ENG2000 Chapter 10 Optical Properties of Materials

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ENG2000 Chapter 10Optical Properties of Materials
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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
• 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

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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

http//www.astronomynotes.com/light/emanim.gif
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• 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

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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
• transparentrelatively little absorption and
  reflection
• translucentlight scattered within the material
  (see right)
• opaquerelatively little transmission

http//www.tekano.pwp.blueyonder.co.uk/tekano/tran
slucent.jpg
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• 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 Lamberts Law (he also has a
  unit of light intensity named for him)

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• 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

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ATOMIC ABSORPTION

• 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

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• 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

absorption
f
f0
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Electronic absorption

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

http//www.nhn.ou.edu/kieran/reuhome/vizqm/figs/h
ydrogen.gif
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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

http//www.sbu.ac.uk/water/images/molecul5.jpg
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• The spectrum of liquid water

http//www.sbu.ac.uk/water/images/watopt.jpg
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• 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

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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 gt 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

emptylevels
T 0K
EF
full levels
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• 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

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• 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

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• 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

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• Reflection spectra for gold and aluminum are

http//www.thermo.com/eThermo/CMA/Images/Various/1
09Image_12275.gif
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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

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• Hence, the absorption coefficients of various
  semiconductors look like

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• 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

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• 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

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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

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• 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 v(µrer) ( ver for many
  materials)

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• 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

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• Since E hv/?, and ? doesnt 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

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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 Is 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

n2
n1
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Spectra

• So we have seen that reflection and absorption
  are dependent on wavelength
• and transmission is whats left over!
• Thus the three components for a green glass are

Callister Fig. 21.8
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Colours

• 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

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• 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

http//www.valleydesign.com/images/sapp.jpg
http//home.achilles.net/jtalbot/glossary/photopu
mping.gif
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Translucency

• 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

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• 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

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• 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

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Dispersion

• 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

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Luminescence

• 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!

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• 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

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• 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 emission10-12s per hop
fluorescence, 10-5s
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• 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 gt 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
• ZnSAg gives blue
• YVO4Eu gives red

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Optical fibres

• Fibre-optic technology has revolutionised
  telecommunications owing to the speed of data
  transmission
• equivalent to gt3 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

optical
optical
encoder
conversion to optical
repeater
detection
decoder
http//www.ngflscotland.gov.uk/connected/connected
5/images/fibreoptic.jpg
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• 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!

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

water
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• 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

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

http//www.datacottage.com/nch/images/fibreconstru
ct.gif
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• 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

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• 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

signal
signal
t
t
in
out
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• 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)

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• 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 lt1µm 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)

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• 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

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http//ghuth.com/Porous20silicon.jpg
http//porous.silicon.online.fr/images/poreux.jpg
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Lasers

• 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

http//www.007sdomain.com/gf_laser.jpg
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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

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• 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

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• 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

http//kottan-labs.bgsu.edu/teaching/workshop2001/
chapter4a_files/image022.gif
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• 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

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http//www.repairfaq.org/sam/laserop.gif
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• 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

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• Some laser characteristics are given in the
  following table

Callister
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Summary

• 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

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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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THE END