Eng2000 chapter 10 optical properties of materials
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ENG2000 Chapter 10 Optical Properties of Materials. Overview. The study of the optical properties of materials is a huge field and we will only be able to touch on some of the most basic parts

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ENG2000 Chapter 10 Optical Properties of Materials

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ENG2000 Chapter 10Optical Properties of Materials


  • The study of the optical properties of materials is a huge field and we will only be able to touch on some of the most basic parts

  • So we will consider the essential properties such as absorption/reflection/transmission and refraction

  • Then we will look at other phenomena like luminescence and fluorescence

  • Finally we will mention applications, in particular optical fibres and lasers

Nature of light

  • Light is an electromagnetic wave:

    • with a velocity given by c = 1/(00) = 3 x 108 m/s

  • In view of this, it is not surprising that the electric field component of the wave should interact with electrons electrostatically


  • Many of the electronic properties of materials, information on the bonding, material composition etc. was discovered using spectroscopy, the study of absorbed or emitted radiation

    • evidence for energy levels in atoms

    • evidence for energy bands and band-gaps

    • photoelectric effect

General description of absorption

  • Because of conservation of energy, we can say that I0 = IT + IA + IR

    • Io is the intensity (W/m2) of incident light and subscripts refer to transmitted, absorbed or reflected

  • Alternatively T + A + R = 1 where T, A, and R are fractions of the amount of incident light

    • T = IT/I0, etc.

  • So materials are broadly classed as

    • transparent:relatively little absorption and reflection

    • translucent:light scattered within the material (see right)

    • opaque:relatively little transmission


  • If the material is not perfectly transparent, the intensity decreases exponentially with distance

  • Consider a small thickness of material, x

  • The fall of intensity in x is I so I = -a.x.I

    • where  is the absorption coefficient (dimensions are m-1)

  • In the limit of x  0, we get

  • The solution of which is I = I0 exp(–x)

  • Taking “ln” of both sides, we have:

    • which is known as Lambert’s Law (he also has a unit of light intensity named for him)

  • Thus, if we can plot -ln(I) against x, we should find  from the gradient

  • Depending on the material and the wavelength, light can be absorbed by

    • nuclei – all materials

    • electrons – metals and small band-gap materials


  • How the solid absorbs the radiation depends on what it is!

  • Solids which bond ionically, show high absorption because ions of opposite charge move in opposite directions

    • in the same electric field

    • hence we get effectively twice the interaction between the light and the atoms

  • Generally, we would expect absorption mainly in the infrared

    • because these frequencies match the thermal vibrations of the atoms

  • If we think of our atom-on-springs model, there is a single resonance peak:

  • But things are more complex when the atoms are connected – phonons

    • recall transverse and longitudinal optical phonons




Electronic absorption

  • Absorption or emission due to excitation or relaxation of the electrons in the atoms


Molecular materials

  • Materials such as organic (carbon containing) solids or water consist of molecules which are relatively weakly connected to other molecules

  • Hence, the absorption spectrum is dominated by absorptions due to the molecules themselves

  • e.g. water molecule:


  • The spectrum of liquid water


  • Since the bonds have different “spring constants”, the frequencies of the modes are different

    • when the incident illumination is of a wavelength that excites one of these modes, the illumination is preferentially absorbed

  • This technique allows us to measure concentrations of different gas species in, for example, the atmosphere

    • by fitting spectra of known gases to the measured atmospheric spectra, we can figure out the quantities of each of the gases

Optical properties of metals

  • Recall that the energy diagram of a metal looks like:

    • EF is the energy below which, at 0K, all electron states are full and above which they are empty

    • this is the Fermi Energy

  • For T > 0, EF is the energy at which half of the available energy states are occupied

  • Semiconductors also have a Fermi level

    • for an intrinsic material EF is in the middle of the bandgap

    • nearer Ec for n-type; nearer Ev for p-type


T = 0K




  • This structure for metals means that almost any frequency of light can be absorbed

  • Since there is a very high concentration of electrons, practically all the light is absorbed within about 0.1µm of the surface

  • Metal films thinner than this will transmit light

    • e.g. gold coatings on space suit helmets

  • Penetration depths (I/I0 = 1/e) for some materials are:

    • water: 32 cm

    • glass: 29 cm

    • graphite: 0.6 µm

    • gold: 0.15µm

  • So what happens to the excited atoms in the surface layers of metal atoms?

    • they relax again, emitting a photon

  • The energy lost by the descending electron is the same as the one originally incident

  • So the metal reflects the light very well – about 95% for most metals

    • metals are both opaque and reflective

    • the remaining energy is usually lost as heat

  • In terms of electrostatics, the field of the radiation causes the free electrons to move and a moving charge emits electromagnetic radiation

    • hence the wave is re-emitted = reflected

  • The metal appears “silvery” since it acts as a perfect mirror

  • OK then, why are gold and copper not silvery?

    • because the band structure of a real metal is not always as simple as we have assumed

    • there can be some empty levels below EF and the energy re-emitted from these absorptions is not in the visible spectrum

  • Metals are more transparent to very high energy radiation (x- & - rays) when the inertia of the electrons themselves is the limiting factor

aluminum spectrum is relatively flat

gold reflects lots of red wavelengths



  • Reflection spectra for gold and aluminum are:






Electronic absorption in non-metals

  • Dielectrics and semiconductors behave essentially the same way, the only difference being in the size of the bandgap

  • We know that photons with energies greater than Eg will be absorbed by giving their energy to electron-hole pairs

    • which may or may not re-emit light when they relax

  • Hence, the absorption coefficients of various semiconductors look like:






  • Semiconductors can appear “metallic” if visible photons are all reflected (like Ge) but those with smaller Eg, such as CdS look coloured

    • yellow for CdS which absorbs 540nm and above

  • The above picture is good for pure materials but impurities can add extra absorption features

  • Impurity levels divide up the bandgap to allow transitions with energies less than Eg

  • Recombination can be either radiative (photon) or non-radiative (phonon) depending on the transition probabilities

  • Practical p-n diodes usually contain a small amount of impurity to help recombination because Si has a relatively low recombination “efficiency”

    • for the same reason that Si is inefficient at generating light

Refraction in non-metals

  • One of the most important optical properties of non-metallic materials is refraction

  • This refers to the bending of a light beam as it passes from one material into another

    • e.g. from air to glass

  • We define the index of refraction to be

    n = c/v

    • where c is the speed of light in a vacuum and v is the speed of light in the material (which is in general wavelength-dependent)

  • A familiar example is the prism where the different amounts of bending separates out the wavelengths

  • Refraction is also vital for other applications, such as:

    • optical fibres – keeps the light in

    • semiconductor laser – keeps the light in the amplifying cavity of the laser

  • Given that

    • where µ and µ0 (= µrµ0) are the permeability of the material and free space, respectively (a magnetic property)

    • and e and e0 (= ere0) are the permittivity of the material and free space, respectively (an electrostatic property)

  • We find that n = √(µrer) (≈ √er for many materials)

  • Since light is an electromagnetic wave, the connection with both the dielectric permittivity () and the magnetic permeability (µ) is not surprising

  • The index of refraction is therefore a consequence of electrical polarization, especially electronic polarization

  • Hence, the radiation loses energy to the electrons


  • Since E = hv/, and  doesn’t change, the velocity must be smaller in the material than in free space

    • since we lose E to the atoms, v must also decrease

  • Electronic polarization tends to be easier for larger atoms so n is higher in those materials

    • e.g. glass: n ~ 1.5

    • lead crystal: n ~ 2.1 (which makes glasses and chandeliers more sparkly!)

  • n can be anisotropic for crystals which have non-cubic lattices

Reflection in non-metals

  • Reflection occurs at the interface between two materials and is therefore related to index of refraction

  • Reflectivity, R = IR/I0, where the I’s are intensities

  • Assuming the light is normally incident to the interface:

    • where n1 and n2 are the indices for the two materials

  • Optical lenses are frequently coated with antireflection layers such as MgF2 which work by reducing the overall reflectivity

    • some lenses have multiple coatings for different wavelengths




  • So we have seen that reflection and absorption are dependent on wavelength

    • and transmission is what’s left over!

  • Thus the three components for a green glass are:

Callister Fig. 21.8


  • Small differences in composition can lead to large differences in appearance

  • For example, high-purity single-crystal Al2O3 is colourless

    • sapphire

  • If we add only 0.5 - 2.0% of Cr2O3 we find that the material looks red

    • ruby

  • The Cr substitutes for the Al and introduces impurity levels in the bandgap of the sapphire

  • These levels give strong absorptions at:

    • 400nm (green) and 600nm (blue)

    • leaving only red to be transmitted

  • The spectra for ruby and sapphire look like:

  • A similar technique is used to colour glasses or pottery glaze by adding impurities into the molten state:

    • Cu2+: blue-green, Cr3+: green

    • Co2+: blue-violet, Mn2+: yellow




  • Even after the light has entered the material, it might yet be reflected out again due to scattering inside the material

  • Even the transmitted light can lose information by being scattered internally

    • so a beam of light will spread out or an image will become blurred

  • In extreme cases, the material could become opaque due to excessive internal scattering

  • Scattering can come from obvious causes:

    • grain boundaries in poly-crystalline materials

    • fine pores in ceramics

    • different phases of materials

  • In highly pure materials, scattering still occurs and an important contribution comes from Rayleigh scattering

  • This is due to small, random differences in refractive index from place to place

  • In amorphous materials such as glass this is typically due to density or compositional differences in the random structure

  • In crystals, lattice defects, thermal motion of atoms etc. also give rise to Rayleigh scattering

  • Rayleigh scattering also causes the sky to be blue. The reason for this is the wavelength-dependence of Rayleigh scattering

    • scattering goes as l-4

    • so since lred ~ 2lblue blue light is scattered ~16 times more than red light

  • This mechanism is of great technological importance because it governs losses in optical fibres for communication

  • But before we get onto fibres, we will mention a couple more basic effects


  • Dispersion is a general name given to things which vary with wavelength

  • For example, the wavelength-dependence of the index of refraction is termed the dispersion of the index

  • Another important case arises because the speed of the wave depends on its wavelength

  • If a pulse of white light is transmitted through a material, different wavelengths arrive at the other end at different times

    • this is also called dispersion


  • Luminescence is the general term which describes the re-emission of previously absorbed radiative energy

  • Common types are photo- , electro-, and cathodo-luminescence, depending on whether the original incident radiation was

    • light of a different wavelength – e.g. fluorescent light

    • electric field – e.g. LED

    • electrons – e.g. electron gun in a cathode ray tube (CRT)

  • There is also chemo-luminescence due to chemical reactions which make the glowing rings seen at fairgrounds!










  • Luminescence is further divided into phosphorescence and fluorescence

  • Fluorescence and phosphorescence are distinguished by the electron transitions requiring no change or a change of spin, respectively

    • hence fluorescence is a faster process because no change of spin is required, around 10-5 – 10-6s

    • phosphorescence takes about 10-4 – 101s

  • Thus the energy diagram might be like:

  • If the energy levels are actually a range of energies, then:

  • So the light emitted by fluorescence is of longer wavelength than the incident light

    • since the energy is smaller

    • and phosphorescent light is typically longer wavelength than fluorescent light

phonon emission~10-12s per hop

fluorescence, ~10-5s

  • In fluorescent lights, the plasma generates UV light, and a fluorescent coating on the walls of the tube converts this to visible light

    • these lights have a visible flicker because (60Hz)-1 > 10-5s

  • Rather confusingly, materials that do this are generally called phosphors

  • To obtain a white light, a mixture of phosphors must be used, each fluorescing at a different wavelength

  • TV tubes usually use materials doped with different elements to give the colours:

    • ZnS doped with Cu+ gives green

    • ZnS:Ag gives blue

    • YVO4:Eu gives red

Optical fibres

  • Fibre-optic technology has revolutionised telecommunications owing to the speed of data transmission:

    • equivalent to >3 hrs of TV per second

    • 24,000 simultaneous phone calls

    • 0.1kg of fibre carries same information as 30,000kg of copper cable

  • Owing to attenuation in the cable, transmission is usually digital and the system requires several sections:





to optical





  • Obviously, the loss in the cable is important because is determines the maximum uninterrupted length of the fibre

  • We know that losses depend on the wavelength of the light and the purity of the material

    • recall the penetration depth for glass was ~30cm

  • In 1970, 1km of fibre attenuated 850nm light by a factor of 100

  • By 1979, 1km of fibre attenuated 1.2µm light by a factor of only 1.2

    • this light is infrared

  • Now, over 10km of optical fibre silica glass, the loss is the same as 25mm of ordinary window glass!

  • For such high-purity materials, Rayleigh scattering is the dominant loss mechanism:


  • The Rayleigh scattering results from minute local density variations which are present in the liquid glass due to Brownian motion and become frozen into the solid

  • The really clever part about optical fibres is that the light is guided around bends in the fibre

  • This is achieved by total internal reflection at the boundary of the fibre

  • Thus, the cross section of the fibre is designed as follows



  • The light is transmitted in the core and total internal reflection is made possible by the difference in the index of refraction between the cladding and the core

  • A simple approach is the “step-index” design:

  • The main problem with this design is that different light rays follow slightly different trajectories

  • So different light rays from an input pulse will take slightly different paths and will therefore reach the output at different times

  • Hence the input pulse is found to broaden during transmission:

  • This limits the data rate of digital communication








  • Such broadening is largely eliminated by using a “graded-index” design:

  • This is achieved by doping the silica with B2O3 or GeO2 parabolically as shown above

  • Now, waves which travel in the outer regions, do so in a lower refractive index material

    • and their velocity is higher (v = c/n)

  • Therefore, they travel both further and faster

    • as a result, they arrive at the output at almost the same time as the waves with shorter trajectories

  • Anything that might cause scattering in the core must be minimised

    • Cu, Fe, V are all reduced to parts per billion

    • H2O and OH concentrations also need to be very low

  • Variations in the diameter of the fibre also cause scattering

    • this variation is now <1µm over a length of 1km

  • To avoid dispersion of different wavelengths, lasers are used as the light sources

    • many data channels are possible using wavelength division multiplexing (WDM)

  • A convenient fact is that compound semiconductor lasers can emit IR light close to the 1.55µm wavelength where the fibre absorbs least

  • Referring back to the system diagram, it would be advantageous to integrate the encoder and transmitter

    • so the circuits and the light emitter can be integrated

  • This is why there is so much interest in getting light out of porous silicon or Si compounds

    • where thin strands of material exhibit quantum-mechanical effects which adjust the Si band structure to facilitate efficient light emission




  • LASER stands for Light Amplification by the Stimulated Emission of Radiation

  • The key word here is “stimulated”

  • All of the light emission we have mentioned so far is spontaneous

    • it happened just due to randomly occurring “natural” effects

  • Stimulated emission refers to electron transitions that are “encouraged” by the presence of other photons

  • Einstein showed that an incident photon with E ≥ Eg was equally likely to cause stimulated emission of light as to be absorbed


equally likelyas

  • The emitted light has the same energy and phase as the incident light (= coherent)

  • Under normal circumstances, there are few excited electrons and many in the ground-state,

    • so we get predominantly absorption

  • If we could arrange for more excited than non-excited electrons, then we would get mostly stimulated emission

  • Since we get more photons out than we put in, this is optical amplification

    • hence lAser

    • this system was first used to amplify microwaves for communications (maser)

  • Such a condition is called a population inversion

  • This stimulated emission is what gives the laser its coherent output

    • which is what makes it useful for holography, for example

  • Clearly, random spontaneous emission “wastes” electron transitions by giving incoherent output

    • so we minimise them by using transitions for which the spontaneous emissions are of low probability

    • so-called metastable states

  • The energy levels of a laser material therefore look like:

  • Ruby is a common laser material, which we saw was Al2O3 (sapphire) with Cr3+ impurities


  • So all we need to make a laser is to achieve

    • (i) a population inversion

    • (ii) enough photons to stimulate emission

  • The first is achieved by filling the metastable states with electrons generated by light from a xenon flash lamp

  • The second condition is achieved by confining the photons to travel back and forth along the rod of ruby using mirrored ends

    • next slide

  • The ruby laser has an output at 694.3 nm


  • In order to keep the coherent emission, we must ensure that the light which completes the round trip between the mirrors returns in phase with itself

  • Hence the distance between the mirrors should obey 2L = Nl

    • where N is an integer, l is the laser wavelength and L is the cavity length

  • Semiconductor lasers work in just the same way except that they achieve the population inversion electrically

    • by using a carefully designed band structure

  • Some laser characteristics are given in the following table:



  • We have looked at how the electronic structure of atoms and their bonding leads to varying optical behaviours in materials

  • In particular, properties such as absorption and emission are closely related to the electrons

  • Applications of this knowledge include

    • anti-reflective coatings for lenses

    • fibre-optic communications

    • lasers

Closing remarks

  • this first half of ENG2000 is an introduction to a subject area that is very subtle, and the course covers a huge range of subjects

  • As you gain more experience, the pieces of the jigsaw will fit better and better

  • So, if all the connections etc are not crystal clear right now, have patience!

  • For me, the success of the course is how often you say “oh yes, we saw that in ENG2000” !


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