ENG2000 Chapter 10 Optical Properties of Materials

ENG2000: R.I. Hornsey Optic: 1

ENG2000 Chapter 10Optical 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

• 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/(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


• 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

http://www.tekano.pwp.blueyonder.co.uk/tekano/translucent.jpg


• 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 = -.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)

€

dIdx

=−αI

€

αx=−ln II0

⎛ ⎝ ⎜

⎞ ⎠ ⎟


• 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


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


• 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


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


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


• The spectrum of liquid water

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


• 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

fulllevels

emptylevels

T = 0K

EF


• 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


• 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


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


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

. .

0 .2 0 .4 0 .6 0 .8 1 .2 1 .4 1 .6 1 .8

W vlnth ( )

In 0 .5 3G 0 .4 7As

G

S i

In 0 .7G 0 .3As0 .64P0 .3 6

InP

G As

-S i:H

123450 .9 0 .8 0 .7

1 0 3

1 0 4

1 0 5

1 0 6

1 0 7

1 0 8

Photon nry (V )

1 .0

Fi. 9.19: Absorption cofficint () vs. wvlnth (l) forvrious s iconuctors (Dt slctivly collct n co binfro vrious sourcs.)From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca


• 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

phononhf1

hf2


• 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 ben = 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 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= 1εμ

and c= 1ε0μ0


• 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/l, and l 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

€

R= n2 −n1n2 +n1

⎛ ⎝ ⎜

⎞ ⎠ ⎟ 2

n1 n2


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


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


• 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.jpghttp://home.achilles.net/~jtalbot/glossary/photopumping.gif


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


• 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


S c a t t e r e d w a v e s

I n c i d e n t w a v eT h r o u g h w a v e

A d i e l e c t r i c p a r t i c l e s m a l l e r t h a n w a v e l e n g t h

Fig. 9.21: Rayleigh scattering involves the polarization of a smalldielectric particle or a region that is much smaller than the lightwavelength. The field forces dipole oscillations in the particle (bypolarizing it) which leads to the emission of EM waves in "many"directions so that a portion of the light energy is directed away from theincident beam.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca


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


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!


• 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


• 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:

encoder conversionto optical

repeater detection decoder

optical optical

http://www.ngflscotland.gov.uk/connected/connected5/images/fibreoptic.jpg


• 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!


.

0 .0 5

0 .1

0 .5

1 .0

5

1 0

0 .6 0 .8 1 .0 1 .2 1 .4 1 .6 1 .8 2 .0

L a t t i c e

a b s o r p t i o n

R a y l e i g h

s c a t t e r i n g

W a v e l e n g t h ( µ m )

O H-a b s o r p t i o n

p e a k s

1 3 1 0 n m

1 5 5 0 n m

Fig. 9.22: Illustration of a typical attenuation vs. wavelength characteristicsof a silica based optical fiber. There are two communications channels at1310 nm and 1550 nm.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

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

water


• 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

http://www.datacottage.com/nch/images/fibreconstruct.gif


• 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


• 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 communicationin out

signal

t t

signal


• 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


• 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


http://porous.silicon.online.fr/images/poreux.jpg

http://ghuth.com/Porous%20silicon.jpg


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


• 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 likelyas


• 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

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


• 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


http

://w

ww

.repa

irfaq

.org

/sam

/lase

rop.

gif


• 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:

Callister


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


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” !


THE END

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ENG2000 Chapter 10 Optical Properties of Materials

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