Chapter 5 Light matters

  How do you generate light? There many different ways: common light bulbs, based on glowing metal filaments, as well as『fluorescent』 tubes; laser pointers; tell-tale lights on electrical equipment, from toasters to car dashboards; sunlight and starlight; even, for those in the northern and southern extremities of the planet, the aurorae; fireflies and glow-worms, and the phosphorescence in the wake of boats. What is the means by which these very different things all generate the same thing:light?

  The key is that they all involve matter. More specifically, they involve electric charges moving about. When these charges accelerate—that is, when they change their speed or their direction of motion—then a simple law of physics is that they emit light. Understanding this was one of the great achievements of the theory of electromagnetism. An electric field has its origin in an electric charge, such as an electron in an atom. The electric field,attracting oppositely charged particles, such as protons, extends throughout all space, although it gets weaker quite quickly as you move away from the electron. As I noted in Chapter 3, this is the force that arises from static electricity.

  Oscillating atoms and bending electrons

  Now say the electron moves with a sudden jerk. The field surrounding it must move also, since it is linked inextricably to the electron. The change in the field is illustrated in Figure 25, as a 『kink』. A remote proton will notice that the electron has moved only when the change in the field that arises from the electron movement has had time to make its way to the proton. This will take time since the kink, and therefore the information that the electron has moved, propagates at about the speed of light.When the change does get to the proton, it will move according to whether the electron moved closer to it (thus making the field experienced by the proton stronger, so that it feels a stronger force) or further away (leading to a weaker field and a weaker force).

  Now say the electron were to move back and forth. Then changes would occur in the field surrounding it in synchrony with this oscillation and propagate away to the proton, which would then be induced to oscillate in turn as it received this information. But an oscillating electric field (and associated magnetic field, but that need not bother us here) is exactly what we mean by light.

  25. Lines in the electric field of a. a stationary electron and b. anaccelerating electron. When the electron accelerates, the changes inthe field—the 『kinks』 in the field lines—propagate away from theelectron at the speed of light.

  Since a hydrogen atom—the simplest one—consists of a single electron and a single proton, we can understand from this picture how atoms can generate light. First, let’s think about what happens when light irradiates an atom sitting quietly on its own.The light forces both charged particles—the electron and the proton—inside the atom to move. But since the electron is much lighter than the proton, it moves more easily with a given application of force, and we can consider its motion with respect to the more or less stationary proton. In fact, the electron oscillates at the frequency of the light’s electric field, being alternately accelerated or decelerated as the electric field varies.

  This process is a bit like pushing a child on a swing. The best way to get the swing to oscillate is to push on it in synchrony with the natural oscillation period—a gentle push each time the swing reaches the bottom of its motion. Even so, it takes effort to get the child up to a height that thrills him or her. The child experiences maximum acceleration at the apices of the swing’s oscillation, and maximum speed as she passes under the point of suspension. So it is with the atomic electrons—the energy of the light beam is absorbed by the atom, and converted into the motion of electrons.

  Let’s say you now stop pushing on the swing. What happens? The child gradually swings in arcs of lesser and lesser amplitude to rest. Again, so it is with the atom. The electrons gradually stop oscillating, and give up their motional energy by reradiating light. This is the process of light emission, and is the basis of many light sources, such as neon signs, fluorescent lights, and laser pointers.

  

  Now in this picture I have assumed that some light beam itself is used initially to get the atomic electrons oscillating. But in a sense that begs the question of how one generates light in the first place.In fact it is possible to use other means to 『excite』 the atoms. First,one can simply heat up the material. This is what is done in an ordinary light bulb, where by passing an electric current through a metal filament the metal heats up to a very high temperature—several thousand degrees. As the material heats up, the electrons start to jostle and collide with the atoms and with one another more and more, and this both excites the atoms and causes the electrons to accelerate and decelerate rapidly. This produces a very broad range of colours that depends only on the temperature to which the material is heated, and not upon the particular type of atoms of which it is made.

  Electricity may also be used in other ways. In light-emitting diodes (LEDs) for example, as used in displays, an electrical current—or flow of electrons through the material—can be captured directly by an atom, so the light is generated much more efficiently than in a thermal source. A fluorescent tube also uses an electrical current to directly excite atoms, only this time in a nebulous gas with which the tube is filled. Finally, many different chemical or biological reactions can release energy, some of which leaves the atoms or molecules in the form of light. This is the origin of the light given off by fireflies, for example.

  We noted previously that acceleration has two parts to it: it can mean a change of speed, as we have just seen for the electron and proton in a hydrogen atom, or it can mean a change of direction without a change in speed. This latter characteristic of acceleration is familiar from the experience of going around corners in a car: you are pushed against the door or the side of the seat and experience a force that turns you with the car. The force is larger the faster you are moving as you enter the turn, and this is an indication that you are accelerating, even though you may not be speeding up or slowing down.

  Even this kind of acceleration, when experienced by charged particles, causes them to radiate light. Imagine a bunch of electrons forced to move in a circle, as if they were stuck on the rim of a rotating wheel. They generate light, the wavelength of which gets shorter and shorter (so the photon energy gets larger and larger) the faster they move around the circuit, because of this angular acceleration. The light generated in this way is called synchrotron radiation, and it is a common means to generate X-rays. It is also related to the light seen in the northern and southern aurorae, which are produced when charged particles from the Sun are forced to spiral by the Earth’s magnetic field as they enter the atmosphere.

  Quantum light emission processes

  These basic mechanisms underpin all light sources. But the details of how the atoms act as a group can have a strong influence on the characteristics of the light that is eventually emitted—as I noted in Chapter 1, a light bulb emits a very different sort of light than a laser pointer, for instance. In order to understand this, we need to delve a little deeper into the structure of atoms, since the process of emitting light from an atom is not completely encompassed by the analogy with swings. Something needs to be added in order to accommodate the fact that atoms and molecules are quantum mechanical entities.

  For our purpose this simply means that the electrons in the atom or molecule can only hold energy in fixed amounts. Using our swing model, it means that the maximum extension of the swing amplitude cannot be anything you like. Rather, it is restricted to certain particular values: it is quantized. More particularly, the energy of the swing comes in discrete packets, or quanta, and when you push it you can only make it jump by one or more quanta. In the atom, this means the energy of the electron can change only in the same discrete units when it absorbs or emits a single photon.The energies involved in making these jumps are very small by everyday standards. Take a light in your house. This consumes energy at a rate of, say, 60 W, or 60 Joules per second. A single photon emitted by the atoms in the light bulb possesses about one billion billionth of a Joule. So a light bulb is emitting more than ten billion billion photons per second.

  26. An atom undergoing a. absorption, b. spontaneous emission, andc. stimulated emission.

  An atom can be prepared in an excited state simply by shining light of the right frequency on it, as shown in Figure 26a.(Of course, this begs the question, but we』ve also seen that the excitation can also be accomplished in other ways, for instance by running an electrical current through the medium.) Now,according to quantum theory a corollary of the 『jumpiness』 of the electron motion is that the atomic electrons are pretty much stable against the emission of light once in one of these discrete states.They are like a ball on a shelf in a cupboard—in principle it can lower its energy by dropping to a lower shelf, but this cannot happen in practice unless you give it a little push so that it rolls off the shelf.

  So it would appear that quantum physics suggests that atoms cannot emit light, since once you have put them in these stable states—that’s it. Well, it turns out that, except for the lowestenergy state of the electron in the atom, a push is available to allow the electron to drop from a more energetic state to a less energetic state. And the surprising thing is that the shove arises from nothing.

  In Chapter 4, I noted one of the strangest features of quantum physics: even the emptiness of space is a seething background of activity, filled with 『vacuum fluctuations』. These fluctuations in the electromagnetic field can cause the atomic electron to drop to a lower energy level and to give up the energy difference in the form of emitted light. This process, by which an atom (or molecule)undergoes a transition from one stable state (the excited state) to another of lower energy (the ground state), emitting a photon on the way, is called spontaneous emission (Figure 26b). It is something that each atom does on its own. It was originally proposed by Einstein in order to account for the proper energy balance between a light beam and the matter on which it was shining. If spontaneous emission does not occur, then the atoms hold on to the energy from the light beam and the situation we see everywhere around us, where most things are in a stable state in equilibrium with their surroundings, would be impossible.

  Einstein understood the central mystery of spontaneous emission:that it was a random process. You just cannot say exactly when any given atom will make a jump. All you can say is that on average, after some amount of time (that depends on the particular atoms, but is roughly 1,000 billionth of a second), in a large collection of atoms, about two-thirds of them will have emitted a photon. But the origin of the fundamental randomness remained a mystery until, in 1927, Paul Dirac’s quantum field theory introduced the idea that quantum vacuum fluctuations were at the root of this. The notion that a field containing no photons at all can cause an excited atom to be unstable is at odds with our intuition, and it took until the 1950s for Lamb’s measurements to show that Dirac’s explanation was right.

  What this means is that even everyday occurrences—the picture generated on a TV screen by means of LEDs, for example—have at their heart this fundamentally random characteristic arising from quantum mechanics. By contrast, the emission of light by atoms when they are pushed to give up their energy by the application of another light field is called stimulated emission (Figure 26b). This form of recouping energy from atoms into the light field does not have random character. And this makes possible a very different kind of light: that of the laser.

  Coherence: acting all together

  When atoms and charged particles behave individually, 『doing their own thing』, the light they emit when there are many of them is a sort of uncoordinated set of waves. Even a very small LED,with a size of much less than a millimetre, contains a vast number of atoms, so this is a common situation.

  A feature of this uncoordinated emission is that each atom emits its photons at random, with no acknowledgement of what the adjacent atoms are doing: the light goes off in many different directions, and the photons are all emitted at different times. In effect, the randomness of the emission process is reflected in the randomness of the resulting light intensity.

  Let’s say we put a photo detector in front of a light bulb. (A photo detector works like a light bulb in reverse. It uses the photoelectric effect—light incident on it produces an electrical current that can be measured.) What we would see is that the electrical current from the detector was very noisy, because the light incident on the detector has an intensity that changes quickly and randomly,corresponding to the arrival of random numbers of photons at each instant of time.

  But what if it were possible to coordinate the atoms, so that they acted together? We can think back to our earlier analogy: imagine a collection of swings, each with the same oscillation frequency.The swings may be all oscillating at random: that is, with each at a different point in its repetitive trajectory at any instant. Or, they may be in synchrony, with the differences in trajectory between adjacent swings being a fixed amount—like a wave caused by the adjacent spectators in the crowd at a football match standing up and sitting down in sequence. In the first case, the light that is emitted from these uncorrelated atoms is like that from a light bulb or LED and is said to be incoherent. In the second case,however, the atoms oscillate in lock-step, and the light they emit is given off in a coherent fashion—all of the photons are emitted in the same direction. This is what happens in stimulated emission(Figure 26c), and is the basis for the laser.

  Laser light

  The laser is perhaps the most important invention in optics in the last century. This device produces extraordinarily useful beams of light that have revolutionized the range and capabilities of applications. Not only is it a specific source of illumination, in microscopy and spectroscopy for example, but it also provides a means to direct significant energy on to a particular target in a tailored way, and thereby to control the dynamics of matter. An extreme example of the latter application is laser-driven fusion of atoms, discussed in Chapter 7, that may enable new forms of nuclear energy which can draw upon a very large supply of fuel.

  A laser consists of an optical amplifier, or gain medium, that generates light from atoms by means of stimulated emission,placed between two mirrors (and possibly other optical elements)that form an optical cavity. The number of photons in the cavity builds up as the atoms emit light until there is a balance between the energy put into the light beam from the atoms, and the energy leaking out of the cavity through the mirrors. As the amplifier is turned on, by providing a means to excite the atoms, the light emitted from the amplifier is reflected back into it by the end mirror of the cavity. That causes further stimulation of radiation from the excited atoms, and thus the light in the cavity increases in brightness. At the other mirror, some of the light is transmitted out of the cavity as a useful output. Some is reflected back into the gain medium. When the rate at which light is put into the cavity by the amplifier equals the rate at which it is extracted through the output mirror, the laser is said to be at threshold. Beyond this point, any increase in the amplifier gain (the rate at which atoms are put into their excited states) leads to an increase in the intra-cavity intensity, and thus to an increase in the output light.The optical cavity also imposes a restriction on the colours of the laser. It turns out that the frequencies that experience the most gain are those for which the light waves add with constructive interference on each round trip. This means that the length of one round trip of the cavity should be equal to a multiple of half of a wavelength. The frequencies that satisfy this resonant condition are said to be the cavity modes.

  The reason that lasers are important is related to the fact that the light they emit is coherent: all the photons go in more or less the same direction, with the same colour. The direction is defined by the laser cavity: the colour by the atoms in the gain medium and the allowed modes of the cavity. This leads to the property that the light is in the form of a beam—the laser beam—which is about as close to a 『ray』 of light as you can imagine. It diverges as it propagates due to diffraction, but has the smallest divergence possible. This property also means that it can be focused to a very small spot using lenses or mirrors.

  A second feature that contrasts the light emitted from lasers with that from light bulbs is that laser light is usually very pure in colour. In other words, it consists of only a few wavelengths,whereas lamps often emit a broad range of wavelengths. The light intensity is very stable (registering as very low noise in a photodetector output), and the light can be emitted continuously or as a sequence of pulses.

  The ability of laser light to be focused to a very small spot makes it useful for microscopy, and there are a number of different ways in which, by scanning the laser spot across an object at the focus of the microscope lens, and detecting the light scattered or re-emitted from the object, three-dimensional images of the object can be made.This approach is very useful in looking at animal tissue, for example,and optical microscopies of this kind are widely used in biomedicine.

  Many applications of lasers in manufacturing also stem from this property of laser light. The ability to mark, cut, drill, or weld metals, for instance, requires that a lot of energy be deposited in a small region of the metal in a short time. So high-power lasers producing coherent light beams in the form of pulses that can be focused are ideal for such materials processing.

  Similar properties are needed for some medical applications of lasers, also involving materials—this time skin, teeth, or hair.Laser correction of vision and laser dentistry are now commonplace, as is the use of lasers to remove tattoos by heating up the ink until the drops break up, and for hair removal—although unfortunately not hair regrowth! Other familiar devices that make use of laser light’s ability to address a very small spot are the CD, DVD, Blu-ray, and some computer disk storage devices. Very tiny spots of light in the recording medium allow the very high-density storage of data in the material.

  The very pure colours achievable with laser light make it possible to distinguish the constituent atoms and molecules of different mixtures by means of spectroscopy. As noted in Chapter 1, different atoms, and indeed different molecules, have characteristic frequencies at which they absorb and radiate light, due to their different structures. Extending the analogy developed in this chapter, they are like swings in which the chains or ropes holding the seat are of different lengths—their natural oscillation frequencies are dependent upon the way in which they are put together.

  In fact, each atom and molecule has a range of different absorption and emission frequencies, corresponding to the excitation of different electron configurations. Typically these lie in the blue part of the visible light spectrum, but some molecules absorb at much shorter wavelengths, invisible to humans. Many molecules also absorb light at wavelengths longer than the red end of the visible spectrum. This absorption arises from the vibrations between the atomic nuclei that make up the molecule. Since nuclei are much heavier than electrons, they tend to oscillate at much lower frequencies. This set of frequencies is a sort of molecular『fingerprint』 that enables identification of a particular species.

  The catalogue of these fingerprints is of importance, of course, in chemistry, since it allows the different elements involved in a reaction to be identified. It is also used in molecular biology, and even in cell biology, when the movement of particular 『tag’molecules can be studied. It is critical, too, for astrophysics, in which the elements present in astronomical objects—stars,galaxies, nebulae—can be determined, as well as in atmospheric physics and meteorology, for the remote sensing of pollutants or particles. Such monitoring provides key data in assessing the impact and origin of climate change.

  By combining the outputs of several different lasers—say one emitting red light, one green, and one blue—it is possible to make a laser projector. By changing the intensities of each laser individually according to the video signal output of a computer or Internet link, perhaps by means of a liquid crystal cell, movies can be projected on a big screen with vivid, highly saturated colours.The combination of red, green, and blue (RGB) light is sufficient to make up a complete colour palette and lasers produce very bright images on a screen.

  X-rays

  When the wavelength of the light is very short, in the X-ray region of the spectrum, a different kind of spectroscopy arises.X-ray photons are energetic enough to excite the most tightly bound of the electrons in atoms—not just the outermost electrons. This means that X-rays can be used to look into the heart of atoms and molecules, and to understand their local environment, which can shift the binding energies of the electrons. X-ray absorption spectroscopy is widely used in the study of materials for a variety of applications, from detecting trace pollutants to understanding the structure of glasses. As noted in Chapter 3, X-rays are also used to study the structure of crystals by means of diffraction. When the X-ray wavelength is close to the spacing between atoms in the crystal, then the crystal acts as a 『diffraction grating』 and scatters the X-rays in discrete directions. By detecting these diffraction patterns on a camera, it is possible to reconstruct the three-dimensional structure of highly complex crystals using advanced inversion algorithms.Today this is a routine process for characterizing isolated biologically and chemically relevant molecules, determining the structures of possible new molecules in order to design them for a specific function.

  Some of the best light sources for this sort of spectroscopy are synchrotrons. In order to produce X-rays at the required short wavelengths, synchrotrons have to produce very energetic electron beams, and accelerate them around a big ring. Experimental stations catch a glint of light as the electrons rush by, leading to short bursts of X-rays that are used for diffraction imaging. For example, the Diamond Light Source at Harwell in England accelerates electrons to more than a billion volts in a ring that is more than half a kilometre long. The next generation of X-ray light sources is being built using linear particle accelerators, which produce extremely bright X-rays beams. The X-ray diffraction pattern shown in Figure 20 was taken using the Diamond synchrotron.

  Ultrashort light pulses

  Laser light can also come in short bursts. There are several ways to arrange for this to happen. The method that produces the briefest pulses is called mode-locking. This requires a gain medium that has a large bandwidth—that is, it can amplify light over a broad spectrum. This allows several of the modes of the optical cavity to experience gain. If it is also arranged that these modes all have the same phase, then light waves of many different frequencies add constructively to yield a single pulse inside the cavity, bouncing back and forth between the mirrors. The brevity of the pulse is determined by how many frequencies are locked—the wider the range of frequencies, the shorter the pulse.

  The possibility of creating very short duration laser light pulses enables a kind of measurement called dynamical or time-resolved spectroscopy. It allows us to see how things change in time, based on an old principle: the stroboscope. The general idea of how you use light to 『freeze』 rapid motion stems back to the work of Eadweard Muybridge in the late 19th century. He invented the idea of using a fast camera shutter to photograph a horse trotting.The legs of a horse move too fast for the human eye to resolve, and it was not known at that time whether all four legs left the ground at any point during the stride. To settle the matter, Muybridge set up a bank of cameras, each of which had its shutter opened by a trip wire, which was triggered when the horse passed the camera.This enabled him to 『slice』 a short pulse from the light reflected from the horse. The duration of this pulse of light was shorter than the time over which the horse’s legs moved. The outcome of his work was that he was able to inform Leland Stanford, the funder of his research, that in fact there is a point in a horse’s stride at which none of its legs touch the ground.

  Mechanical shutters on conventional cameras could close very fast, but not fast enough to see some forms of animal motion,such as the flapping of the wings of a hummingbird. Even faster physical events such as an explosion, where things change on timescales of thousandths of a second, were out of reach. To solve this problem, Harold Edgerton at MIT in the 1950s invented a new kind of non-mechanical shutter, based on an optical switch.He was able to take 『still』 photographs of explosions, for instance,using this device.

  These shutters are what we might call 『passive』 instruments. They simply allow a slice of light to pass through when they are open,so are suitable to events that are well illuminated (the horse in California sunshine) or emit a lot of light themselves (the explosion). But we can imagine an 『active』 instrument, one that generates a short pulse of light to illuminate a moving object.Think of the light pulses emitted by the flash unit on a camera.A flash of light with a duration that is short compared to the time taken for the thing we’re looking at to move provides an image of the object 『frozen』 in time, even when using a camera shutter speed that is much longer than the changes of the object. A second flash freezes the motion at a later time. The same is the case for subsequent flashes.

  A movie composed of the sequence of frames taken on repeated trials of the event reveals very rapid changes in the system, on a timescale that is much faster than could be observed by the eye.Indeed, the brevity of events that can be seen in this way is truly breathtaking. Edgerton invented a 『stroboscope』 of this kind in1931, and some of his most iconic images, such as a bullet passing through an apple or a playing card (Figure 27), were taken with this device.

  27. A bullet frozen in motion using stroboscopic imaging.

  Using modern pulsed lasers as the 『flash』 it is possible to observe not just the frozen motion of bullets but even the motion of atoms in a molecule involved in a chemical reaction (for which the 1999Nobel Prize in Chemistry was given to Ahmed Zewail) and the much, much faster motion of electrons whizzing around the nucleus of an atom. The timescales for these motions are staggeringly small—less than one tenth of a million-millionth of a second(100 × 10-15 seconds, or 100 femtoseconds (100 fs)) in the case of molecules, and a few tens of billion-billionths of a second(100 × 10-18 seconds, or 100 attoseconds (100 as)) in the case of atomic electrons. These fields—femtochemistry and attoscience respectively—are at the forefront of what is possible in the interaction of light and matter. I shall consider them further in Chapter 7.