2. ENG2000: R.I. Hornsey Optic: 2
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
3. ENG2000: R.I. Hornsey Optic: 3
Nature of light
• Light is an electromagnetic wave:
with a velocity given by c = 1/(00) = 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
4. ENG2000: R.I. Hornsey Optic: 4
• 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
5. ENG2000: R.I. Hornsey Optic: 5
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
http://www.tekano.pwp.blueyonder.co.uk/tekano/translucent.jpg
6. ENG2000: R.I. Hornsey Optic: 6
• 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 a is the absorption coefficient (dimensions are m-1)
• In the limit of x 0, we get
• The solution of which is I = I0 exp(–ax)
• 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)
dI
dx
aI
ax ln
I
I0
7. ENG2000: R.I. Hornsey Optic: 7
• Thus, if we can plot -ln(I) against x, we should
find a 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
9. ENG2000: R.I. Hornsey Optic: 9
• 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
f0
f
absorption
10. ENG2000: R.I. Hornsey Optic: 10
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/hydrogen.gif
11. ENG2000: R.I. Hornsey Optic: 11
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
14. ENG2000: R.I. Hornsey Optic: 14
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
full
levels
empty
levels
T = 0K
EF
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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:
blue red
gold reflects lots of
red wavelengths
aluminum
spectrum is
relatively flat
http://www.thermo.com/eThermo/CMA/Images/Various/109Image_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
EC
EV
EG
hole
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• Hence, the absorption coefficients of various
semiconductors look like:
21. ENG2000: R.I. Hornsey Optic: 21
• 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
EC
EV
phonon
hf1
hf2
22. ENG2000: R.I. Hornsey Optic: 22
• 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
24. ENG2000: R.I. Hornsey Optic: 24
• 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 and 0 (= r0) are the permittivity of the material and
free space, respectively (an electrostatic property)
• We find that n = √(µrr) (≈ √r for many materials)
v
1
and c
1
00
25. ENG2000: R.I. Hornsey Optic: 25
• 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
+
–
26. ENG2000: R.I. Hornsey Optic: 26
• 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
27. ENG2000: R.I. Hornsey Optic: 27
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
R
n2 n1
n2 n1
2
n1 n2
28. ENG2000: R.I. Hornsey Optic: 28
Spectra
• 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
29. ENG2000: R.I. Hornsey Optic: 29
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
30. ENG2000: R.I. Hornsey Optic: 30
• 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/photopumping.gif
31. ENG2000: R.I. Hornsey Optic: 31
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
32. ENG2000: R.I. Hornsey Optic: 32
• 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
33. ENG2000: R.I. Hornsey Optic: 33
• Rayleigh scattering also causes the sky to be
blue. The reason for this is the wavelength-
dependence of Rayleigh scattering
scattering goes as -4
so since red ~ 2blue 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
35. ENG2000: R.I. Hornsey Optic: 35
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
36. ENG2000: R.I. Hornsey Optic: 36
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!
37. ENG2000: R.I. Hornsey Optic: 37
• 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:
E2
E1
E3
phosp.
phosp.
fluor.
incident
flip
flip
38. ENG2000: R.I. Hornsey Optic: 38
• 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
39. • 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
40. ENG2000: R.I. Hornsey Optic: 40
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:
encoder conversion
to optical
repeater detection decoder
optical optical
http://www.ngflscotland.gov.uk/connected/connected5/images/fibreoptic.jpg
41. ENG2000: R.I. Hornsey Optic: 41
• 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!
42. ENG2000: R.I. Hornsey Optic: 42
• For such high-purity materials, Rayleigh
scattering is the dominant loss mechanism:
water
43. ENG2000: R.I. Hornsey Optic: 43
• 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
44. ENG2000: R.I. Hornsey Optic: 44
• Thus, the cross section of the fibre is designed as
follows
http://www.datacottage.com/nch/images/fibreconstruct.gif
45. ENG2000: R.I. Hornsey Optic: 45
• 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
n
46. ENG2000: R.I. Hornsey Optic: 46
• 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
in out
signal
t t
signal
47. ENG2000: R.I. Hornsey Optic: 47
• 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)
n
48. ENG2000: R.I. Hornsey Optic: 48
• 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)
49. ENG2000: R.I. Hornsey Optic: 49
• 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
51. ENG2000: R.I. Hornsey Optic: 51
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
52. ENG2000: R.I. Hornsey Optic: 52
• 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
equally likely
as
53. ENG2000: R.I. Hornsey Optic: 53
• 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
54. ENG2000: R.I. Hornsey Optic: 54
• 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
55. ENG2000: R.I. Hornsey Optic: 55
• 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
57. ENG2000: R.I. Hornsey Optic: 57
• 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 = N
where N is an integer, 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
58. ENG2000: R.I. Hornsey Optic: 58
• Some laser characteristics are given in the
following table:
Callister
59. ENG2000: R.I. Hornsey Optic: 59
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
60. ENG2000: R.I. Hornsey Optic: 60
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” !