Optical Properties Of Solids

Type of physical science: Condensed matter physics

Field of study: Solids

The important optical properties of solids produce the bending, reflection, absorption, emission, transmission, or polarization of light. These properties arise from the energy states of atoms, are altered by their arrangement in the solid, and respond to external electric and magnetic fields, sound waves, and the light itself.

Overview

The character and specific arrangement of the individual atoms that form a solid determine the optical properties of that solid. Atoms contain negatively charged electrons bound to a positively charged nucleus. The electrons give the atoms shape and chemical activity, while the minute nucleus gives the atom almost all of its mass. The electrons within atoms vibrate under the influence of light. Within a solid, these electronic vibrations and the vibrations of the atoms produce the optical properties of the solid.

One of the prime optical characteristics of individual atoms is the set of discrete energy levels that are available to the electrons, which normally fill up these energy levels from the bottom. These atomic energy levels determine the strength of the interaction between the atoms and the light. When the atoms crowd together within the solid, the energy levels shift and broaden into bands that control the optical response of the solid in rather surprising ways. The manner in which the energy bands fill with electrons determines whether the solid becomes an insulator, a semiconductor, or a metal, each of which has distinct optical properties.

By the Pauli exclusion principle, atoms can accept either one or two electrons within each energy level, but no more. Insulators form when the highest atomic energy level that holds electrons fills with two electrons. Consequently, the filled atomic energy level broadens into a filled band in the insulator. The electrons in the solid are tied to their band even if an electric field pushes them. The field tries to move the electrons, but there is no place for the electrons to flow and no electrical current results. Semiconductors are insulators with a relatively small energy difference between their uppermost filled band and their lowermost empty band. Metals, on the other hand, have an uppermost band which is half-filled. In this case, an electric field can move the electrons about within the band and inside the solid, producing an electrical current.

A major optical difference between insulators and metals lies in their optical absorptions. When a packet of light (photon) falls on a solid, absorption occurs if the energy of the light photon coincides with the energy difference between a single filled energy level and an empty level which is higher in energy. With insulators, the lower energy level must lie in a filled band and the upper energy level in the next highest empty band. A substantial energy gap exists in which light cannot be absorbed by the solid. Thus, insulators are transparent to light whose energy falls within the insulator gap.

Light consists of photons, whose energy increases with frequency. Visible light starts with low frequencies in the red band and progresses through yellow, green, and blue to the high frequencies of the violet band. The transmission frequencies of many insulators cover the visible spectrum, and such insulators are good candidates for the visual transmission of optical elements.

Semiconductors have small transmission gaps and are not transparent to visible light, although they are transparent to frequencies below the red band, such as infrared light.

Because metals have half-filled bands, however, the higher energy level for metals in absorption can fall at any energy within the upper half of the metallic band. No energy gap exists for metals, and so metals do not transmit throughout the infrared and visible spectra. The upper frequency limit at which metallic absorption can take place is determined by the plasma frequency of the metal. The electrons within the half-filled metal band act as if they were free, as in a plasma. The plasma frequency is the highest frequency at which the plasma responds to electromagnetic waves and has metallic properties. The plasma frequency falls in the ultraviolet range for many metals.

Surprisingly, metals with smooth surfaces do not absorb most of the light that falls on their surface, instead reflecting the light. The strong absorption tendency of the metal causes the light intensity to drop very rapidly at the metal surface. Any mismatch between optical conditions outside and within a solid surface prompts reflection from the surface, and the strong intensity mismatch produces high metallic reflection. Silver, for example, absorbs only 1 to 2 percent of the visible light that falls on its surface; the remainder reflects. Interestingly, the high visible absorption of many semiconductors confers a metallic reflection sheen to their surfaces despite the basic insulating nature of the semiconductors.

Another important optical property of solids is associated with the physical process of absorption. Light consists of waves that have electric crests and magnetic fields that are perpendicular to the direction in which the light is traveling. In isolated atoms, optical absorption strongly peaks at the light frequency whose energy coincides with the energy difference between the absorbing atom levels. Yet, even when absorption does not occur, the atom's levels influence the light radiation that passes by. Even light whose frequency is well outside the absorption peak, but below the absorption frequency, senses nearby atoms. As a result, the passing photons scatter in various directions. The wave crests of the scattered photons shift, altering the phases of the photons. Absorption and phase shift are intertwined in solid optical materials.

The phase shifting that accompanies absorption extends to all frequencies below the absorption band. In a solid, the phase shifts in the photons that are scattered by nearby atoms interfere with one another, causing light cancellation in all directions except the one in which the light was headed. Amazingly, the enormous scattering within a solid at frequencies outside the absorption band produces no visible trace and leaves the solid transparent. Nevertheless, the phase shifts do exact a toll. The net interference in the forward direction slows down the light passing through the solid, thus raising its refractive index.

The refractive index of a material is the ratio of the light speed in a vacuum to the light speed in the solid. For example, the visible refractive index of common window glass is about 1.5, so that the speed of light in such glass is about two-thirds of that in a vacuum. The absorption band that is mainly responsible for the phase shifts that produce this index in glass is at higher frequencies, in the near ultraviolet range, where glass is strongly absorbing.

When a light ray in air enters a solid through its surface, the light speed must suddenly decrease. The only way for this decrease to occur with the light keeping the same frequency inside the solid as outside it is for the light ray to bend perpendicular to the surface of the solid.

The larger the decrease in speed, the greater is the bending. Snell's law gives the relationship between refractive index and angle of bend, which is called refraction. When measured, refraction yields the refractive index and light speed in the solid. In anisotropic crystals, the index depends on the orientation of the light's electric field with respect to directions within the crystal. Crystals that display double refraction have fast and slow directions within them. With such crystals, a single light ray may suffer two bendings at the surface, or double refraction, and split into two.

The electronic phase shifts that are produced by the atoms in a solid decrease at light frequencies that are farther from the absorption band. This decrease produces a change in refractive index called dispersion. Glass has its highest index in the violet band and suffers a small progressive decrease in index across the visible spectrum, from violet to red. White light that strikes a glass surface bends more in the violet band and less in the red. This effect disperses white light into a fan of colored beams.

The mismatch of light speed between air and a solid, or between two different solids, does more than bend light entering a surface: The mismatch of speeds and indices produces reflection at the surface. At a surface between glass and air, the reflection is about 4 percent for a beam entering perpendicular to the surface. Rutile, one crystal form of titanium dioxide, has one of the largest refractive indices (2.9) in the visible spectrum for a common material along one crystal axis. Almost 24 percent of light falling perpendicular to a surface with this index will reflect.

Aside from the electrons within atoms, the solid atoms themselves produce optical absorption and increase in refractive index at frequencies below the absorption region. Since atoms are much heavier than electrons, the absorption bands that are attributable to atomic absorption fall at lower frequencies than the electronic absorption bands. For most solids, atomic absorption lies at frequencies in the infrared spectrum.

Applications

There is an enormous number of applications of the atomic properties of solid materials. For simplicity, these applications are split into the passive, in which the material is not influenced externally, and the active, in which external means such as the light itself alter the solid's properties.

The design of solids that are used in passive optical elements, such as lenses, reflectors, polarizers, color selectors, optical filters, and optical fibers, requires the control of the absorption in bands and atomic impurities and of the refraction that is associated with this absorption.

The glass or plastic used in lenses must have a broad transmission region in the visible spectrum and a sufficiently high refractive index to produce significant bending at the curved lens surface. In lenses, dispersion is detrimental because it blurs any colored image. This problem must be overcome by the proper design of the lens and the choice of dispersive glasses in a lens train.

Reflectors often employ metals to redirect light. Since metallic reflection occurs within a very thin surface layer, only a small amount of metal suffices. A thin film of silver, aluminum, or gold covering a smooth base makes an inexpensive and excellent reflector. Some heat mirrors must transmit visible light from a hot source while reflecting infrared heat rays in order to assure a cool illumination behind the mirror. These unique mirrors often employ an insulator which is heavily doped (containing a considerable amount of dopant, an impurity), such as indium tin oxide. The tin oxide is transparent in the visible spectrum, while the dopant, indium, supplies carriers that form a plasma which is dense enough to have an infrared plasma frequency.

Reflection takes place for the hot infrared frequencies below the plasma frequency.

In certain strongly anisotropic materials or crystals, the absorption is strongest when the electric field of the light points along one direction in the material. These anisotropic materials act as polarizers that restrict the electric field of a light ray to the direction that is perpendicular to the ray direction. Unpolarized light has its electric field pointing in random directions. When unpolarized light travels through the anisotropic material, it becomes polarized with the electric field pointing in the weakly absorbing direction. Therefore, anisotropic materials produce polarized light from unpolarized light. If the incident light is already polarized along the strongly absorbing direction, however, then the light is not transmitted; the material blocks the light. This action is the basis of Polaroid sunglasses, which block out surface reflections that are highly polarized.

By introducing isolated atoms into a solid, an otherwise transparent solid becomes colored in the broadened band of frequencies that surrounds the sharp peak of the isolated atom.

The transmission color of the solid tends to be the complement of the absorption color. Some sunglasses have impurities that block out harmful violet and ultraviolet rays, and these sunglasses appear green or amber in transmission.

Low-absorption optical filters use multiple, thin insulating layers with alternating high and low refractive indices. Designers use the wave interference of the multiple reflections in the filters to produce high reflection in desired regions of the spectrum, often for laser applications.

High-reflectivity metal layers are sometimes incorporated in order to reduce the number of insulating layers or produce heat mirror properties in the infrared range.

Optical fibers are the connection lines of the communication age. Typically, a thin core of silicon and germanium oxide glass, one-millionth of a meter thick, threads through a germanium glass cladding (metal coating bonded to a metal core) whose index is slightly lower than the core. The mismatch in indices provides optical guiding with low loss for tens to hundreds of kilometers. Such a phenomenal transmission demands extremely pure glasses.

Minute amounts of hydroxyl ions (from water contamination) and copper and iron ions devastate the extremely high transmission of the fibers that are needed for long-distance communications.

Active optical solids use a variety of external means to influence the conditions within the solid. Light sources demand excited electrons in the solid bands or within individual atoms in the solid. The collapse of the excited electrons to empty energy levels produces light.

Incandescence occurs most easily with hot metals, such as the tungsten filament in a light bulb.

Collapsing electrons produce a broad spectrum of light from the visible spectrum well into the hot infrared range. Strong ultraviolet emission from the mercury vapor plasma of a fluorescent lamp induces fluorescence from the white phosphor coating on the envelope. Electrons within the insulating phosphor crystals absorb the ultraviolet light, jump to higher energy levels, and reemit a tailored spectrum of cool visible light.

Solid-state lasers operate through a variety of excitation, or pumping, mechanisms.

Flash-lamp pumping induces the red fluorescence of chromium in solid ruby lasers, while flash lamps, incandescent lamps, and other lasers can pump neodymium lasers to fluorescence.

Multilayer dielectric mirrors feed the induced light back into the ruby or neodymium rods to produce laser action. Semiconductor lasers, however, operate by the very efficient, direct injection of electrical charges into their highly doped bands. The recombination of electrons and holes, which are merely empty levels in the lower band, produces the laser light. The refractive index of gallium arsenide is about 3.3 for the recombination light, and its reflectivity is almost 29 percent at its surfaces, so no external mirror coatings are needed for this semiconductor laser.

Optical communications demands methods that modulate and direct the light beams connecting the source and the receiver. Engineers use electric and magnetic fields, or strong sound or pressure waves, to modulate the beam and alter its direction. The directions of the external fields produce a nonuniformity within an otherwise isotropic material, while the strength of the fields changes the refractive indices of the materials that pass the light.

Electro-optic devices use an external electric field to alter the ability of a solid to polarize passing light. If the material is isotropic to begin with, then the electro-optic effect that is produced is called the Kerr effect. In nonuniform crystals, such as potassium dihydrogen phosphate and gallium arsenide, the electro-optic effect is called Pockel's effect. The Faraday effect produces a magneto-optic rotation of polarization with an external magnetic field. The repetitive strains accompanying a sound wave traveling though a solid, such as lithium niobate, produce an acoustic-optic effect. These strains induce an acoustic grating of altered refractive indices in the solid, which acts like a real optical grating to deflect light beams that meet the sound.

The fields within light itself can alter the solid through which the light moves, which occurs at the very high power per unit area that is possible with pulsed lasers. The electric field in the light from such lasers may be a fraction of the electric field that fixes the electrons to the solid. The light itself alters the refractive index of the solid and creates many novel optical effects. The most important of these effects is harmonic generation, in which the highly intense light produces a laser image of itself at double or triple the frequency. For example, properly designed laser conditions allow the near-infrared light from a neodymium laser to produce doubled visible green light and tripled ultraviolet light.

Context

As with much of classical physics, the understanding of light traces back to Sir Isaac Newton (1642-1727). Newton used dispersion in a wedge of glass to prove that white light consisted of a spectrum of colors, which he interpreted as light particles. He thought that light refraction was attributable to the speedup of these light particles in a solid, which is incorrect--in part: Light waves slow down in solids. In addition, James Clerk Maxwell (1831-1879) unified the laws of electricity and magnetism and, in so doing, predicted the correct value for the velocity of these light waves. The discovery that light does indeed come in particle-like packets (photons) set the stage for the understanding of the atomic processes underlying the optical properties of solids.

At the very start of the twentieth century, Max Planck (1858-1947) produced a theoretical derivation which matched experimental data on hot, black bodies. In his derivation, Planck was forced to assume that light energy came in multiples of a basic unit, the photon.

Therefore, it was shown that light waves did behave like particles. The photon energy increased with light frequency, and Niels Bohr (18851962) showed that the light spectrum observed with hydrogen could be explained if electron particles behaved as waves as well. The wave-particle duality of quantum physics was born. The Bohr atom came with only very discrete energy levels, whose differences corresponded to the photon energies that could be emitted or absorbed.

In 1925, Wolfgang Pauli (1900-1958) announced the exclusion principle and laid the basis for a systematic explanation of the periodic arrangement of atoms. In addition to recognizing that discrete atom energy levels broaden into solid-state bands, the exclusion principle created a theoretical foundation for the optical transparency of insulators, which are solids that have a filled band separated by a substantial energy gap from a higher-energy empty band. In the early part of the twentieth century, Paul Drude (1863-1906) and Hendrik Antoon Lorentz (1853-1928) presented an elementary theory of metals in which electrons acted as a gas within the solid. By 1930, Arnold Sommerfeld (1868-1951) employed Pauli's principle to explain how a partially filled metallic band allowed the presence of a free-electron gas in the solid metal.

This explanation is the basis for understanding the reflective properties of conducting metals, and it completed physicists' understanding of the atomic-level behavior of the optical properties of solids.

Principal terms

ABSORPTION: a process which results in a progressive loss of light energy as the light moves through a solid

ATOM: the smallest particle of an element; small isolated groups of similar or different atoms form molecules, while large fixed groups form solids

ENERGY LEVELS: the discrete energy states of individual atoms, which allow the selective absorption or emission of light whose energy matches the difference between levels; in a solid, the discrete energy levels broaden into energy bands

LIGHT: loosely, waves that contain electric and magnetic fields traveling at 299,000 kilometers per second in empty space; more precisely, those electromagnetic waves that the human eye can see

POLARIZATION: the orientation of the electric, and thus magnetic, field of light

REFLECTION: the bouncing away of some of the light energy that falls on a surface

REFRACTION: the bending of a path of light, often at a solid's surface

REFRACTIVE INDEX: the ratio of the speed of light in a vacuum to its speed in a particular material

TRANSMISSION: the passage of some light energy through a material

Bibliography

Baker, Adolph. MODERN PHYSICS AND ANTIPHYSICS. Reading, Mass.: Addison-Wesley, 1970. A fine account of several topics in modern physics. The wave-particle duality prompted by Max Planck's study at the turn of the century is still an up-to-date mystery that is explored for the general reader in chapters 12 through 15. Asks questions and presents selected answers.

Feynmann, Richard P. QED: THE STRANGE THEORY OF LIGHT AND MATTER. Princeton, N.J.: Princeton University Press, 1985. This 158-page book is a delight. Presents a readable account of the physical nature of light, photons, and quantum theory and delves into the unsolved mystery of their behavior. Events such as light reflection are presented clearly by this pioneer of modern quantum theory.

Jenkins, Francis A., and Harvey E. White. FUNDAMENTALS OF OPTICS. New York: McGraw-Hill, 1976. A revised version of an introductory optics text which contains equations and assumes some background in physics. Much of the material is descriptive and understandable, however, while the equations are often simple and unnecessary.

Jones, Edwin R., and Richard L. Childers. CONTEMPORARY COLLEGE PHYSICS. New York: Addison-Wesley, 1990. A fine elementary physics text. Chapter 30 discusses condensed matter (solid matter), while chapters 21 through 23 discuss optics. Readable and beautifully illustrated, with attractive diagrams. Unfortunately, simple equations are scattered throughout.

Pedrotti, Frank L., and Leno S. Pedrotti. INTRODUCTION TO OPTICS. Englewood Cliffs, N.J.: Prentice-Hall, 1987. Pages 527-531 contain a complete listing of more than one hundred SCIENTIFIC AMERICAN articles on optics. In general, these articles are lucid and have attractive layouts and informative illustrations. Includes articles by Arthur L. Schawlow, F. F. Morehead, Ali Javan, G. H. Heilmeier, Amnon Yariv, Eitan Abraham, Colin T. Seaton, and S. Desmond Smith.

Electrons and Atoms

Polarization of Light

The Effect of Electric and Magnetic Fields on Quantum Systems

Reflection and Refraction