Slide 1
This is the third class of our course. Here we will see the basics for glasses optical proprerties.
As usual you will find at our website the text related to the slides and also some related papers
and of course the quizz.
Slide 2
Lets warm-up with some pictures.
These are images from the south of Brazil. More specifically, images from Rio Grande do Sul.
Our beautiful state located in the south, making frontiers with Uruguay and Argentina.
There you will find the best barbecue in the world. You will also see people drinking Chimarrão
in the streets, at work, relaxing in parks, everytwhere. Chimarrão is the hot water infusion of
“erva mate” that “gauchos” (those born in Rio Grande do Sul are called “gauchos) drink all the
time.
It is very good for the health. “It is very good for everything” like they use to say.
It is also the State of beautiful landscapes, modern cities, good Universities and nice people.
I hope that you can visit Rio Grande do Sul when coming to Brazil.
Slide 3
So, let´s start our class on basic Optical Properties
Slide 4
Lets start by giving you another important link to those interested in glasses. At Lehigh
University in US you will find the “International Materials Institute for New Functionality in
Glass, IMI.
Text in the slide
The IMI is coordinated by our dear friend Professor Himanshu Jain from Lehigh University. You
can contact him directly of go the Institute website in order to get more information or even
apply for a scholarship to work with them.
They also offer on-line courses like this one and in fact you will see that some slides presented
here were adapted from a course given by Professor Pierre Lucas from Arizona State – US on
Glass properties.
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Slide 5
We will talk about optical properties of glasses. Optical properties obviously refer to the
consequences of the interaction of the electromagnetic radiation with materials.
You must remember that light propagates in space. Two perpendicular fields, the electric and
the magnetic, propagate at the well known light speed (109 kms/ hour!!). In silicate glasses
this velocity is about 30% lower.
In fact we will see that the ratio of the light speed in vacuum and in a given material defines
what we call refractive index of that material.
Slide 6
Optical waves propagate through insulators and do so with characteristics determined by the
dielectric constant and refractive index of the material and by any absorptive or scattering
process.
As a result, insulators have a broad window of transparency over some part of the optical
spectrum. In this transparency window the dielectric constant generally has a weak dispersion.
Therefore the material transmits light with very little loss.
Wavelengths outside the transparency region can induce strong polarization processes that
cause a dispersion in the dielectric constant or refractive index, with an associated increase in
propagation loss or absorption
Slide 7
Ordinary Glasses are highly transparent in the visible for three reasons:
1-Their polarization processes are either too slow or too fast to keep up with the oscillations in
electromagnectic fields associated with the visible optical wave; consequently the refractive
index is only weakly dependent on wavelength in that region of the electromagnetic spectrum.
2-Their constituents do not have electronic states that allow free-electron or bound-electron
transitions in the visible
3-Their microstructure is homogeneous and isotropic, and their refractive index is dependent
on neither spatial position nor direction
Slide 8
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If we look at polarization processes, we see that insulators can undergo several major changes
in polarization over the electromagnetic spectrum. All such changes will affect the dispersion
in refractive index and cause absorption. These changes consist of polarization processes
associated with the following structural excitations:
Orientational or dipolar polarization:
If polar molecules are present in the insulator, thermal agitation keeps the dipoles randomly
oriented. Applied electric fields will align the dipoles. This alignment takes a certain time p,
characteristic of the orientational motion of the polar molecule.
Ionic polarization:
The core electrons around each ion, and valence electrons involved in bonding, are polarizable
through a slight shift in the electron cloud and the ionic core, leading to the formation of
induced dipoles. The characteristic time for distortion of the electronic cloud i is much shorter
than the orientational polarization time p.
Electronic polarization:
Valence electrons can be photoexcited out of their bonding states, providing free electrons
that contribute to the polarization as in metals. This process is very fast and its characteristic
time e is much shorter than i or p
In between these regions of resonance, the polarization processes are either too slow or too
fast for the incident electromagnetic wave.
In the case where the polarization processes are too slow, the molecules or electrons do not
have time to respond to the applied oscillating field, so they cannot extract energy from it.
In the case where the polarization processes are too fast, the ions or electrons react
immediately to the change in direction of the applied oscillating field and remain in phase with
it. Again this does not lead to any exchange of energy (or absorption).
Only when the period of the wave matches the reaction time of the polarization process there
is an exchange of energy. In this case, as the field is applied, the dipoles begin to reorient;
however, by the time they have aligned themselves with the field, it has changed direction.
This maximizes the phase difference between the applied field and the induced polarization,
leading to maximum energy extraction from the wave.
Slide 9
The refractive index and absorption coefficients are affected in a way similar to that for the
induced polarization as shown in the figure.
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“Normal dispersion” corresponds to a decrease in refractive index with increasing wavelength
(decreasing frequency).
“Anomalous dispersion” refers to the opposite behavior.
In other words, in the normal-dispersion regime, the higher-frequency (blue) light will travel
more slowly (and thus have a larger refractive index) than the lower-frequency (red) light.
We will come back to refraction basics in a moment.
Slide 10
A monocrystal will have optical properties defined mainly by the optical constants. Optical
quality is good. But they are difficult to prepare.
Polycrystalline insulators have microstructure that can have additional effects on transparency.
If multiple phases are present, or in the presence of grain boundaries within a sngle phase,
strong scattering processes may occur from any region with a sharp change in refractive index,
and this scattering makes the insulator opaque.
(Another source of opacity in insulators can come from dopants that absorb light through
bound-electron excitation. Transition-metal and lanthanides oxides are important examples of
such absorbing species, ant they add color to insulators)
Ordinary glasses are transparent in the visible region as already mentioned
The interesting thing concerning glasses is the freedom of chemical compositions. We use to
say, as a joke, that you can add all the periodic table to your glass!!
In fact we can tune, by the chemical composition, in which region of the spectrum they will be
transparent.
Moreover glasses are also much easier to prepare (in most cases!!)
Slide 11
Light incident upon an insulator undergoes several processes besides the dispersion during
propagation already mentioned. Still related to the refractive index is the property of
birefringence which is the variation of the refractive index between different polarization
directions (glasses as isotropic media do not present that property)
Considering a glass one can observe:
-Reflection from any boundary that is associated with a change in refractive index;
-Absorption;
-Scattering (absorption and elastic re-emission in random directions)
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The transmitted beam will therefore be affected by all these mentioned processes.
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Slide 17
Still with our “Basics” reflection and refraction. As you know our indians living in the Brazilian
forests know very well the basics of optics.
They know very well that the fish (“peixe” in the figure) is not where it looks to be, thanks to
the Snell-Descartes Law
(French say “Descartes Law”. British say “Snell Law”. Let´s be peaceful and please both French
and British, and call the law “Snell-Descartes Law”).
This law relates the incidence angle  and refractive index n
Slide 18
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Slide 21
Have you ever heard about “Metamaterials”?
Well, things begin to be a little bit strange when the refractive index is negative!
Yes!! it can be negative. Of course this is not related to natural materials.
But the material can be structured in a way that the effective refractive index can be negative.
Our indians would face problems fishing in a medium with such a refractive index!!
In this review available at the school website you will have a taste on this interesting and hot
subject.
We will come back to it later!!
Slide 22
We have already commented here about the dispersion of the refractive index with the
wavelength.
The dispersion is in fact a very important property for someone interested in materials optical
properties.
The figure shows typical dispersion curves for optical glasses of high, medium and low index.
Slide 23
An universal parameter proposed in this sense is the “Abbe Number” defined here.
The Abbe number is also frequently referred to as the V-value, the -value or the reciprocal
dispersive power. One can see that the lower the Abbe number the greater the dispersive
power, that is the greater the chromatic dispersion for a lens for example.
Various families of glasses fall within well-defined ranges of Abbe numbers and refractive
index as shown in the figures
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Slide 24
This is the same plot where the classification of different glasses is shown
If V<50 we call the glass a Flint Glass. If V>50 the glass will be a crown glass
Glasses can then be categorised by their composition and position on the diagram.
This can be a letter-number code, as used in the Schott Glass catalogue
and shown in this figure
Abbe numbers are used to calculate the necessary focal lengths of achromatic
doublet lenses to minimize chromatic aberration.
Slide 25
In practice the dispersion can be fitted to the Sellmeier equation if some values of refractive
index are known for some wavelngths. The parameters A, B, and C are then treated as
adjustables.
While written for one-component glasses the equation is normally used for multi-component
glass compositions.
Slide 26
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Slide 28
This is the prism-coupling method.
A prism is coupled to the sample surface.
Laser light incident at the prism surface at an angle corresponding to angles lower than the
critical angle will lead to total reflection of the light and maximum light intensity at the
detector.
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By changing the angle of incidence ot the laser, when the critical angle is reached light will
enter the sample and therefore the intensity of the light at the detector falls down.
Knowing the refractive index of the prism and by using the Snell-Descartes law the refractive
index of the sample can be determined with accuracy comparable with that of the minimum
deviation method
The picture shows the equipment we have in our lab with 3 different wavelangths available.
Slide 29
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Slide 31
Description of the measurement in an elipsometer
Slide 32
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Slide 35
This figure shows a typical absorption spectrum of a silicate based glass.
It shows the absorption coefficient as a funtion of the energy and wavelngth.
In fact all dieletric materials will display a spectrum with this V-shape.
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The first thing to note is the huge variation of the absorption coefficient. 10 orders of
magnitude!!
You also see that the visible range is a small range of the x-axis.
The spectrum run from the UV to the infrared.
The absorption edges at both sides are governed by fundamental processes related to the
material chemical composition.
In the UV side the increase in the absorption is due to electronic transitions related to the
energy difference between valence and conduction bands. The energy-gap is usually obtained
from the edge position.
At the Infrared side the increase in the absorption is due to multiphonon transitions. This is the
language of physics. You remember that for periodic structures (crystals) phonons with energy
of vibrations motions propagate in the material. In glasses, lacking long-distance order, we use
to say that phonons cannot propagate. They are localized!!
I prefer the chemistry language in this case. “Localized phonons” characterize “molecular
groups”. The vibrational modes are molecular ones.
The “multiphonon process” refers then to harmonics of fundamental vibrational modes.
Therefore the exact position of the minimum in absorption will be dictated by the chemical
nature of the glass.
Silica is transparent in the visible as everybody knowns.
However the minimum in absorption is not in the visible range. The minimum in absorption for
silica glass occurs around 1.5 microns. That is therefore the wavelength of choice for telecom
signals.
Slide 36
This is the “bottom” of the spectrum
Is shows the minimum occuring at 1.54 microns and indicated as the 3rd telecom window
where as we said before the telecom signal run.
The spectrum also shows the 2nd and the 1st windows use before. 1st, 2nd na 3rd windows
tell us the historical evolution of telecom signals.
You can also see in the figure the attenuation units used by telecom and fibers people.
Decibel or dB is the unit used to report losses. It is related to the our well known chemical
“Absorbance”.
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The number of decibels is tem times the logarithim to base 10 of the ratio of the two power
quantities.
You can also observe the peak occuring at around 1.49 m for silica fibers. It is in fact related
to OH- groups occuring (and not desirable) in silica. 1 ppm of OH- in silica fibers lead to 4dB/km
at this wavelength.
New methods of fabrication of fibers claim to remove this residual OH- groups!!
Coming back to the spectrum, you see that for 1cm of optical path absorbance of silica glasses
in the visible range is 5.10-5. A normal spectrophotometer that we use in our labs is not able to
measure such a low absorbance. Our spectrophotometer here in Araraquara is able to read
values of absorbance of 10-4.
And in addition, as we already said, the visible is not the region of minimum absorbance. In the
infrared, conidering 1 cm optical path the absorbance of a silica glass will be 10-7.
For 1 cm optical path this is really nothing.
But consider an optical fiber. For 1km of optical path this means 96% of the initial light
intenstiy arriving at the end of the fiber!! You see that the signal would experience na
important attenuation for some kilometers.
Slide 37
This brings us to the first question of the quizz number 3
Araraquara is around 270 kms from the the city of São Paulo.
If 1W of power (at 1.5microns) is injected in a fiber here in Araraquara, what is the power that
will arrive in São Paulo? (considere for this calculation the attenuation value of 0.2 db/km)
To calculate this value you will just take into account the intrinsic absorption for silica which is
0.2 dB/km. Of course in the real world the attenuation is composed of different terms such as
scattering loss, bending loss, radiation loss, leaky modes... We will come back to this, talking
about optical fibers
Slide 38
The V-shape spectra can be calculated for different materials, by taking into account the
Rayleigh scattering losses at the high energy side and the multiphonon losses at the lower
energy side. This figure, taken from wikipedia, shows that kind of calculation for the fluoride
based ZBLAN glass compared to real values. The figure also shows the shift when ZBLAN and
silica are compared.
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Slide 39
This figure shows the same kind of spectrum for different materials.
Slide 40
The transmission window for different glasses will therefore be determined by the chemical
nature of the glass
In this figure you have the transmission windows for silica and germanium selenide glasses.
You see that germanium selenide glass is transparent above 10 microns suggesting application
in infrared devices such as night vision devices.
Slide 41
The transmission window spectrum is in fact a composition of spectra obtained in two
different equipments. Spectrophotometers are usually operational from the UV to the near
infrared (NIR). FTIR- Fourier transform infrared spectrometers opperate in in the infrared.
Slide 42
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Slide 43
In the infrared, interferometers are used instead of dispersion monochromators. A lot of
sensitivity is obtained by using this.
This is the interferometer. It consists of two mirrors and one beam-splitter. The IR light is sent,
half to a fixed mirror, and half to a moving mirror.
The light resulting from the light coming from both mirrors is sent to the sample.
The interference pattern obtained with the different positions of the mirror gives the
interferogram. The interferogram is modified by the sample and the resulting interferogram
will have all the information concerning the vibrational modes of the sample.
FT analysis of the interferogram will give us the spectrum in some seconds.
Slide 44
As we have already mentioned at the high energy side of the transmission window absorption
is due to electronic transitions. Inter-band transitions.
You remember the description of the electronic structure of a solid in terms of “bands”.
Taking again the chemistry language a band is obtained gathering together molecular orbitals.
A sodium crystal may be constructed from isolated sodium atoms.
Two sodium atoms will lead to a diatomic molecule with the valence two s electrons occupying
two molecular orbitals, one lower energy bonding molecular orbital and one higher energy
antibonding molecular orbital.
Increasing the number of atoms of that molecule the number of molecular orbitals will also
increase. The huge number of molecular orbitals will form a “band”. In this case for the sodium
atoms, a “s-band”.
The same holds for polyatomic molecules with bands of different energies being formed.
Forbidden energy regions for electrons will define the “gaps”.
The energy difference between the lower energy band, the valence band, and the first excited
one, the conduction band, will define what we call the energy gap. The size of the gap defines
insulators, semiconducting and conducting materials.
This is the model.
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Slide 45
The same model can be used to qualitatively explain the so-called “quantum size effect”
known for semiconductor nanoparticles or “quantum-dots”.
In this case we go from the solid, with its valence and conduction bands, to the molecule, with
its HOMO (Highest occupied molecular orbital) and LUMO (Lowest unoccupied molecular
orbital). Here again we gather together the Physics and Chemistry languages.
In this diagram you can observe the increase in the band-gap.
CdS powders for example are orange in color for micron sized grains. Decreasing the size of the
crystals one observes an yellow color for nanometer sized crystals.
Concerning “materials” the interesting point here is that “quantum-dots” behave as surface
matter since most of the atoms are at the surface. This table gives you an idea of that feature.
A 2.1 nm crystal of gold atoms will display 63% of the atoms at the surface.
This nanometric size will lead to novel chemical and optical properties that are in fact at the
heart of what we call “nanotechnology”.
Slide 46
These are some absorption and emission spectra of CdSe nanocrystals. The ‘quantum-size”
effect leads to shifts in spectra as a function of the crystals size.
Slide 47
But let´s come back to the transparency window of solids.
Sodium chloride is completely transparent in the visible. The energy gap is of 8.5 eV or 146 nm.
Silicon is black. It absorbs visible light. The energy gap is of 1.1 eV or 1128 nm.
It is a semiconducting material, the base for our photovoltaic cells.
Slide 48
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These are the absorption spectra for these two materials.
The cut off wavelength is the equivalent to the energy band-gap.
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Slide 49
At this table you will find the value of the energy gap for some materials.
It shows also the exciton Bohr diameter, that defines the smallest structure that will exhibit
bulk behavior.
Slide 50
These are the absorption spectra for some glasses. You see that materials displaying colors
spanning the visible range can be prepared.
Slide 51
At the low energy side the so-called multiphonon edge will define the transparency window.
The simplest model for a bond is the one that considers atoms as mass spheres and chemical
bonds as coils. The heavier the constituints the lower will be the energy of vibrational modes
whose harmonics will define the multiphonon edge.
In this figure you see the mukltiphonon edge for silica, fluorides and chalcogenide glasses.
Slide 52
The multiphonon edge is not the only property that will depend on the vibrational modes
energy.
In this figure we have the raman spectrum obtained for a fluorindate glass. The harmonics of
the highest energy vibrational mode are the ones that will define the absorption edge as we
have already said.
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The other important consequence, that we will explore in next sections, is the depopulation or
desactivation of electronic excited states. Vibrational modes will define the non-radiative
transition rates between excited states in lanthanide ions.
The lowest the energy of the vibrational modes, the lowest the non-radiative decays will be.
Slide 53
Glasses transparent in the infrared may have interesting applications.
For example in thermal imaging.
As we have seen chalcogenide glasses are transparent in the region around 10 microns. This is
the spectral region of the light our bodies emit due to the temperature.
You can check at the internet how these systems work.
Slide 54
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Slide 55
This is another example of application that you can find in the magazine Laser focus World
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Slide 56
Just to end this class let me give you some news about the footbal world.
Brazil has won the Conferations Cup.
We won the match with Spain. 3x0. The champion is back!!
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