From lasers to random lasers

Lasers are among the most useful and popular of all optical devices, with countless applications ranging from biology to astronomy. First predicted by Letokhov [292] and measured experimentally by Lawandy [269] and others [174, 319], random lasers [495, 529] connected for the first time the physics of ordinary lasers with that of disordered systems, boosting spectacularly in the early 1990s the interest of the scientific community in complex photonics. The possibility of using intrinsically disordered structures to create novel optical systems is attractive, not only from the applications point of view, but also fundamentally, allowing scientists to connect the theoretical paradigms of complexity, nonlinearity, disorder, and even glass physics with photonics.

Laser stands for Light Amplification by Stimulated Emission of Radiation, thus the amplifier is its fundamental element. A coherent optical amplifier is capable of increasing the amplitude of an optical field while maintaining its phase. If a monochromatic beam is injected into such a device the output will have the same frequency, while the phase can be the same or shifted by a fixed amount. In contrast, an amplifier that increases the intensity of an optical wave without preserving the phase is an incoherent amplifier. An amplifier based on stimulated emission is coherent: the stimulation process allows a photon in a given mode to induce an atom lying in an excited state to undergo a transition to a lower energy level, emitting a photon that is identical to the exciting photon, thus preserving frequency, direction, polarization and phase. If stimulation happens in a material in which the population is inverted (i.e. the majority of the atoms lie at the excited level), then an avalanche process in which every photon creates a duplicate of itself, is ignited exponentially, increasing the amplitude in the mode.

Cleaning optical surfaces

You can clean a seriously stained or corroded surface by gentle polishing with a fine wet rag and a dab of rouge or cerirouge. This is a last resort of course, on a surface which would otherwise be discarded. Apart from this you should never, never touch a dirty optical surface with any solid other than a fine sable-hair artist's brush dipped in a suitable solvent such as analytical quality iso-propyl alcohol. The sweat on your fingers (which helps in fingerprinting) is acid enough to etch glass. There is never any reason to allow a cloth to touch an optical-quality glass surface, as it will almost certainly have abrasive silica particles embedded in it.

Camera lenses

Camera lenses are best kept with a permanent anti-ultra-violet filter in place. If it is necessary to clear dust, a blower-brush is the proper device. If the glass surface has stains or dried water-spots, then the solvent of choice is iso-propyl alcohol. Diethyl ether can also be used in a well-ventilated place and ethyl alcohol too, although it is not such a good solvent for lipids. Diethyl ether evaporates quickly and the consequent cooling of the surface may cause water-drop condensation in high humidity surroundings. Ethyl alcohol will dissolve water.

The most famous and illustrious mis-user of an optical instrument is Sherlock Holmes. There is an iconic figure of him with Inverness cape, deerstalker hat and calabash pipe, peering though a magnifying glass, the latter held at arm's length, to inspect a possible blood stain.

This is the wrong way to use a magnifying glass – which incidentally should always have a plano-convex lens rather than the biconvex lens with which many cheap versions are provided. The glass should be held close to the eye, plane side facing, and the object brought in until it is in clear focus at a comfortable distance for viewing. This gives the clearest image, the widest field and the minimum of optical aberrations. It is the attention to small detail like this which helps ensure success. Watchmakers do it properly, with a loupe, a lens held, like a monocle, in the eye socket.

In experimental science, especially in physics laboratories, it is sometimes found, when beginning a new piece of basic research, that no appropriate apparatus exists and that it is necessary to improvise. The traditional laboratory stand-and-clamp then comes into its own, followed, after some experimentation, by a properly designed system with an optical bench or table with lenses, mirrors and other basic optical elements for measuring and analysing radiation. Skills in the design and assembly of such provisional devices are part of the true experimenter's art.

Interferometry

Interferometers, as the name implies, rely on the wave nature of light and of the constructive and destructive interference between wave-trains. They are devices, often of great ingenuity, with many applications to fine measurement (~10−9 m) or ultra-fine measurement (~10−12 m) and as such they have led the way to many advances in science, not least in provoking the theory of relativity and in confirming the predictions of quantum mechanics. After overcoming formidable technical problems in construction and stability, interferometers are now in everyday use, particularly in spectroscopy, fine measurement and quality control.

Oscillation, phase and phase-difference

The word ‘oscillator’ applies as much to the electric vector of a beam of radiation as it does to a swinging pendulum. Two oscillators are ‘in phase’ when they reach a maximum displacement in the same direction at the same time and are ‘out of phase’ if their displacements are exactly opposite. We then say that their phase-difference is 180° or that they have π radians phase-difference. Their phase-difference is measured as an angle because it is convenient to use the mathematics of a circle to do so: there are no physical lines or angles involved.

Introduction: polarized light

James Clerk Maxwell (1831–1879) discovered the first unified field theory when in 1865 he showed, drawing on Faraday's experiments, the Biot–Savart law and other results, that interacting electric and magnetic fields and forces could be described by the same set of equations. Oliver Heaviside (1850–1925) reduced the twenty quaternion equations of Maxwell's theory to the four vector equations that ordinary mortals could understand. Maxwell showed that a wave equation could be deduced and that the consequent electromagnetic field propagates in a direction perpendicular to its electric and magnetic field vectors, and at a velocity which could be calculated from two quantities (permittivity and susceptibility) measurable in separate laboratory experiments. The resultant computed velocity was very close indeed to the experimentally measured speed of light. It was an easy conjecture then, that light was electromagnetic radiation. It was a further logical extension to predict radio waves, later confirmed by David Hughes' and Heinrich Hertz's spark-gap experiments.

The mutually perpendicular electric and magnetic field vectors oscillate in amplitude at about 5 × 1014 Hz for red light. If the direction of propagation is the positive z-direction, then the electric and magnetic vectors lie in the x−y plane. The light is said to be plane polarized if the angle the electric vector makes with the x-axis is constant in time.

Introduction: the photographic lens

A simple plano-convex lens has one surface plane and the other spherical. Its focal surface is also approximately spherical. The image of a point source at −∞ on the optic axis is never a point because of spherical aberration, and the image is more and more distorted by other aberrations as the field angle increases.

Eighteenth century telescope makers such as John Dollond had discovered these aberrations long before the first photo-sensitive chemical materials were discovered, and they knew that both chromatic aberration and spherical aberration could be corrected (i.e. reduced to a satisfactorily small level) by combining two lenses with spherical surfaces, a positive one made of crown glass and a negative of flint glass, into an achromatic doublet, usually but not always a cemented doublet, in which the second and third surfaces were complementary and the two were joined by a thin film of Canada balsam. This was the first step on a long road which has led to the wide-aperture zoom lenses of current cameras.

A significant milepost on this road was the Gauss achromat, a positive meniscus followed by a negative meniscus: an air-spaced doublet which by its ‘bendings’, i.e. changing the shapes of the elements without changing their powers, reduced the aberrations. It was originally designed by C. F. Gauss at the request of Repsold the Hamburg lens maker, who needed an achromatic telescope objective of improved performance.

The limits of Gaussian optics

The initial layout of an optical instrument is usually made using simple Gaussian optics, where all apertures and pupils are infinitesimal and all angles are considered small, so that the approximations sin θ = tan θ = θ and cos θ = 1 are adequate.

Geometrical optics, however, is a non-linear discipline and ray-tracing, using the proper values of sines and cosines, quickly reveals that rays do not arrive in the expected places to make sharp images. The quality of an image can be tested by modifying the Gaussian optics to the approximations that sin θ = θ − θ3/6, cos θ = 1 and tan θ = θ + θ3/3 and adjustments can then be made to the positions, curvatures and refractive indices of the various elements of a system to produce better images at the focal surface. Except in rare instances, perfection is not to be expected, and the art of the optical designer is to adjust the values to produce an acceptable result. The problem confronting the designer is that the adjustments all interfere with each other, making the problem miserably complicated.

The problem was first analysed by Ludwig von Seidel of Munich (1821–1896), who codified the five so-called Seidel aberrations of a monochromatic system and derived formulae for computing them.

The visual telescope

This is an elementary type of optical instrument.

The historically acknowledged function of a telescope is to produce an enlarged virtual image of a distant object for inspection by the observer's eye. Both object and image are at −∞ in normal focusing mode, but by shortening the tube a little the image can be brought nearer to the observer's eye to allow for myopia. In effect the objective forms a real image of a distant object and the eyepiece re-collimates the light so that the final image, like the object, is at −∞. The lens of the observer's eye then focuses this virtual image on to the retina.

An unusual but equally valid alternative is to regard a telescope as a device which puts an enlarged, real image of the observer's eye-pupil at the telescope's objective. If the telescope is properly designed, the image of the eye-pupil will exactly correspond in position and diameter to the clear aperture of the objective. The enlarged, virtual eye would then see the distant object exactly as the actual observer sees it, but in appropriately greater detail.

What all this implies is that the observer's eye-pupil and the telescope objective are conjugate points in the complete optical system of telescope and eye.

The traditional silver halide camera

Silver halide photography, from its invention in the 1830s, relied almost exclusively on finely ground silver bromide crystals suspended in a gelatine emulsion. These, it was discovered, were altered by the absorption of light so that they could be reduced chemically to black, colloidal silver by a variety of sensitive reducing agents to produce a negative image in the emulsion. This could then be changed, usually by copying to positive images in transparent emulsion or on sensitized paper. The sensitivity was restricted at first to light of short wavelengths in the blue to ultra-violet region of the spectrum until a chemist, H. W. Vogel, at the University of Berlin, discovered the technique of dye-sensitization to make orthochromatic emulsions sensitive to yellow and orange light. Later improvements in this technique eventually made red-sensitive panchromatic emulsions available – at a price – in the early years of the twentieth century. S. M. Prokudin–Gorskii, in particular, led the way by making simultaneous exposures through red, green and blue filters to give negatives, from which diapositives could be made for simultaneous projection with three projectors and the same colour filters, on to a screen, thus producing the first colour photography slide shows.

Which device is to be used to detect radiation depends very much on the kind of radiation. Heat, for example, the far infra-red that is, needs a bolometer; the UVOIR region relies on the interaction of radiation with electric charge, and the far ultra-violet relies on fluorescence or the photoelectric effect.

The geometry of radiation measurement

Two things are fundamental.

1. (1) There is no power in a parallel beam: power depends on divergence into a finite solid angle.

2. (2) There is no power from a point source. The power radiated is proportional to the source area if the radiation is incoherent, and is proportional to the square of the source area if the radiation is coherent across the area.

The two useful ideas – a point source and a parallel beam – are, like light rays themselves, among the ‘convenient fictions’ of physics.

Extended sources

As we can see from the remarks above, all sources are extended to some degree. Even a single atom radiates a spectral line from an ‘area’ of about λ2 because you cannot ‘localize’ the emitter to better than this, using this radiation. Light sources then are distinguished by their surface brightness, the power emitted per unit area per unit solid angle.

The common properties of optical instruments

Optical instruments come in all shapes and sizes, from fly-on-the-wall surveillance cameras to 10 metre segmented astronomical reflecting telescopes, and in shapes from microscopes to sextants to periscopes to spectrographs to cine-projectors.

Whatever their purpose, they all have two things in common.

1. (1) They are image-forming devices, intended to make a picture, to form an image of a luminous source. The image may be on a cinema screen, on a photographic emulsion, on a CCD surface or on the retina of an eye.

2. (2) They are, with one important exception, centred systems. That is to say they comprise a series of curved surfaces of transparent materials or reflecting materials or both. The centres of curvature of the various elements all lie on a straight line called the optic axis. Light passes from the object, through successive elements until it emerges to form an image.

This is a slight over-simplification of course. There are occasional plane reflectors along the path, as in a periscope for example, but these are for convenience rather than for any peculiar optical properties they possess.

Optical elements

There are four basic optical elements: the lens, the mirror, the diffraction grating and the prism. What follows now concerns the first two of these. The others have chapters of their own.

The celestial sphere

For the purposes of observational astronomy and celestial navigation, it is adequate to assume that the Sun, stars and planets all lie on the surface of a transparent sphere of ‘immeasurably’ large diameter with the Earth, or sometimes the observer, at its centre. The positions of the stars on this sphere are given by coordinates similar to those of latitude and longitude on Earth, but known generally as declination (latitude) and celestial longitude, measured westward from ‘the first point of Aries’. This is the place on the sky where the Sun crosses the equator going northwards each (northern) Spring and was once in the constellation of Aries. (Because of the ‘precession of the equinoxes’ it is now in the constellation of Pisces.)

Formerly longitude was measured eastward from the first point of Aries. It was called ‘right ascension’ and was measured in hours and minutes rather than degrees. These hours were sidereal hours not solar hours, with the understanding that Earth rotates through 360° in 24 sidereal hours, or 23 hours 56 minutes of solar mean time. Sidereal clocks gain 4 minutes each day on ordinary clocks since the Earth rotates through approximately 361° from one midday to the next.

Microscopes and projectors have this in common: they illustrate the universal requirement that the passage of light through an instrument must be closely controlled. Neither is likely to be improvised by the reader, but one should understand the way they work.

Projectors

In this section we deal chiefly with the diapositive projector, the old-time ‘magic lantern’ as our Victorian forefathers knew it, which projects images of transparencies on to a large screen for public viewing. Two things are necessary for its design:

1. (1) it must project a clear sharp image of the transparency on to a distant flat surface, and

2. (2) it must illuminate the transparency uniformly with light – there must be no dark corners to the picture.

The ingredients for this are a bright source of light, ideally an extended source, but failing that either an array of white LEDs or a filament lamp with a series of coiled filaments as shown in Figure 9.1, arranged so that the space between parallel coils is equal to the width of the coil.

Behind the filament is a spherical mirror placed so that the filament is at its centre of curvature and slightly offset laterally so that the images of each coil fall between the coils themselves.

Eyepieces

When you look through a telescope or binocular you focus the distant scene by first pulling out then slowly retracting the tube, or by turning the appropriate screw. For visual observation you should always extend the tube beyond the point of good focus and then draw it in until the scene is seen to be sharp and well focused. This is to avoid the eye strain which comes from a prolonged accommodation of the eye to a close object. (The same is true when using a hand-lens. Bring the object in from a distance; do not start with it too close because, although it will be in focus well enough, the image will be close to the eye instead of at −∞ where it belongs.)

The telescope field of view is bounded by a circular stop which is usually sharply in focus. There may be an eyepiece adjustment to make it so. It is a stop placed at the prime focus, and it is there to prevent scattered light from the outer, unusable part of the field from entering the eye, thereby reducing the contrast of the scene. A second such stop, with the same purpose, is at the intermediate pupil of an erecting telescope. The two stops are optically conjugate.