This document discusses the optical properties of solids. It begins by defining optical properties as light-matter interactions like reflection, absorption, transmission and refraction. Optical processes are classified into reflection, propagation and transmission. Key optical parameters discussed include refractive index, absorption coefficient, dielectric constant, and complex refractive index. Beer's law relating light intensity and absorption is explained. The properties of insulators, semiconductors, glasses and metals are then summarized. Insulators and semiconductors are highly transmitting in visible ranges with absorption in UV and IR. Glasses like fused silica are also highly transmitting but with shorter ranges. Metals are highly reflective across most frequencies.

1. 1

2. OPTICAL PROPERTIES OF SOLIDS
Presented BY
IMRAN AHMAD
Center of Excellence in Solid State Physics University Of The Punjab Lahore
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3. contents
What are optical properties
 Classification of optical
process
Optical parameters
Beer’s law
Absorption
Refraction
Scattering
Optical properties of insulators
Optical properties of
semiconductors
Optical properties of glasses
Optical properties of metals

4. What are optical properties
 Light matter interaction

 Light interact with matter in many ways
 There are large number of optical properties
but the basic properties are reflection,
absorption, transmission, refraction etc.
 As optical properties are associated with light
therefore we must know the basic knowledge
about light
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5. light
Light is an electromagnetic wave
 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
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6. Classification of optical process
The wide ranging optical properties
observed in solid state physics can be
classified into small number of general
phenomenon the simplest group namely
Reflection
Propagation
transmission
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7. Optical parameters
i. Refractive index ( n=c/v)
ii. Absorption coefficient
iii. Dielectric constant
iv. Transmission coefficient
v. Reflection coefficient
vi. Extinction coefficient
vii. Complex refractive index
viii.Optical density
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8. Refractive index
Refractive index is define as the ratio speed of light in free space to speed
of light in medium
Formula is given as
 𝒏 =
𝒄
𝒗
Where c=speed of light in free space which is 3 x 108 m/s
 v= speed of light in medium under study
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9. Absorption coefficient
Describe the intensity attenuation of light passing
through the material
Relation with extinction coefficient
𝜶 =
𝟒𝝅𝜿
𝝀
𝛼 is the absorption coefficient unit 𝑐𝑚−1
𝜅 is the extinction coefficient
𝜆 is wavelength of light used in nm
Depends on the material and wavelength of light
used
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10. Dielectric constant
Also called relative permittivity is the ratio of the permittivity
Of substance to the permittivity of space or vacuum
Expressed as 𝝐𝒓 =
𝝐
𝝐𝟎
𝜖0=8.84×10−12 𝑐2
(𝑁𝑚)2
 𝜖𝑟 is the relative dielectric constant
 relation between 𝜖𝑟 and n
Using standard results derived from Maxwell equations
n = ϵr
Important parameter to understand propagation of the light
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11. Transmission coefficient
Ratio of transmitted power to the incident power
T =
P(transmitted)
P(incident)
In optics transmission is the property of substance to permit the
passage of light
Conservation of energy
R+T=1
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12. Reflection coefficient
Reflection at the surfaces is describe by the
coefficient of reflectivity
Ratio of reflected power to the power of incident
R =
P(reflected)
P(incident)
It is closely related to the transmission coefficient
R = 1 - T
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13. Extinction coefficient
Extinction coefficient refers to several different measure of the
absorption of light in the medium
It is related with the absorption coefficient as
𝜶 =
𝟒𝝅𝜿
𝝀
𝛼 is the absorption coefficient unit 𝑐𝑚−1
𝜅 is the extinction coefficient
𝜆 is wavelength of light used in nm
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14. Complex refractive index
The absorption and refraction of a medium described
 formula of complex refractive index is given by
𝑛~
= n + i 𝜿
n is the refractive index it indicate phase velocity
𝜿 𝒊𝒔 𝒕𝒉𝒆 𝒆𝒙𝒕𝒊𝒏𝒄𝒕𝒊𝒐𝒏 𝒄𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕 𝒊𝒏𝒅𝒊𝒄𝒂𝒕𝒆 𝒂𝒎𝒐𝒖𝒏𝒕 𝒐𝒇 𝒂𝒕𝒕𝒆𝒏𝒖𝒂𝒕𝒊𝒐𝒏
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15. Important result
Relation between extinction coefficient and dielectric
constant is given by
𝜿 =
𝟏
𝟐
[−𝜺𝟏 ± 𝜺𝟏𝟐 + 𝜺𝟐𝟐 ]1/2
Similarly relation between refractive index and dielectric
constant is given by
𝐧 =
𝟏
𝟐
[𝜺𝟏 ± 𝜺𝟏𝟐 + 𝜺𝟐𝟐 ]1/2
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16. When light propagate through material medium the intensity of
the light decreases this is known as beer’s law
If the beam is propagating in z-direction and intensity at
position z is I(Z) then decrease in intensity in an increment slice
of thickness dz is given by
𝒅𝑰 = −𝒂𝒅𝒛 × 𝑰
𝒅𝑰
𝑰(𝒛)
= −𝒂𝒅𝒛
𝑰𝟎
𝑰(𝒛) 𝒅𝑰
𝑰(𝒛)
= − 𝟎
𝒍
𝒂𝒅𝒛
𝐥𝐧[
𝑰(𝒛)
𝑰𝟎
] = −𝒂𝒍
Beer’s law
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17. Beer’s law
𝑰 𝒛 = 𝑰𝟎 𝒆−𝒂𝒍
Where l= length of sample
From there we can define the coefficient of
tramission which is given by the following formula
𝑰
𝑰𝟎
=T= 𝒆−𝒂𝒍
Where T is the coefficient of transmission
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18. Refraction
Refraction causes the light waves to propagate with
a smaller velocity than in free space
This reduction of velocity leads to the bending of
light rays at interfaces describe by Snell's law of
refraction
Refraction itself does not effect the intensity of the
light wave as it propagate
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19. Absorption
Absorption occur during the propagation
if frequency of the light is resonant with
the transition frequency of the atoms in
the medium
Beam will be attenuated as it progresses
Unabsorbed light will be transmitted
Selective absorption cause the coloration
in the material
For example rubies are red
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20. scattering
Phenomenon in which the light changes direction and possibly also changes its frequency
after interacting with medium
Total number of photons remains unchanged but number of photons going forward
direction decreases
Types of scattering
Elastic scattering
If the frequency of the scatter wave will remain unchanged then it is said to be elastic
scattering
Inelastic scattering
If the frequency of the scatter wave will change then it is said to be inelastic scattering
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21. scattering
Condition for scattering
the condition for the scattering is that target must have the thickness
smaller than the wavelength of incoming light
Cause of scattering
The presence of defects and impurities in the material are the cause of
scattering
Scattering may be defined as the phenomenon in which the incident light
having frequency smaller than the target interact with target light scatter
in all direction having frequency less than the incident frequency
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22. Reyleigh scattering
If the size of the scattering center is much smaller then the wavelength
of light then it is called reyleigh scattering
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24. Types of optical materials
Optical materials can loosely be classified into the following categories
Crystalline insulators &semiconductors
Glasses
Metals

25. Crystalline insulator &semiconductors
Transmission spectra of crystalline
sapphire( Al2 O3 )
it shows the main features observed
in all insulators
High transmission (0.2-6𝝁𝒎)
Dip in transmission in IR (3𝝁𝒎) and
sharp drop in transmission (𝜆>6𝝁𝒎)
caused by vibrational absorption
Transmission drops sharply in UV
region

26. Crystalline insulator &semiconductors
Insulators do strongly absorb in UV and IR region
but it is hidden from human eye
The transparent region between UV and IR is
useful to making optical windows and lenses
Transparency range and refractive index of some
materials is shown in the table

27. The optical properties of semiconductors
Similar to insulator except electronic and vibrational
transition occur at longer wavelengths
Transparency range lies outside the visible region
Dark metallic appearance
Light emission

28. The optical properties of semiconductors
Table shows
transparency range of
different semiconductors

29. Glasses
Extremely important optical material
Fused silica
Pure fused silica is an insulator and shows all the properties of the
insulator
Transparent in the visible region and absorb in the ultra violet due to
electronic transition of the sio2 molecules and in IR due to vibrational
absorption
Transparency range goes from around 200 nm in UV to beyond
2000nm in IR
Stained glass and colour filters

30. Glasses
Refractive index of synthetic fused
silica versus wavelength

31. Glasses
Composition, refractive index and ultraviolet transmission of common
glasses

32. Metals
The chacteristic optical feature of metal is
that they are shiny
High reflection coefficient
Fig shows reflectivity of silver from IR to
UV region
Reflection is 100% in IR region and 80% in
whole visible region the drop sharply
General behaviour is observed in all metals
Strongly reflection for all frequencies below
a characteristic cutt of frequencies called
plasma frequency
Metal reflect in IR and Visible and transmit