inside of the body through natural openings or small incisions have made surgery safer and more effective. Laser light techniques are used to cure many eyesight defects.

Perhaps the most far-reaching cultural influence of optics has been through photography. Visual reports of the larger universe from telescopes and space probes have radically revised our notions of the universe and our place in it. We have seen through photographs that we share space with trillions of other stars spread across unthinkable distances. Our view of earthly life has also been changed. Many painters have responded to photography by mimicking it (photorealism) or declining to represent objects at all (abstraction). American scholar Susan Sontag (1933–2004) famously described the psychological changes wrought by photography in her book On Photography (1977). “In teaching us a new visual code,” Sontag wrote, “photographs alter and enlarge our notions of what is worth looking at and what we have a right to observe.” The greatest change wrought by photographs, according to Sontag, is that they “give us the sense that we can hold the whole world in our heads—as an anthology of images.”

Modern Cultural Connections

Optics continues to be an active field; new discoveries are frequent. The substitution of photons for electrons in computing devices would allow greater speed for less power, so several schemes for optical computing are being studied. Some would produce optical equivalents of the logic circuits found in conventional, electronic devices. Another approach is optical quantum computing, which combines optical methods with the quantum-information approach to computing. In some optical quantum computing experiments, a single atom confined in a microscopic chamber has been used as a source of photons with perfectly uniform properties. Single photons can be manipulated, as single atoms are in other quantum-computing schemes, to store “qubits” (short for “quantum bits”) that can be used to perform computations with far greater speed than ordinary computers.

Culturally, the rapid spread of the digital camera and personal computer since the 1980s have made it possible for people in industrialized societies to capture, edit, and share images more quickly and cheaply and in far greater numbers than the film camera ever did. Millions of people are now posting and viewing online stills and videos of themselves (and of other people, not always with permission), with poorly understood social consequences. Thanks to the Internet video sharing site YouTube and similar venues, the production and distribution of video materials is in the process of being democratized, as millions of amateurs realize they do not have to submit their ideas to editorial selection. This will surely have ongoing effects on the visual arts.

The near-universal presence of imaging systems thanks to cellular telephones and other devices has made it more difficult to control the visual record of events: the photos of prisoner abuse by U.S. soldiers at the Abu Ghraib prison in Iraq released in 2004 and the illicit cell-phone video of the hanging of former Iraqi dictator Saddam Hussein in 2006, which showed executioners mocking the condemned on the scaffold, are prominent examples. The popularization of instant, digital imaging systems has provided many people with nearly unfettered and unfiltered access to world events. However, computerized imaging systems can also be used to watch people in public spaces or protect property. Some find these uses of imaging systems an invasion of privacy, while others find them a useful tool in preventing crime.

IN CONTEXT: DOING THE WAVE

Under many conditions, light can be viewed as a wave moving through space. Unlike a wave in water or air, light is not a wave in something. It is an electromagnetic wave, that is, an electric field paired with an electric field, each reversing direction over and over again as the wave moves forward through space.

All electromagnetic waves have certain properties. First, they all move at the same speed in a vacuum, traditionally called the speed of light or c. The speed of light in a vacuum is 670,635,728 miles per hour (1,079,252,849 kilometers per hour). In substances such as water or glass, it moves more slowly. In fact, it can be slowed to a crawl in the laboratory.

Secondly, every electromagnetic wave, including every light wave, has a particular frequency. This is the number of times that the fields making up the wave reverse direction each second. We perceive visible light at shorter wavelengths as bluer and at longer wavelengths as redder.

Thirdly, every light wave has a fixed wavelength, the distance between any two neighboring peaks (or troughs) in the wave. Each frequency corresponds to one particular wavelength: a longer wavelength means a lower frequency and a shorter wavelength means a higher frequency. Shorter wavelengths tend to be more penetrating: The only difference between a beam of light that can be stopped by a piece of cardboard and a beam of X rays that can penetrate the body is that the X rays have a much higher frequency.

This is only the beginning, not the end, of a full description of the properties of light.

Primary Source Connection

The invisibility cloak is a staple utility of fantasy literature and science fiction novels. However, new research in optics is paving the way for invisibility devices. Newly

IN CONTEXT: ARE GLASSES SPOILING OUR GENES?

Over half the population of the industrialized world wears corrective optics—glasses or contact lenses. Some people have concluded that eyeglasses must be injuring the human genetic heritage. Their logic goes like this: In primitive times, people with bad vision would have died young. Natural selection would have screened out genes for badly formed eyes. Since the invention of glasses, however, people with bad eyes have been able to survive and pass on their bad genes. This idea was recently stated in scientific language by several scientists in the journal Trends in Genetics in 1998: “Poor vision would normally put one at a tremendous selective disadvantage, but the modern contrivance of corrective lenses has facilitated the maintenance of relevant myopia genes, and has led to a general weakening of visual capacities.”

Yet myopia, or nearsightedness, one of the most common vision problems, is not simply caused by genes: rather, individuals (more in some ethnic groups) have genes that make them more vulnerable to developing the condition when they engage in much close-focusing work, such as reading, in childhood. Until civilization comes along and invents fine print, our genetic predisposition to myopia isn't activated. What's more, as The Quarterly Review in Biology said in 1991, “Corrective lenses were invented far too recently to have allowed a substantial increase in genes that cause myopia.”

This might sound like a case of two groups of scientists contradicting each other—Trends in Genetics versus The Quarterly Review in Biology—but it's not. The only reference cited by the Trends in Genetics authors for their claim that glasses have “facilitated the maintenance of relevant myopia genes” is the paper in The Quarterly Review in Biology already quoted—which says the exact opposite.

Bottom line: Glasses have not injured the human gene pool, but preconceived ideas can cause intellectual myopia.

developed structures that bend, refract, and deflect light may help make targets “invisible” to observers. The following article notes that such a device, if ever fully developed, could have practical and military uses.

INVISIBILITY CLOAKS POSSIBLE, STUDY SAYS

Rarely, if ever, does physics news pique the interest of Pentagon brass, Harry Potter fans, and aspiring Romulans—those cloaking-device-wielding Star Trek baddies.

But a paper in tomorrow's issue of the journal Science might. In it researchers lay out design specs for materials that they say will be able to bend electromagnetic radiation around space of any size and shape.

The translation for Star Trek fans: Invisibility shields may not be science fiction for much longer.

The theoretical breakthrough is made possible by novel substances called metamaterials.

Invented six years ago, the man-made materials are embedded with networks of exceptionally tiny metal wires and loops.

The structures refract, or bend, different types of electromagnetic radiation—such as radar, microwaves, or visible light—in ways natural substances can't.

“[Metamaterials] have the power to control light in an unprecedented way,” said Sir John Pendry, a theoretical physicist at England's Imperial College London.

“They can actually keep it out of a volume of space, but they can do so without you noticing that there's been a local disturbance in the light.”

Theoretical Proof

The new study is by Pendry and physicists David R. Smith and David Schurig of Duke University in Durham, North Carolina.

The report explains not only how an invisibility cloak might work but also how to make one … in theory, at least.

While their study did not produce cloaking devices, the team offers mathematical proof that the materials work, as well as technical requirements for their creation.

The underlying idea, Pendry said, is that “you can take either rays of light or an electric field or a magnetic field, and you can move the field lines wherever you want.”

“So in the specific instance of cloaking, you take the rays of light, and you just move them out of the area that you don't want them to go in. … Then you return them back to ‘their’ original path.”

Schurig likens the effect to a rock in a stream. The rock symbolizes a metamaterial cloaking shell. The water plays the role of electromagnetic radiation flowing around the cloaking shell.

“Downstream you can't necessarily tell that there was an object distorting the flow,” he said, adding that, even from the side, the disturbance is hard to discern.

In theory, planes, tanks, cars, and even entire buildings could be concealed.

“There's no limit on what you put inside,” Schurig said. “If you build a cloak with a certain hold volume, you can swap things in and out of there, and it doesn't matter what they are.”

But there are some catches—money, for starters.

While the raw materials (copper wire, for example) are relatively cheap, metamaterials are, for now, labor intensive and therefore expensive to manufacture.

Currently, a lab's typical output in a single go might fill a coffee cup.

Knights and Wizards

So far researchers have only developed metamaterials that divert radar and microwaves—rather than light waves, which are the key to invisibility.

While that's good news for Air Force generals who want to conceal warplanes, it's bad news for wannabe wizards hoping for a magic cloak.

Metamaterials that control visible light are particularly elusive in large part because the required matrix of metal loops and wires must be “nanosize,” or exceptionally small.

That's not to say the stuff can't be manufactured. But so far no one has figured out how, says Gennady Shvets, a physicist at the University of Texas at Austin, who studies metamaterials of optical frequencies.

Of the study, Shvets said, “It was not a result that could be achieved by brute force but required some ingenuity…. I think it's great.”

Pendry, the lead study author, points out another limitation. “You can't design a cloak, even in theory, that's perfect at every frequency” of electromagnetic radiation.

But the physicist, who earned a knighthood for his earlier work with metamaterials, says the cloaks should be able to work over a range of frequencies.

“There is, in fact, a trade-off between how thick you let me make the cloak and how much bandwidth I can give you,” he said.

An invisibility cloak, for example, would need to be quite thick in order to bend the rainbow of colors, or wavelengths, that make up the spectrum of visible light—a broadband cloak.

“If you let me make a very thick cloak with lots of design flexibility, I can give you a broadband cloak. If you say, ‘Well, I want it to be really thin,’ then the more narrowband it has to be.”

Stealth capabilities may get all the attention, but the researchers say there are many other applications. “What we have here is a completely new way of controlling light and electric fields,” Pendry said.

“We've thought of a few simple things, like cloaking or excluding magnetic fields. But I'd be very surprised if those are the most important things you could do with it.”

Smith, one of the Duke physicists, co-developed the first metamaterial while at the University of California, San Diego. He agrees with Pendry's optimistic forecast.

“This is just the start of what I think amounts to a lot of interesting things to come.”

Sean Markey

markey, sean. “invisibility cloaks possible, study says.” national geographic news (may 25, 2006).

See Also Physics: Articulation of Classical Physical Law; Physics: Maxwell's Equations, Light, and the Electromagnetic Spectrum; Physics: Optics; Physics: Spectroscopy; Physics: Wave-Particle Duality.

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Ronchi, Vasco. The Nature of Light: An Historical Survey. Cambridge, MA: Harvard University Press, 1970.

Sontag, Susan. On Photography. New York: Picador, 2001.

Steffens, Henry John. The Development of Newtonian Optics in England. New York: Science History Publications, 1977.

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Cotter, D., et al. “Nonlinear Optics for High-Speed Digital Information Processing.” Science 286 (1999): 1,523–1,528.

Knight, J.C. and P.St.J. Russell. “New Ways to Guide Light.” Science 296 (2002): 276–277.

Krieger, Kim. “Lens Once Deemed Impossible Now Rules the Waves.” Science 303 (2004): 1,597.

Markey, Sean. “Invisibility Cloaks Possible, Study Says.” National Geographic News (May 25, 2006).

Schork N.J., L.R. Cardon, and X. Xu. “The Future of Genetic Epidemiology.” Trends in Genetics 14; 7 (2004): 266–272.

Walmsley, Ian A., and Michael G. Raymer. “Toward Quantum-Information Processing with Photons.” Science 307 (2005): 1,733–1,734.

Larry Gilman