Download Chapter 21

Optical Properties
ISSUES TO ADDRESS...
• What phenomena occur when light is shined on a material?
• What determines the characteristic colors of materials?
• Why are some materials transparent and others are
translucent or opaque?
• How does a laser operate?
Chapter 19 - 1
Optical Properties
Light has both particulate and wavelike characteristics
– Photon - a quantum unit of light
hc
E  h 

E  energy of a photon
   wavelength of radiation
  frequency of radiation
h  Planck’
s constant (6 .62 x 10 34 J  s)
c  speed of lightina vacuum (3.00 x 10 8 m/s)
Chapter 19 - 2
Speed of Light
• electromagnetic radiation is wave-like,
– Consisting of electric and magnetic field components that
are perpendicular to each other
• In vacuum, the speed of light is
– 𝑐=
1
,
𝜖0 𝜇0
• 𝜖0 : permittivity of vacuum
• 𝜇0 : permeability of vacuum
• In a medium
– 𝑣=
1
,
𝜖𝜇
• 𝜖0 , 𝜇0 : permittivity & permeability of the medium
Chapter 19 - 3
Light within solid
•
Polarization
– distorts electron clouds.
• Energy is absorbed
• Retardation of light wave
no
transmitted
light
•
+
transmitted
light
+
electron
cloud
distorts
Electron transition
– ∆𝐸 = ℎ𝑣
• h: Plank’s constant
• v: frequency
– Recall
• Energy is discrete
• Only photon whose energy is equal
to ∆𝐸 is absorbed in excitation
• All the energy of photon is absorbed
– Excited electron decays back into ground
state (releasing energy)
Chapter 19 - 4
Light Interactions with Solids
• Incident light is reflected, absorbed, scattered, and/or
transmitted: I0  IT  IA  IR  IS
Reflected: IR

Absorbed: IA
Transmitted: IT
Incident: I0
Scattered: IS
• Optical classification of materials:
Transparent
Translucent
Opaque
single
crystal
polycrystalline
dense
Adapted from Fig. 21.10, Callister
6e. (Fig. 21.10 is by J. Telford,
with specimen preparation by P.A.
Lessing.)
polycrystalline
porous
Chapter 19 - 5
Optical Properties of Metals:
Absorption
• Absorption of photons by electron transitions:
Energy of electron
unfilled states
DE = h required!
filled states
Planck’s constant
(6.63 x 10-34 J/s)
freq.
of
incident
light
Adapted from Fig. 19.4(a),
Callister & Rethwisch 3e.
• Unfilled electron states are adjacent to filled states
• Near-surface electrons absorb visible light.
Chapter 19 - 6
Reflection of Light for Metals
• Electron transition from an excited state produces a photon.
Energy of electron
IR
photon emitted
from metal
surface
unfilled states
“conducting” electron
Electron transition
filled states
Adapted from Fig. 19.4(b),
Callister & Rethwisch 3e.
Chapter 19 - 7
Reflection of Light for Metals (cont.)
• Reflectivity = IR /I0 is between 0.90 and 0.95.
• Metal surfaces appear shiny
• Most of absorbed light is reflected at the
same wavelength
• Small fraction of light may be absorbed
• Color of reflected light depends on
wavelength distribution
– Example: The metals copper and gold absorb light
in blue and green => reflected light has gold color
Chapter 19 - 8
Optical Property of Metal
• High energy band is partially filled
– Have continuous available empty electron states
• Visible light excites electrons above fermi energy
-> Incident radiation is absorbed
-> Opaque
• Transparent to x- and gamma rays.
• Absorbed radiation is reemitted -> reflected light
• Color is determined by reflected wavelength
Chapter 19 - 9
Refraction
n = index of refraction 
1
𝜖0 𝜇0
c (velocity of light in vacuum)
v (velocity of light in medium)
1
𝜖𝜇
•
Recall 𝑐 =
•
Thus,
•
𝑛= =
•
permeability
For many materials 𝜇𝑟 ~ 1, so 𝑛~ 𝜖𝑟
𝑐
𝑣
𝜖0 𝜇0
𝜖𝜇
=
and 𝑣 =
𝜖𝑟 𝜇𝑟 , 𝜖𝑟 , 𝜇𝑟 : dielectric constant & relative magnetic
-- Adding large ions (e.g., lead) to glass
decreases the speed of light in the glass.
-- Light can be “bent” as it passes through a
transparent prism
Material
n
Typical glasses ca. 1.5 -1.7
Plastics
1.3 -1.6
PbO (Litharge)
2.67
Diamond
2.41
Selected values from Table 19.1,
Callister &Chapter
Rethwisch
19 - 3e.
Total Internal Reflectance
n 2 > n1
n1 sin 2

n2 sin 1
2
n2
n1


c
1
1 = incident angle
2 = refracted angle
c = critical angle
c exists when 2 = 90°
For 1 > c light is internally
reflected
• Fiber optic cables are clad in low n material so that light will
experience total internal reflectance and not escape from the optical
fiber.

Chapter 19 - 11
Example: Diamond in air
• What is the critical angle c for light passing from diamond
(n1 = 2.41) into air (n2 = 2.41)?
• Solution: At the critical angle,
and
Rearranging the equation
1  c
2  90
n1 sin 2

n2 sin 1

 n
n2
2
sin 1  sin c  sin(90) 
n1
n1

Substitution gives

sin c
1

2.41
c  24.5
Chapter 19 - 12
Reflectivity of Nonmetals
•
•
For normal incidence and light passing from vacuum into a solid having
an index of refraction n:
n 12
R  reflectivity  

n  1
High index of refraction -> high reflectivity

• Example: For Diamond n = 2.41
2
 2.41  1 
R 
  0.17
2
.
41

1


 17% of light is reflected
•
Between two materials with indices of refraction n1 & n2:
 n 2  n1 

R reflectivi
ty 
 n 2  n1 
2
Chapter 19 - 13
Light Absorption
• Two factors:
– Polarization:
• If the light freq. is near relaxation freq. of atom
• Relaxation frequency: 1 / minimum reorientation time (for polarization)
– Electron transition
• Between valence band and conduction band
Chapter 19 - 14
Selected Light Absorption in
Semiconductors
Absorption of light of frequency  by by electron transition
occurs if h > Egap
Energy of electron
Examples of photon energies:
blue light: h = 3.1 eV
red light: h = 1.7 eV
unfilled states
Egap
incident photon
energy h
filled states
Adapted from Fig. 19.5(a),
Callister & Rethwisch 3e.
• If Egap < 1.8 eV, all light absorbed; material is opaque (e.g., Si, GaAs)
• If Egap > 3.1 eV, no light absorption; material is transparent and
colorless (e.g., diamond)
• If 1.8 eV < Egap < 3.1 eV, partial light absorption; material is colored
Chapter 19 - 15
Computations of Minimum
Wavelength Absorbed
(a) What is the minimum wavelength absorbed by
Ge, for which Eg = 0.67 eV?
Solution:
hc
(6.63 x 1034 J s)(3 x 10 8 m/s)
Ge (min) 

Eg (Ge)
(0.67 eV)(1.60 x 1019 J/eV)
Ge (min)  1.86 x 10 -6 m  1.86 m

(b) Redoing
this computation for Si which has a band gap
of1.1 eV
 Si (min)  1.13 m
Note: the presence of donor and/or acceptor states allows for light
absorption at other wavelengths.

Chapter 19 - 16
Light Absorption
The amount of light absorbed by a material is
calculated using Beer’s Law



IT I0e
 = absorption coefficient, cm-1
 = sample thickness, cm
IT= incident light intensity
I0= transmitted light intensity
Rearranging and taking the natural log of both sides

of the equation
leads to

 IT 
ln    
 I 0 
Chapter 19 - 17
Color of Nonmetals
• Color determined by the distribution of wavelengths:
-- transmitted light
-- re-emitted light from electron transitions
• Example 1: Cadmium Sulfide (CdS), Eg = 2.4 eV
-- absorbs higher energy visible light (blue, violet)
-- color results from red/orange/yellow light that is transmitted
Chapter 19 - 18
Color of Nonmetals
• Example 2: Ruby = Sapphire (Al2O3) + (0.5 to 2) at% Cr2O3
• alters the band gap
• blue and orange/yellow/green
light is absorbed
• red light is transmitted
• Result: Ruby is deep
red in color
Transmittance (%)
-- Sapphire is transparent and
colorless (Eg > 3.1 eV)
-- adding Cr2O3 :
80
sapphire
70
ruby
60
50
40
0.3
wavelength,  (= c/)(m)
0.5
0.7
0.9
Adapted from Fig. 19.9, Callister & Rethwisch 3e.
(Fig. 19.9 adapted from "The Optical Properties of
Materials" by A. Javan, Scientific American, 1967.)
Chapter 19 - 19
Luminescence
• Luminescence – reemission of light by a material
– Material absorbs light at one frequency and reemits it at
another (lower) frequency.
– Trapped (donor/acceptor) states introduced by
impurities/defects
Conduction band
Eg
trapped
states
Eemission
activator
level
Valence band
• If residence time in trapped state is
relatively long (> 10-8 s)
-- phosphorescence
• For short residence times (< 10-8 s)
-- fluorescence
Example: Toys that glow in the dark.
Charge toys by exposing them to light.
Reemission of light over time—
phosphorescence
Chapter 19 - 20
Photoluminescence
Hg atom
UV light
electrode
electrode
• Arc between electrodes excites electrons in mercury atoms in
the lamp to higher energy levels.
• As electron falls back into their ground states, UV light is emitted
(e.g., suntan lamp).
• Inside surface of tube lined with material that absorbs UV and
reemits visible light
- For example, Ca10F2P6O24 with 20% of F - replaced by Cl • Adjust color by doping with metal cations
Sb3+ blue
Mn2+ orange-red
Chapter 19 - 21
Cathodoluminescence
• Used in cathode-ray tube devices (e.g., TVs, computer monitors)
• Inside of tube is coated with a phosphor material
– Phosphor material bombarded with electrons
– Electrons in phosphor atoms excited to higher state
– Photon (visible light) emitted as electrons drop back into
ground states
– Color of emitted light (i.e., photon wavelength) depends on
composition of phosphor
ZnS (Ag+ & Cl-)
(Zn, Cd) S + (Cu++Al3+)
Y2O2S + 3% Eu
blue
green
red
• Note: light emitted is random in phase & direction
– i.e., is noncoherent
Chapter 19 - 22
The LASER
• The laser generates light waves that are in phase
(coherent) and that travel parallel to one another
– LASER
•
•
•
•
•
Light
Amplification by
Stimulated
Emission of
Radiation
• Operation of laser involves a population inversion of
energy states process
Chapter 19 - 23
Population Inversion
• More electrons in excited energy states than in ground states
Fig. 19.14, Callister & Rethwisch 3e.
Chapter 19 - 24
Operation of the Ruby Laser
• “pump” electrons in the lasing material to excited states
– e.g., by flash lamp (incoherent light).
Fig. 19.13, Callister & Rethwisch 3e.
– Direct electron decay transitions — produce incoherent light
Chapter 19 - 25
Operation of the Ruby Laser (cont.)
• Stimulated Emission
– The generation of one photon
by the decay transition of an
electron, induces the emission
of other photons that are all in
phase with one another.
– This cascading effect produces
an intense burst of coherent
light.
• This is an example of a
pulsed laser
Fig. 19.15, Callister
& Rethwisch 3e.
Chapter 19 - 26
Continuous Wave Lasers
•
•
•
•
Continuous wave (CW) lasers generate a continuous (rather
than pulsed) beam
Materials for CW lasers include semiconductors (e.g., GaAs),
gases (e.g., CO2), and yttrium-aluminum-garret (YAG)
Wavelengths for laser beams are within visible and infrared
regions of the spectrum
Uses of CW lasers
1.
2.
3.
4.
5.
6.
Welding
Drilling
Cutting – laser carved wood, eye surgery
Surface treatment
Scribing – ceramics, etc.
Photolithography – Excimer laser
Chapter 19 - 27
Semiconductor Laser Applications
• Apply strong forward bias
across semiconductor layers,
metal, and heat sink.
• Electron-hole pairs generated
by electrons that are excited
across band gap.
• Recombination of an
electron-hole pair generates
a photon of laser light
electron + hole  neutral + h
recombination
ground state
photon of
light
Fig. 19.17, Callister & Rethwisch 3e.
Chapter 19 - 28
Semiconductor Laser Applications
Chapter 19 - 29
Semiconductor Laser Applications
• Compact disk (CD) player
– Use red light
• High resolution DVD players
– Use blue light
– Blue light is a shorter wavelength than red light so it
produces higher storage density
• Communications using optical fibers
– Fibers often tuned to a specific frequency
• Banks of semiconductor lasers are used as flash lamps
to pump other lasers
Chapter 19 - 30
Other Applications - Solar Cells
• p-n junction:
• Operation:
P-doped Si
conductance
Si
electron
Si P Si
-- incident photon of light produces elec.-hole pair.
-- typical potential of 0.5 V produced across junction
-- current increases w/light intensity.
light
Si
n-type Si
p-n junction
p-type Si
n-type Si
p-n junction
p-type Si
Si
B
-
- -
+
+ + +
• Solar powered weather station:
Si
hole
creation of
hole-electron
pair
Si
Si
B-doped Si
polycrystalline Si
Los Alamos High School weather
station (photo courtesy
P.M. Anderson)
Chapter 19 - 31
Other Applications - Optical Fibers
Schematic diagram showing components of a
fiber optic communications system
Fig. 19.18, Callister & Rethwisch 3e.
Chapter 19 - 32
Optical Fibers (cont.)
• fibers have diameters of 125 m or less
• plastic cladding 60 m thick is applied to fibers
Fig. 19.20, Callister &
Rethwisch 3e.
Chapter 19 - 33
Optical Fiber Designs
Step-index Optical Fiber
Graded-index Optical Fiber
Fig. 19.21, Callister & Rethwisch 3e.
Fig. 19.22, Callister & Rethwisch 3e.
Chapter 19 - 34
SUMMARY
• Light radiation impinging on a material may be reflected
from, absorbed within, and/or transmitted through
• Light transmission characteristics:
-- transparent, translucent, opaque
• Optical properties of metals:
-- opaque and highly reflective due to electron energy band
structure.
• Optical properties of non-Metals:
-- for Egap < 1.8 eV, absorption of all wavelengths of light radiation
-- for Egap > 3.1 eV, no absorption of visible light radiation
-- for 1.8 eV < Egap < 3.1 eV, absorption of some range of light
radiation wavelengths
-- color determined by wavelength distribution of transmitted light
• Other important optical applications/devices:
-- luminescence, photoconductivity, light-emitting diodes, solar
cells, lasers, and optical fibers
Chapter 19 - 35
Scattering of Light in Polymers
• For highly amorphous and pore-free polymers
– Little or no scattering
– These materials are transparent
• Semicrystalline polymers
– Different indices of refraction for amorphous and
crystalline regions
– Scattering of light at boundaries
– Highly crystalline polymers may be opaque
• Examples:
– Polystyrene (amorphous) – clear and transparent
– Low-density polyethylene milk cartons – opaque
Chapter 19 - 36
ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems:
Chapter 19 - 37