In his poem of 1820 entitled Lamia, John Keats complained that cold phi­losophy had destroyed the mystery of nature, and that Newton, through his work on optics, had “unweave[d the] rainbow”. Such a sentiment would find little sympathy with most scientists – or with many artists today for that matter. Indeed, an understanding of natural phe­­nomena can only enhance our ap­preciation of nature and art.

Although it has long been known that a rainbow is produced by the dispersion of white light through rain droplets via refraction, there is far more to this op­tical phenomenon than first meets the eye. More complex and subtle interactions between light and water droplets can also create the “fog-bow”, the “dew-bow” and the “glory”.

Rainbows explained

Despite being a familiar sight (figure 1), rainbows are much harder to understand than one might think. The ingredients are, of course, sunlight and rain droplets. Although the Sun’s rays that reach the Earth are essentially parallel, the light impinges on a spherical droplet at a wide range of angles to the surface, where it undergoes refraction. When the light reaches the back of the droplet, two things can happen (figure 2a). The light can either refract and continue in a forward direction out of the drop, or it can be reflected internally, be­fore passing back out through the front surface of the droplet via another refraction. It is this second process – in which light is refracted, reflected and refracted again – that creates the rainbow, which explains why rainbows only ap­pear when one looks away from the Sun into a rain shower.

1 Bow beautiful

Photograph of a rainbow taken by the author using a 45 mm lens at the Daresbury Laboratory, UK, in 1976.

There are, however, innumerable raindrops at many different heights and positions above the horizon. As a result – and because of the many different angles at which the sunlight strikes the droplets’ surfaces – we receive light rays at many different angles to the “antisolar direction”, which is the di­rection looking away from the Sun towards the shadow of our head. So why does the bright, coloured arc of the rainbow only appear centred on this direction and at a specific and narrow range of angles to it?

Consider first what happens when the incident light strikes the surface of a drop­let head on. Some of the light continues straight through the drop, while the rest reflects directly back. For the lat­­ter, the “angle of deviation” between the incident and reflected beams is 180°. But as the incident light strikes the droplet at a larger angle, the angle of deviation falls below 180°. When the in­cident light strikes at even larger angles, the devi­ation eventually reaches a minimum value, before rising again (figure 2).

At the minimum-deviation angle the rate of change of deviation angle with in­cident angle is zero. What this means is that light striking a droplet over a rel­atively wide range of incident angles emerges concentrated in a narrow – and almost parallel – direction. For example, light rays spanning a 13° interval around the incident angle for minimum devi­ation are focused down to an emerging beam with an angular width of just 1°. Light travelling in this direction has a relatively high intensity and forms part of the standard – or “primary” – rainbow with which we are all familiar.

Different colours have slightly different minimum deviation angles; it is about 140° for short-wavelength violet light and falls to 138° for red light. The violet component of a primary rainbow is therefore on the bow’s inner side – about 40° to the antisolar direction – while the red component is on the outside at about 42° (figure 2c). Other colours fall in between. As the Sun rises, all that changes is that we see less and less of the rainbow’s arc as the “antisolar point” – the centre of the circle of which the rainbow is a part – and the outer limbs of the bow gradually sink below the horizon. Interestingly, if the Sun is higher than 42° above the horizon, minimum-devi­ation rays can only be received from drops located at angles below it, which is why rainbows are generally not visible when the Sun is high in the sky at the middle of the day.

Another interesting property of a primary rainbow is that the intensity of light coming from below it is higher than the background intensity from above it. This effect is visible in ­figure 1. The reason for this is that rain droplets cannot contribute to any light coming from angles above the rainbow because light cannot be bent round a droplet by less than the minimum angle of deviation. Some of the light scattered by the raindrops can, however, reach the observer from below the rainbow, which is therefore brighter than the area above it – but, of course, not nearly as bright as the rainbow itself.

Although a large proportion of light exits the drops after a single internal reflection to form the primary rainbow, some light can undergo two internal reflections. Such twice-reflected rays, which also have minimum-deviation angles and associated intensity maxima, form a “secondary” bow. This appears above the primary bow at an angle of about 52° to the antisolar direction. The secondary bow is fainter than the primary bow and its colours appear in the reverse order. A secondary bow is just visible in figure 1.

What about those light rays that pass out through the drop­lets in the forward direction after two refractions and no re­flection? These have no minimum deviation, which means that this light does not reach a maximum intensity at any ­particular angle. In other words, if we look towards the Sun through rain, we will see no bright rainbow but just an overall forward glare.

However, in principle, a “tertiary” bow can also be formed after the light has undergone three internal reflections in a droplet. This would occur when looking towards the Sun at an angle of about 40°, but it would be fainter than the secondary bow and obscured by forward glare. There have been some reported sightings of a tertiary bow (D E Pedgley 1986 A tertiary rainbow Weather 41 401) but no photographs exist, so far at least!

Supernumeraries and fog-bows

While the main features of a rainbow can be explained by considering the refraction and reflection of light rays, this cannot be the whole story. For example, the intensity of light at the minimum-deviation angle tends to infinity when plotted at finer incident-angle increments. This is clearly not true in re­ality. Moreover, faint, pale “supernumerary” bows can sometimes be observed below the primary rainbow itself. These are concentric circles of smaller radius than the main rainbow.

The answer to these puzzles lies in the fact that light is not a ray but a wave. When this is taken into account, the un­wanted infinity in intensity disappears and is replaced by a maximum in intensity close to the minimum-deviation angle. This maxi­mum can be regarded as a first-order diffraction peak created by the interference of different parts of the wavefront that have reflected off different parts of the drop­let’s back surface, have travelled exactly the same distance and are in phase.

Other parts of the wavefront will have different pathlengths, one wavelength more (or less) than the other, and will interfere to create less intense second- and higher-order diffraction peaks, which are the supernumerary bows. The path dif­ference depends on the size of the drop­lets, which means that supernumeraries are most easily ­visible when the rain droplets are nearly all the same size. If the droplets were not uniform, the supernumerary bows from different-sized drops would have dif­ferent angles and could not be clearly distinguished. A search for the origin of supernumerary bows helped in the de­velopment of the wave theory of light. This work eventually enabled George Airy, then Britain’s Astron­­omer Royal, to solve the problem of infinite intensity and explain supernumeraries in 1838.

Wave theory can also explain a rarer form of bow, known as a “fog-bow”. If the rain droplets are large – say about 1 mm in diameter – the first-order diffraction peaks for the different colours of the rainbow are narrow and well ­separated, which means that the individual colours can be clearly distinguished. However, if the raindrops are smaller than about 50 µm in diameter, the bows of different colours become so broad that they overlap. What one sees in this case is a single, broad white arc. Could this fog-bow be what appears in the famous Buttermere Lake painting by the British artist Joseph Mallord Turner? It shows a white bow above Cromackwater and Buttermere in the Lake District (figure 3).

But while Turner’s bow is white – and so looks like a fog-bow – the width of the white band is much less broad than is expected for a fog-bow; it is instead about as narrow as the coloured band of a rainbow. On closer inspection the painting is even more curious. It represents a view from near Ran­nerdale and contains, on the left, a mountain called Fleetwith Pike, which is 544 m above the level of the lake and some four miles in the distance. The angle subtended by the mountain’s vertical extent above the lake is about 5°. If we imagine that the picture has been taken by a camera, the distance from the lake to the summit on the printed page gives us the effective focal length of the camera and, in turn, the angle subtended by the rainbow. A simple calculation indicates that the white bow has an angular radius of about 7.5° – some five times smaller than a standard rainbow (42°).

The colour and anomalous size of the fog-bow are prob­ably because Turner was using artistic licence to create the image he wanted. Indeed, Turner is known to have painted a white rainbow above the forum in Rome, which – based on the shadows that also appear in the picture – was physically impossible (R Lee and A Fraser 2001 The Rainbow Bridge: Rainbows in Art, Myth and Science).

The halo

Raindrops are not, of course, the only form of precipitation. Light can also refract through ice crystals falling through the air. If the crystals all have the same shape, light refracting through them can create a similar effect to the rainbow – a bright, sometimes coloured, bow known as a “halo”. But what causes the phenomenon of minimum deviation, which plays such a key role in the formation of a rainbow? It appears to be ruled out be­cause a single face of an individual crystal forms only one angle of incidence with the rays from the Sun. The answer lies with the fact that the ice crystals tumble through the air, which orients their axes in random directions. Sun­light can therefore strike the crystal faces at many different angles of incidence, al­lowing minimum deviation to occur.

The most common halo is formed when light passes through an ensemble of poorly aligned hexagonal crystals, which have internal face angles of 120°. Light enters through one face of the crys­tal and is bent so that it leaves not via the neighbouring face but the next-but-one face. In other words, the crystal is acting like a 60° prism. Simple ray optics reveals that there is a minimum-devi­ation angle for light passing through such a crystal of roughly 22°. The halo therefore appears when looking towards the Sun and forms a circle of light, where the angle between the direction of the Sun and any point on the halo is 22°. Furthermore, the colours appear in the reverse order compared with a standard rainbow, because there is no reflection off the inside of the crystal’s faces. In practice, however, only the faint inner red rim is usually visible (figure 4).

The phenomenon of minimum deviation is not the only mechanism that causes haloes. Intensity enhancements in cer­tain directions can also be created by ice crystals as they become aligned while falling through the air. Thin hexagonal plate crystals, for example, will tend to align with the plates horizontal but with the thin, side faces of the hexagon having no preferred angle to the Sun’s direction. This will cause bright regions, dubbed “mock suns”, to appear at the sides of the circular halo. These features can appear as red and yellow smudges of light, without any accompanying circular halo, at an angle of 22° or more from the Sun along the horizontal line through the Sun.

Although one might associate haloes with winter, they can sometimes be seen in the UK during the summer when cirrus clouds are present. These clouds are so high in the atmo­sphere that they contain ice crystals. I have even seen photos of haloes taken as far south as Corsica in June. But, as one might expect, the most dramatic haloes appear in polar re­gions, where conditions can be ideal for creating large amounts of ice crystals. Indeed, the geometric theory of ha­loes was determined as early as 1847 by the French scientist Auguste Bravais, who analysed observations that he and ­others had made in the Arctic. His work is all the more re­markable considering that these observations were made in the field, without any photographic records whatsoever. Pho­to­graphy for use outside a studio was not developed until the end of the 19th century.

The Whymper apparition

Perhaps the most famous halo was that reported by Edward Whymper following the first ascent of the Matterhorn on 14 July 1865. During the descent, one of the climbers in the forward party slipped and dragged down the other three men to whom he was attached. The rope securing the forward party to the rest of the team then snapped and the four fell down the north face of the mountain to their deaths. Shortly after this tragic incident, Whymper and his two Swiss guides – the Taugwalders – observed an amazing apparition (figure 5a). “A mighty arch appeared, rising…high into the sky,” Whymper later wrote. “Pale, colourless, and noiseless, but perfectly sharp and defined, except where it was lost in the clouds, we watched with amazement the development of two vast crosses, one on either side.” Awestruck, Whymper re­cognized the phenomenon to be a type of fog-bow that was formed in the opposite (antisolar) direction to the Sun. Although the apparition had no link with the accident, the timing seemed supernatural.

In a recent paper I have speculated on the possible origins of the Whymper apparition (J Hardwick 2002 Simulation of the Whymper apparition Weather 57 457). Using the HALO3 software developed by physicists Les Cowley and Michael Schroeder, I suggest that it was created by a combination of a fog-bow and ice-crystal arcs. Their program is based on a Monte Carlo technique that tracks rays at a specific solar angle through an ensemble of ice crystals, where the shapes and orientations of the crystals can be chosen. My simulation (figure 5b) tracked rays via the various reflections and refractions of light through cylindrical crystals with hexagonal cross-sections and through others that were a slight variation of these.

The Whymper apparition includes the antisolar horizontal arc and central cross, which can occur if the long axes of the hexagonal cylinders become horizontally aligned. Whymper also observed two bright vertical strips that intersected the ho­ri­zontal arc to create the two vast crosses. I discovered that these features could be created with hexagonal cylinders that were capped with pyramids – a form of ice crystal known to occur at low temperatures. The cylinder axis pointed horizontally, while two of the six sides were oriented vertically.

Taken together with a fog-bow, the computed result is not dissimilar to the picture that appears in Whymper’s The Ascent of the Matterhorn, especially a later sketch that he derived while writing the book (figure 5c). Although the simulation may seem somewhat contrived, a similar alignment of hexagonal cylinders with two opposite hexagonal faces horizontal was required to explain the features of an intricate halo observed by Captain W E Parry in 1820 during his search for the North West Passage.

The glory of glories

Three days after the Matterhorn tragedy, a separate Italian team made the second ascent from the opposite side of the mountain. During their descent – and at about the same time and altitude that the Whymper apparition had been seen – the party found itself above thick cloud when the climbers observed another strange phenomenon. What they saw this time were their own shadows projected onto the cloud, with rainbow-like rings around their own heads. Known as the “Brocken spectre”, the shadow is said to have been named after an incident involving a climber on the Brocken in the Harz Mountains of Germany. Startled by the appearance of his shadow on a cloud, the climber allegedly fell to his death.

The bright, coloured rings are known collectively as a “glory”. Glories are created when light is backscattered from small water droplets in a cloud. It is a complicated process, but one of the major mechanisms occurs when light strikes a spherical water droplet almost tangentially. The light refracts into the drop and is then internally reflected. But rather than refracting out again when it strikes the surface, it can then travel as a surface wave on the droplet, before emerging at the opposite side of the drop at 180° to the direction in which it arrived (figure 6a). The coloured rings are formed when light that has been backscattered in this way from different parts of the droplet edge interferes (H Bryant and N Jarmie 1974 The glory Scientific American July pp60–71).

Glories are not uncommon. While climbing in Snowdonia in north Wales, for example, I and my fellow climbers emerged from a cloud layer into the Sun, where we were greeted by a glory beneath us. At least three orders of interference rings were visible (figure 6b). The rings are much smaller than those of a rainbow but grow bigger as the drop­lets shrink in size. Distinct glories – like supernumerary rainbows – therefore require a uniform droplet size. A detailed mathematical explanation of the glory only became possible once physicists had worked out how electromagnetic radi­ation scatters from spheres, the theory of which is usually attributed to Gustav Mie, who published his work in 1908. However, it was not until 1947 that Hendrik van de Hulst suggested the surface-wave interpretation.

Dew-bows at dawn

Another strange optical phenomenon that can occasionally be seen is the “dew-bow”, which was the subject of a letter last year from Physics World reader and golf enthusiast John ­Wesson (“Golfing beauty”, March 2003). Wesson described a dew-bow that he had seen while out on a golf course early one morning. “Its hyperbolic shape extended into the distance and its vertex was a short distance from my feet,” he wrote. “As I walked forward, my rainbow moved with me – lasting perhaps 15 minutes.”

A dew-bow is created when light re­fracts from water droplets located on a horizontal plane, such as the grass of a golf course. As with a standard rainbow, the observer can be pictured as standing at the vertex of a cone and receiving the rainbow light from angles along the cone’s surface. The observer interprets the shape of the light source as the cross-section that is cut through the cone by the plane containing the droplets. So if sunlight strikes the plane at a very shallow angle, for example in early morning, the dew-bow has a hyperbolic shape. Later in the day, if the droplets are still present, the dew-bow will become an ellipse.

Wesson asks why, given that dew is so common, are dew-bows so rare? He has only ever seen one dew-bow, despite being a regular on the golf course. If he had seen many dew-bows of different brightnesses, we might conclude that their formation depends on dew density. But I do not think that the density of dewdrops plays the key role. Dew-bows probably form only when spherical water drop­lets are present. As with a standard rainbow, this allows sunrays to be internally reflected from the back of the drops. How­ever, experiments with a blade of grass suggest that most drops of water attached to grass are not spheres but hemispheres. Internal reflection would therefore not be poss­ible for the range of angles needed for a complete hyperbola to be seen.

In his classic book Light and Colour in the Open Air, which was originally published in 1954, Marcel Minnaert claims that dew-bows can originate from the fine spherical droplets of dew on cobwebs. But spiders make webs every morning, so why are dew-bows not then seen more often? Maybe it depends on the size of the drops. Perhaps dew-bows are formed only if fine spherical dewdrops condense on and cling to the edges or tip (rather than the faces) of blades of grass. The mystery remains.

Keats’ unweaved rainbow

So has cold philosophy unweaved the rainbow? It seems to me that a fuller understanding of the physical basis of this intricate phenomenon can lead to a proper appreciation of it and also shed light on other, yet more subtle effects that lie outside what Keats called the “dull catalogue of common things”. Each rainbow, halo and glory is unique in that each re­sults from a never-to-be-repeated ensemble of raindrops or ice crystals of particular shapes and sizes. Some forms, like the Whymper apparition, are so rare that you will be lucky to ever seen one in your lifetime.

The physics of the rainbow is perhaps like particle physics, in that each deeper explanation reveals yet another mystery. However, unlike particle physics, we have the final word with Mie scattering theory, which as well as explaining the glory gives a complete theory of the rainbow. But questions still persist. Why, for example, are dew-bows so rare? And why does lightning destroy a rainbow? It appears that some subtleties surrounding the rainbow continue to remain a mystery.

• This article first appeared in the February 2004 issue of Physics World. Since then both third-order and fourth-order rainbows have been photographed.

The ability to manipulate and control light is one of the foremost goals of modern optics. However, it is also something that nature perfected a long time ago. About 500 million years ago an evolutionary “big bang” took place, when animal life began to rapidly diversify. This so-called Cambrian explosion is thought to have been triggered when the manipulation of light began to influence the survival of many animals. When it comes to highly advanced optical systems, it seems there is no more experienced an engineer than nature itself.

It is little wonder, then, that the optical engineers of today have started to keep a curious eye on natural optical systems. These systems offer inspiration for new ideas in optical design and could provide shortcuts for developing advanced photonic systems, which one day may even be grown to order. Without doubt, uncovering nature’s optical secrets has been, and will continue to be, a spectacular journey.

Early beginnings

Some of the most interesting optical systems in nature are hard to miss. They are often brightly coloured, metallic looking or strongly iridescent, and stand out from ordinary objects and surfaces that are coloured by pigmentation alone. In the 18th century Robert Hooke and Isaac Newton were among the first to explain the underlying physics of these systems. They correctly predicted that the iridescent colours of peacock feathers and silverfish scales resulted from their physical structure rather than pigmentation. This was a huge leap of understanding, considering that the means of seeing these structures would not be invented for a further two centuries.

It was left to James Clerk Maxwell in the 19th century to develop the set of mathematical tools that now enable us to fully describe the way electromagnetic radiation interacts with matter. This interaction happens all the time, of course, but it starts to get interesting when it takes place in the presence of structural periodicity. Under the right conditions, periodic structure modifies the character of the light that is transmitted, reflected or absorbed by a material. Roughly speaking, the size of the periodicity has to be about the same size as the wavelength of the light involved. An object with a periodicity of a few millimetres to a few centimetres, for example, could control the propagation of microwaves, while the control of optical wavelengths requires periodicities of tens to hundreds of nanometres.

One very important optical constraint for a material, besides its refractive index, is the number of dimensions exhibited by its periodicity. This offers the potential for light to be controlled in one, two or three directions. If 1D or 2D periodicity is limited to the surface of an object, for example, the structure is commonly known as a diffraction grating. If 2D or 3D periodicity exists within the bulk of an object, however, it becomes what is now called a photonic crystal. It is so named because light interacts with the structure in a manner that is analogous to the way that electrons interact with a periodic crystal of ions. Both these processes result in specific bands of allowed energies that are separated by band gaps – regions in which no states can exist. For photonic systems, these are called photonic band gaps and they underpin the way the flow of light is controlled.

Over the last 10 years or so the physics of 2D and 3D photonic crystals has been examined in great detail, and there is currently significant interest in optical technologies based on photonic structures. Synthetic photonic-crystal fibres – which were pioneered by Philip Russell and co-workers at the University of Bath in the early 1990s – could outperform even optical fibres in their ability to transport light (see “Photonic band gaps deliver the goods”, October 2003).

Nanostructure in nature

Nature learned relatively early about the way light interacts with periodic structures due to the evolutionary selection advantages it offers. Highly reflective and coloured surfaces can play an important role in courtship, or in signalling warnings to predators. The first such optical systems appeared as surface diffraction gratings that have been found in Burgess Shale fossils that are 500 million years old. These comprise near-periodic and parallel corrugations on the external hard surfaces of the creatures. Similar periodic systems are also found in some common present-day insects, such as wasps, flies and moths.

Natural surfaces with 2D gratings are not normally designed for bright-coloured reflection. Indeed, provided they comprise the right sort of nanostructure, such gratings can actually reduce the reflection of light at interfaces. Instead, they are found to form antireflection surfaces on many insect eyes, which increase the efficiency of the animal’s vision and reduce unwanted reflection that might attract predators.

Periodicity within materials, rather than on their surfaces, underpins the vast majority of all structural colour in nature (figure 1). This is the case for the 1D multilayer systems responsible for the characteristic colours we associate with nature’s brightest reflectors: butterflies, birds and fish. The materials that make up these multilayers depend on many things, not least the inherent physiology, ecology and environment with which the animal is associated.

In some butterflies, for example, layers of cuticle are intercalated with layers of air in order to generate efficient interference colours, while in many aquatic vertebrates such as fish, the same trick is performed by platelets of solid guanine separated by cytoplasmic fluid. The occurrence of 1D multilayers is extremely common in insects, and a great many of these systems have been investigated thoroughly over the last 40 years. Furthermore, these structures are not limited to fauna but are also found in some plant leaves, berries and algae.

It is difficult to say how long ago selection pressures led to the evolution of 2D and 3D periodic structures within systems. Compared with 1D multilayers they are rather uncommon, and 2D bulk periodicity is most often found in the form of long fibres. Recently Andrew Parker of Oxford University and David McKenzie of the University of Sydney decided to characterize the structures of the hairs of the Aphrodite – a type of worm that inhabits shallow tropical water. What they found was a 2D photonic-crystal fibre.

Each Aphrodite hair contains thousands of hollow, close-packed and longitudinally oriented cylinders of cuticle, each with a diameter of about 230 nm. Bright colours are produced when the cylinders collectively diffract light that is incident on the side of the fibre. Theoretical models suggest that if the structure contained a centrally located defect – such as that in synthetic photonic-crystal fibres – it would be able to guide light down its length. The absence of such a defect, however, suggests that the purpose of these structures is instead for iridescent signalling.

Full 3D periodicity was first investigated in detail in the 1960s, when it was realized that such a structure underpins the iridescence of gem opals. John Sanders, formerly of the Commonwealth Scientific and Industrial Research Organization in Australia, characterized the close-packed arrangement of silica spheres that make up opal structures, and which interact with light to produce their characteristic iridescent colour. More recently, Andrew Parker and co-workers have discovered an analogous 3D sphere structure in a beetle.

A variation of the opal structure – which is sometimes referred to as inverse opal – has been known to exist in certain butterflies for some time, and has been studied in detail by the author and colleagues in the photonics group at Exeter University in the UK. Instead of close-packed spheres, the butterfly structure comprises a lattice of hollow air-filled voids that are formed within a network of interconnecting cuticle. Given the current technological interest in synthetic 3D photonic crystals, these natural 3D systems are quite astonishing for the very fact that they have developed the way they have. The structure appears to be a minor variation of the diamond-like tetrahedral structure, which offers excellent reflectivity over a broad angle range for the particular difference in refractive index between air and the butterfly cuticle.

To further enhance the angle-independent colour, the 3D structure usually appears divided into domains that are about 5 μm in diameter. Each neighbouring domain has the same structure, but they all face in slightly different directions with respect to each other. As a result, the average overall colour effect is essentially angle-independent. Whereas the production of gem opals is understood to be an artefact – a by-product of the way precipitative silica-gel solution settles – the 3D photonic crystals in butterflies and beetles have evolved for a specific biological purpose, which is thought to be associated with visibility.

Natural periodic structures tend to be associated with high reflection or transmission, but creatures have been discovered that can control light in other ways too. Joanna Aizenberg and co-workers at Bell Labs in the US have characterized a 2D surface array of microlenses on the arms of a light-sensitive brittle star – an animal that resembles a starfish. Each lens is a photonic element that is formed from a single anisotropic calcite crystal, and has a characteristic double-lens design with a focal length of a few microns.

The size and profile of each lens is ideal for the task of collecting and focusing light. Their surfaces are shaped in such a way that spherical aberration is minimized, which means that each lens focuses light to a sharply defined point. Furthermore, the orientation of the constituent calcite crystal removes the effect of birefringence, which would otherwise cause different polarizations to behave in different ways and therefore diminish optical function. By focusing incident light onto photoreceptors beneath them, this astonishingly elegant microlens array provides the means to sense light discretely across the arm of the brittle star.

In the completely separate kingdom of plants, analogous but less specialized microlens arrays have evolved in some shade-adapted plants to increase the efficiency of photosynthesis.

Optical nanotechnology and biomimetics

Biomimetics is the extraction of useful design principles from systems that work well in nature. However, humankind’s development of optical systems over the last 100 years reveals something very curious: of all the optical systems developed so far, virtually none appear to have been the direct result of optical biomimetics. We seem to have expended incredible time, effort and expense to produce systems that nature has been using for millions of years.

One of the best examples of this is the traditional multilayer filter, in which layers with alternate high and low refractive indices control the reflection and transmission of light by means of interference. Multilayer filters are an intrinsic component of lasers, telescopes, gravitational-wave detectors and medical probes, but understanding them has developed completely independently of any knowledge of the multilayers commonly found in butterflies and birds.

It is only recently that interdisciplinary research has brought about dramatic discoveries associated with natural optical systems. Despite detailed work from the 1960s onwards by eminent biologists and zoologists, few physicists paid much attention. The analysis of the photonic-crystal-fibre structure of Aphrodite hairs, for example, was taken seriously by physicists because it had strong similarities with the synthetic photonic-crystal fibres developed by physicists a few years earlier.

However, when a little-known scientist named Wolfgang Schmidt looked at the iridescence associated with the hairs of the Aphrodite in the 1940s, the state of optics and related technologies was such that its importance, and indeed elegance, was entirely overlooked. Similarly, recent studies of the 3D photonic-crystal structure of certain butterflies and moths by the author and co-workers at Exeter were preceded by the work of several biologists in the 1960s. Back then, the implications of a natural 3D structure that could effectively control the flow of light in all three dimensions was simply not appreciated.

Today, with tens of thousands of scientists striving to develop optical technologies for a broad variety of applications, we are much more aware of nature’s optical achievements. Taking this one step further and actually learning from nature is, however, only just beginning, and the science of optical biomimetics is very much in its infancy.

Biomimetic myths

Due to popular myth or otherwise, the origins of some modern optical technologies are widely attributed to inspiration from natural optics. In only very few exceptions, however, has this been the case. Take the current use of antireflective materials to enhance the transparency of certain surfaces, in which a smooth and gradual change in effective refractive index is introduced across the interface between two media. Since most transparent glass or plastic is actually not completely transparent – reflecting up to about 8% of light at normal incidence and even more at grazing incidence – improving its transparency can increase the efficiency of, say, a solar cell, that is housed beneath it. This principle, in fact, already enhances the solar gains of some commercial architectural glazing and solar collectors (figure 2).

As a technology, however, antireflection borrowed little from nature’s expertise. Knowledge of the antireflective effect of the graded index offered by such discrete nanostructure arrays was well known even in the 19th century – long before the development of the electron microscopes required to image them. Even after the advent of the electron microscope, direct biomimicry was not pursued because antireflective periodic structures had already been developed for microwave frequencies. It is no surprise that these had a similar ratio of wavelength to pitch as the antireflective optical nanostructures found in insect eyes.

Where else, then, are the similarities between synthetic and natural optical systems so close that it appears optical biomimicry has occurred? Perhaps an unusual suspect lies in textiles. Some researchers are attempting to link visual and tactile preferences in cloth fibres with fluctuations in the periodicity of their surface irregularities. This has recently led to a new class of textiles – which are referred to in Japan as shin-gosen products – that are more desirable due to their attractive textures and their visual properties.

One particularly intriguing aspect of this research involves fibres of “odd cross-section”. Specialized techniques of extrusion-based manufacturing modify the cross-section of the fibre, which not only allows the fibres to be close-packed but also to produce optical interference and scattering from fine periodic structures within each fibre structure. Curiously, these fine structures also improve the material’s wettability, since capillary forces in the inter-fibre volume are sufficient to carry away liquid perspiration. A designated periodicity within each fibre cross-section, akin to the periodicity associated with the nanostructure on an iridescent Morpho butterfly scale, creates strong colour effects using interference.

A separate range of cloth fibre effects are evident in a product called Microcratered Fibres. The surface of these cloths is uneven on a scale of a few hundred nanometres, which minimizes the scatter of stray light. This property is able to emulate the depth of shade that is associated with quality wool-fibre yarns using only polyester materials. Although its surface very closely resembles that of many black insect surfaces, it is a design that has once again been developed independently of any inspiration from nature. Interestingly, the generic micro-crater design also forms the basis of the ultra-black, metal-alloy surfaces recently developed by Richard Brown and colleagues at the National Physical Laboratory in the UK.

Natural security

But there is an area in which optical biomimicry is starting to work: anticounterfeiting. Many of the recent security measures that have been introduced on banknotes, credit and debit cards, and branded goods rely on complex optical logos, insignia and colour schemes. Nanostructure is pivotal in nearly all these measures (see figure 3), some of which even comprise specialized pigments such as the optically variable ink (OVI) developed by SICPA of Switzerland.

The OVI technique exploits advanced screen-printing methods to produce ink layers of materials with alternating refractive indices, which results in specific iridescent patterns. Other “pearlescent” inks made from clear varnishes are also used. Here, the varnishes are infused with mica flakes that are coated with interference layers of iron and chromium oxides with high and low refractive indices, respectively.

Diffractive, optically variable devices – such as foil patches, stripes and windowed thread – have led to reasonably effective security features on banknotes throughout the world, but they tend not to match the durability of the banknote substrate itself. Embossed holograms and kinegrams have also been used to authenticate bank and credit cards for many years. However, the security they provide is limited by their low surface relief (typically 0.25 μm). This makes the authentication susceptible to counterfeiting because the complete holographic microstructure can be exposed by stripping the hologram from the substrate. Counterfeit tooling can then be made with only the minimum of expertise.

A big improvement in counterfeit deterrence can be gained by the use of high-precision, non-holographic micro-optics and nanostructures, which not only have a surface relief of a few microns but also have sub-surface structure. Some natural optical systems fall straight into this category of micro-optic structure. Chris Lawrence and colleagues at QinetiQ in the UK have been taking specific nanostructure designs directly from butterflies and moths, and trying to replicate them for use as security features in currency.

One specific structure, which was originally characterized by our group at Exeter, comprises a single sculpted multilayer that produces microscopic arrays of two individual structural colours. These colours are juxtaposed in such a way as to produce the appearance of a third colour, in the same way that a colour television creates the full colour spectrum by adding together three individual colours with different intensities. But the specific design of the multilayer of this particular butterfly assigns anomalous polarization properties to only one of the two individual colours. In other words, the reflection of one colour is polarized, while that of the other colour is not. This offers a covert and additional security feature that considerably decreases the risk of counterfeiting.

Designer photonics

Of particular interest in the long term is the way that natural nanostructured systems are self-assembled. In animate systems these schemes are put together in the egg, pupa or as part of normal growth in juveniles. Their formation is therefore controlled at the genetic level, but it also appears to be influenced by external factors such as temperature and nutrition. Other factors, such as exposure to X-rays and laser-mediated heat shock, are also known to alter the development of pigment and structure in specific ways.

Many groups, such as those of Paul Brakefield at Leiden University in the Netherlands and Antonia Monteiro of Buffalo University in the US, are now investigating how variation at the DNA level in developmental genes determines external optical appearance. Once this is completely understood at a fundamental level, it might be possible to change the genetic make-up such that designer nanostructures could be cultured. This is certainly a long way off, but the possibilities are fascinating.

Imagine cultivating a made-to-order 3D photonic crystal on or within an organic light-emitting diode to improve its efficiency, or as part of an optical micro-electromechanical device to improve functionality. Or imagine covering the glass surface of a solar cell with a gene-rich solution that would grow into an antireflective nanostructure array, or onto the surface of a hybrid lens in an advanced camera for it to grow into a large-area microlens array. More useful still, consider the advantages of being able to grow natural photonic-crystal fibres that can guide light, or other 2D crystal structures for optically integrated circuits in all-optical computers.

Rich rewards lie in a variety of established and emerging technologies, not only in taking the design rules and paradigms offered to us by nature’s optical systems, but also in trying to take advantage of some of its self-assembly processes. We have just begun to appreciate how advanced natural optics can be. Even some of our most recent developments in photonic systems, such as photonic crystals and fibres, have in principle already existed for a very long time.

Physicists and engineers would do well not to shy from biological systems but to embrace some of the ideas they offer. There are undoubtedly more lessons to be learned in nature’s optical arena than have come to light in the last few decades. After 500 million years of optical R&D, this is bound to be the case. We should not be surprised at what we find. Given enough time, evolution can do some pretty amazing things.

• This article first appeared in the February 2004 issue of Physics World.