Explaining one of the most beautiful phenomena in meteorology requires a very sophisticated approach. Studying it also helps to understand the role of clouds in climate change.
If you are on a day flight, please take a window seat. And then you may be able to see the plane's shadow on the clouds. But you need to take into account the direction of flight relative to the sun. If you are lucky, you will be rewarded and you will be able to observe a picturesque sight - a multicolored halo, bordering the shadow of the airliner. It is called "gloria". Its origin is due to a more complex effect than the appearance of a rainbow. This phenomenon will be most impressive if the clouds are close, since then it extends to the very horizon.
If you are a mountain climber, you can observe gloria soon after sunrise around the shadow cast by your head on the nearest cloud. We present here the first report on the observation of such a phenomenon by members of the French expedition to the summit of Mount Pambamarca on the territory of present-day Ecuador, published ten years after the ascent, in 1748. “The cloud covering us began to dissipate, and the rays of the rising sun pierced it. And then each of us saw our shadow cast on the cloud. What we found most remarkable was the appearance of a halo, or gloria, consisting of three or four small concentric, brightly colored circles around the head. The most surprising thing was that out of six or seven members of the group, each observed this phenomenon only around the shadow from his own head,I have never seen anything like this around the shadows of my comrades."
Many researchers believed that halos on images of deities and emperors in Eastern and Western iconography represent an artistic fixation of the phenomenon of gloria. (We find an allegorical confirmation of this assumption in the famous poem by Samuel Taylor Coleridge "Fidelity to the Ideal Image"). At the end of the XIX century. Scottish physicist Charles Thomson Rees Wilson invented a "cloud" camera (in Russian terminology - Wilson's chamber) and made an attempt to reproduce this phenomenon in the laboratory.
He failed, but quickly realized that the camera could be used to register particles, and as a result was awarded the Nobel Prize. The shadow of an observer or an airplane plays no role in the formation of the gloria. The only thing that connects them is that the shadow fixes the direction exactly opposite to that of the Sun. This means that gloria is a backscattering effect that deflects sunlight by nearly 180 °. You might think that such a well-known effect, belonging to such a venerable field of physics as optics, should undoubtedly have been explained long ago. Nonetheless, explaining this, according to the authors of the 1748 report, "the effect as old as the world," has presented a serious challenge to scientists for centuries. Even a rainbow is a more complex phenomenon than how elementary physics textbooks describe it. Moreover, the gloria formation mechanism is even more complicated.
In principle, both the gloria and the rainbow are explained in terms of standard theoretical optics, which already existed by the beginning of the 20th century. This allowed the German physicist Gustav Mie to obtain an accurate mathematical solution for the process of light scattering by a water drop. However, the devil is in the details. The Mie method involves the addition of terms, the so-called partial waves. An infinite number of such terms is required to sum up, and although a finite number of them is practically significant, Mee's method requires the calculation of hundreds and thousands of very complex expressions.
If you enter them into a computer, then it will give the correct result, however, it is impossible to understand which physical processes are responsible for the observed effects. Solution Mi-typical mathematical "black box": enter the initial data into it, and it will give the result. It is pertinent to recall here a remark by Nobel laureate Eugene Paul Wigner: “It's great that the computer understood the problem. But I would also like to understand her. " Blind faith in grinding numbers with brute force can lead to wrong conclusions, as will be shown below.
In 1965, I set about developing a research program that would, among other things, lead to a complete physical explanation of gloria. And this goal, on the way to which I was helped by several collaborators, was achieved in 2003. The solution was based on taking into account wave tunneling, one of the most mysterious physical effects that Isaac Newton first observed in 1675. Wave tunneling is at the heart of one of the types of modern touch screens used in computers and cell phones. It is also important to consider it for solving the most difficult and most important problem, how atmospheric aerosols, which include clouds, as well as dust and soot particles, affect climate change.
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Waves and particles
For several centuries, scientists have offered various explanations for gloria, but they all turned out to be incorrect. At the beginning of the XIX century. German physicist Josef von Fraunhofer suggested that sunlight scattered, i.e. reflected back, by drops in the depth of the cloud, diffracts on drops in its surface layer. Diffraction is a phenomenon associated with the wave nature of light and allowing it to "look around the corner", just as sea waves go around an obstacle and spread further, as if it did not exist at all.
Fraunhofer's idea was that this double-scattered light forms colored diffraction rings, resembling a corona, on the clouds surrounding the moon. However, in 1923 the Indian physicist Bidhu Bhusan Ray denied Fraunhofer's suggestion. As a result of experiments with artificial clouds, Ray showed that the distribution of brightness and colors in the gloria and in the corona are different, and that the first occurs directly in the outer layers of the cloud as a result of a single act of backscattering by water droplets.
Ray tried to explain this backscattering in terms of geometric optics, historically associated with the corpuscular theory of light, according to which light travels in straight rays rather than as a wave. When it meets the interface between different media, such as water and air, light is partially reflected, and partially penetrates into another medium due to refraction (refraction is what makes a pencil, half submerged in water, seem to be broken). The light that has penetrated into a drop of water, before leaving it, is reflected one or more times on its opposite inner surface. Ray viewed the beam as it propagated along the axis of the droplet and reflected back towards its entry point. However, even with multiple acts of back and forth reflections, the effect was too weak to explain gloria.
Thus, the theory of the gloria effect should go beyond the limits of geometric optics and take into account the wave nature of light and, in particular, such a wave effect as diffraction. In contrast to refraction, diffraction increases with increasing wavelength of light. The fact that gloria is a diffractive effect follows from the fact that its inner rim is blue, and the outer one is red, in accordance with the shorter and longer wavelengths.
The mathematical theory of diffraction by a sphere such as a drop of water, known as Mie scattering, involves calculating infinite sums of terms, the so-called partial waves. Each partial wave is a complex function of the droplet size, refractive index and collision parameter, i.e. distance from the ray to the center of the drop. Without a high-speed computer, calculations of Mie scattering from droplets of various sizes are incredibly complex. It was only in the 1990s, when fairly fast computers appeared, that reliable results were obtained for droplets in the range of sizes characteristic of clouds. But researchers need other ways of exploring to understand how this actually happens.
Hendrik C. Van de Hulst, pioneer of modern radio astronomy, in the middle of the 20th century. made the first significant contribution to the understanding of the physics of gloria. He pointed out that a light beam penetrating into a drop very close to its edge, inside the drop passes along a Y-shaped trajectory, is reflected from its inner surface, and returns back in almost the same direction in which it came. Since the drop is symmetric, among the entire beam of parallel solar rays, a favorable collision parameter will be realized for their entire cylindrical beam falling on the drop at the same distance from its center. In this way, a focusing effect is achieved, which multiplies the backscatter.
The explanation sounds compelling, but there is one catch. On the way from penetration into the drop to exit from it, the beam is deflected due to refraction (refraction). However, the refractive index of water is not large enough for the beam to be scattered exactly backward by a single internal reflection. The most that a drop of water can do is bounce the beam in a direction about 14 ° from the original.
In 1957, van de Hulst suggested that this deviation could be overcome by additional paths traversed by light in the form of a wave along the droplet surface. Such surface waves, tied to the interface between two media, arise in many situations. The idea is that a ray incident tangentially on a drop passes some distance along its surface, penetrates into the drop, and hits its inner back surface. Here it again slides along the inner surface and is reflected back into the drop. And on the last segment of the path along the surface, the ray is reflected from it and exits the drop. The essence of the effect is that the beam is scattered back in the same direction as it came.
A potential weakness of this explanation was that the energy of surface waves is spent on a tangential path. Van de Hulst suggested that this damping is more than compensated for by axial focusing. At the time he formulated this conjecture, there were no methods to quantify the contribution from surface waves.
Nevertheless, all information on the physical causes of gloria, including the role of surface waves, had to be explicitly included in the series of partial Mie waves.
Reason defeats the computer
A possible solution to the gloria puzzle is not just about surface waves. In 1987, Warren Wiscombe of the Space Flight Center. Goddard at NASA (Greenbelt, Maryland) and I have proposed a new approach to diffraction in which light rays passing outside the sphere can make a significant contribution. At first glance, this seems absurd. How can a drop affect a ray of light that does not pass through it? Waves, and light waves in particular, have the unusual ability to "tunnel," or penetrate a barrier. For example, light energy in some circumstances can seep outside, when one would believe that light should remain within the given environment.
Typically, light propagating in a medium such as glass or water will be completely reflected from the interface with a medium with a lower refractive index, such as air, if the beam hits this surface at a sufficiently small angle. For example, this total internal reflection effect keeps the signal inside the optical fiber. Even if the light is completely reflected, the electric and magnetic fields that form the light wave do not vanish immediately beyond the interface. In fact, these fields penetrate the boundary over a short distance (of the order of the wavelength of the light wave) in the form of a so-called "non-uniform wave". Such a wave does not carry energy beyond the interface, but forms an oscillating field on its surface, similar to a guitar string.
What I have just described does not yet contain the tunneling effect. However, if a third medium is placed at a distance from the boundary less than the length of the inhomogeneous wave, then the light will resume its propagation into this medium, pumping energy there. As a result, the internal reflection in the first medium weakens, and light penetrates (tunnels) through the intermediate medium, which served as a barrier.
Significant tunneling occurs only if the gap between the two media does not significantly exceed one wavelength, i.e. not more than half a micron in the case of visible light. Newton observed this phenomenon as early as 1675. He investigated the interference pattern, now known as Newton's rings, which occurs when a plano-convex lens is applied to a flat glass plate. The rings would only have to be observed when light passes directly from the lens into the plate. Newton found that even when a very small distance separated the lens surface from the plate, i.e. the two surfaces were not in contact with each other, some of the light that should have undergone total internal reflection, instead penetrated through the gap.
Tunneling is clearly counterintuitive. Physicist Georgy Gamov was the first to reveal this phenomenon in quantum mechanics. In 1928, with his help, he explained how certain radioactive isotopes can emit alpha particles. He showed that alpha particles inside the core do not have enough energy to break away from a heavy core, just as a cannonball cannot reach escape velocity and break away from the Earth's gravitational field. He was able to show that due to its wave nature, an alpha particle can still penetrate the barrier and leave the nucleus.
Contrary to popular belief, however, tunneling is not only a purely quantum effect; it is also observed in the case of classical waves. A sunbeam passing in a cloud outside a drop of water can, contrary to intuitive expectation, penetrate it through the tunneling effect and thus contribute to the creation of gloria.
Our initial work with Wiskomb was concerned with the study of the scattering of light by fully reflecting silver balls. We found that the partial waves of a ray passing outside the sphere can, if the distance to the droplet surface is not too great, tunnel to its surface and make a significant contribution to diffraction.
In the case of transparent spheres such as water droplets, after tunneling to their surface, light can penetrate inward. There it strikes the inner surface of the sphere at an angle small enough to undergo total internal reflection, and therefore remains trapped inside the drop. A similar phenomenon is observed for sound waves, for example, in the famous Whispering Gallery under the arches of St. Paul in London. A person whispering while facing one wall can be heard in the distance at the opposite wall, because sound undergoes multiple reflections from rounded walls.
In the case of light, however, a wave that has tunneled into the droplet can also leave it due to tunneling. For certain wavelengths, after multiple internal reflections, the wave is amplified by constructive interference, forming the so-called Mie resonance. This effect can be compared to the swinging of a swing due to jolts, the frequency of which coincides with their natural frequency. In connection with the acoustic analogy, these resonances are also called the whispering gallery effect. Even a slight change in wavelength is enough to break the resonance; therefore, Mi resonances are extremely sharp and provide a significant increase in intensity.
In summary, we can say that three effects contribute to the gloria phenomenon: the axial backscattering considered by Ray in accordance with geometric optics; edge waves, including van de Hulst surface waves; Mie resonances arising from tunneling. In 1977, Vijay Khare, then at the University of Rochester, and I evaluated the contribution of edge rays, including van de Hulst waves. The resonances were reviewed by Luiz Gallisa Guimaraes of the Federal University of Rio de Janeiro in 1994. In 2002, I made a detailed analysis of which of the three effects is most important. It turned out that the contribution of axial backscattering is negligible, and the most significant is the effect of resonances due to off-edge tunneling. The inevitable conclusion that follows from this is this:gloria is a macroscopic effect of light tunneling.
Gloria and the climate
In addition to providing pure intellectual satisfaction to the gloria problem, the tunneling effect of light has practical applications as well. The whispering gallery effect has been used to create lasers based on microscopic water droplets, hard microspheres, and microscopic discs. Light tunneling has recently been used in touchscreen displays. A finger approaching the screen acts as a Newtonian lens, allowing light to tunnel inside the screen, scatter in the opposite direction, and generate a signal. An inhomogeneous light wave generated by tunneling is used in such important technology as near-edge microscopy, which can resolve details that are smaller than the wavelength of light, thereby breaking the so-called diffraction limit.which in conventional microscopy for objects of this size gives a blurry image.
Understanding the scattering of light in water droplets is especially important to assess the role of clouds in climate change. Water is highly transparent in the visible region of the spectrum, however, like carbon dioxide and other greenhouse gases, it absorbs infrared radiation in some bands. Since Mie resonances are usually associated with a very large number of internal reflection events, a small droplet can absorb a significant fraction of the radiation, especially if the water contains impurities. The question arises: will the cloud cover, as its average density change, keep the Earth cool, reflecting most of the sunlight into space, or will it contribute to its heating, acting as an additional blanket that traps infrared radiation?
Until about ten years ago, modeling of light scattering by clouds was performed by calculating Mie resonances for a relatively small set of droplet sizes that were considered representative of typical clouds. This reduced the counting time on the supercomputer, but it posed an unexpected trap. As I showed in 2003, using my own methods for analyzing rainbow and gloria, standard modeling methods could lead to errors of up to 30% for some narrow spectral bands. Thus, when calculating the scattering from droplets with preselected sizes, it is easy to miss an important contribution from many narrow resonances associated with droplets of intermediate sizes. For example, if the calculation was performed for droplets with a diameter of one, two, three, etc. micron, a very narrow resonance at 2.4 microns was passed. My prediction was confirmed in 2006. In studies that took into account the real distribution of droplet sizes in the atmosphere, in recent years the models have been improved by considering droplets, the sizes of which have been broken down into much smaller intervals.
As predicted by Wigner, the results obtained even with the help of a perfect supercomputer, if not illuminated by physical thought, are not credible. There is something to think about, especially if next time your seat on the plane is by the window.