1. 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?

2. Optical Properties
Light has both particulate and wavelike characteristics
Photon - a quantum unit of light

3. 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 𝜖 0 𝜇 0 ,
𝜖 0 : permittivity of vacuum
𝜇 0 : permeability of vacuum
In a medium
𝑣= 1 𝜖𝜇 ,
𝜖 0 , 𝜇 0 : permittivity & permeability of the medium

4. Light within solid + Polarization distorts electron clouds. electron
Energy is absorbed
Retardation of light wave
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) + no
transmitted
light
electron
cloud
distorts

5. Light Interactions with Solids
• Incident light is reflected, absorbed, scattered, and/or
transmitted:
Incident: I0
Absorbed: IA
Transmitted: IT
Scattered: IS
Reflected: IR
• Optical classification of materials:
Adapted from Fig , Callister 6e. (Fig is by J. Telford, with specimen preparation by P.A. Lessing.)
single crystal
polycrystalline dense
polycrystalline porous
Transparent
Translucent
Opaque

6. Optical Properties of Metals: Absorption
• Absorption of photons by electron transitions:
Energy of electron
unfilled states
DE = h required!
Incident photon
of energy h
filled states
freq.
Planck’s constant of
(6.63 x J/s)
incident
Adapted from Fig. 19.4(a), Callister & Rethwisch 3e.
light
• Unfilled electron states are adjacent to filled states
• Near-surface electrons absorb visible light.

7. Reflection of Light for Metals
• Electron transition from an excited state produces a photon.
photon emitted from metal surface
Energy of electron
filled states
unfilled states
Electron transition IR
“conducting” electron
Adapted from Fig. 19.4(b), Callister & Rethwisch 3e.

8. 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 8 8

9. 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

10. Refraction n = index of refraction Material n
Recall 𝑐= 1 𝜖 0 𝜇 0 and 𝑣= 1 𝜖𝜇
Thus,
𝑛= 𝑐 𝑣 = 𝜖 0 𝜇 𝜖𝜇 = 𝜖 𝑟 𝜇 𝑟 , 𝜖 𝑟 , 𝜇 𝑟 : dielectric constant & relative magnetic permeability
For many materials 𝜇 𝑟 ~ 1, so 𝑛~ 𝜖 𝑟
n = index of refraction
-- 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
Selected values from Table 19.1,
Callister & Rethwisch 3e.
Typical glasses ca
Plastics
PbO (Litharge)
Diamond
Material n

11. Total Internal Reflectance
n2 > n1 n2
f1 = incident angle
f2 = refracted angle n1
fc = critical angle
fc exists when f2 = 90°
For f1 > fc 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.

12. 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
Substitution gives

13. Reflectivity of Nonmetals
For normal incidence and light passing from vacuum into a solid having an index of refraction n:
High index of refraction -> high reflectivity
Between two materials with indices of refraction n1 & n2:
Example: For Diamond n = 2.41

14. Light Absorption Two factors: Polarization: Electron transition
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

15. Selected Light Absorption in Semiconductors
Absorption of light of frequency  by by electron transition occurs if hn > Egap
Adapted from Fig. 19.5(a), Callister & Rethwisch 3e.
blue light: h = 3.1 eV
red light: h = 1.7 eV
incident photon energy hn
Energy of electron
filled states
unfilled states
Egap
Examples of photon energies:
• 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

16. Computations of Minimum Wavelength Absorbed
(a) What is the minimum wavelength absorbed by Ge, for which Eg = 0.67 eV?
Solution:
(b) Redoing this computation for Si which has a band gap of 1.1 eV
Note: the presence of donor and/or acceptor states allows for light absorption at other wavelengths.

17. Light Absorption
The amount of light absorbed by a material is calculated using Beer’s Law
 = absorption coefficient, cm-1  = sample thickness, cm = incident light intensity = transmitted light intensity
Rearranging and taking the natural log of both sides of the equation leads to

18. 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

19. Color of Nonmetals
• Example 2: Ruby = Sapphire (Al2O3) + (0.5 to 2) at% Cr2O3
-- Sapphire is transparent and colorless (Eg > 3.1 eV)
-- adding Cr2O3 :
• alters the band gap
• blue and orange/yellow/green light is absorbed
• red light is transmitted
• Result: Ruby is deep
red in color
Adapted from Fig. 19.9, Callister & Rethwisch 3e. (Fig adapted from "The Optical Properties of Materials" by A. Javan, Scientific American, 1967.) 40 60 70 80 50
0.3
0.5
0.7
0.9
Transmittance (%)
ruby
sapphire
wavelength,
l (= c/)(m)

20. 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
activator level
Valence band
Conduction band
trapped states Eg
Eemission
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

21. 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
Sb blue
Mn orange-red

22. 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-) blue
(Zn, Cd) S + (Cu++Al3+) green
Y2O2S + 3% Eu red
Note: light emitted is random in phase & direction
i.e., is noncoherent

23. 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

24. Population Inversion
More electrons in excited energy states than in ground states
Fig , Callister & Rethwisch 3e.

25. Operation of the Ruby Laser
“pump” electrons in the lasing material to excited states
e.g., by flash lamp (incoherent light).
Fig , Callister & Rethwisch 3e.
Direct electron decay transitions — produce incoherent light

26. 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 , Callister & Rethwisch 3e.

27. 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
Welding
Drilling
Cutting – laser carved wood, eye surgery
Surface treatment
Scribing – ceramics, etc.
Photolithography – Excimer laser

28. 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 , Callister & Rethwisch 3e.

29. Semiconductor Laser Applications

30. 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
checkout scanner

31. Other Applications - Solar Cells
• p-n junction:
• Operation:
-- incident photon of light produces elec.-hole pair.
-- typical potential of 0.5 V produced across junction
-- current increases w/light intensity.
n-type Si
p-type Si
p-n junction
B-doped Si Si B
hole P
conductance
electron
P-doped Si
n-type Si
p-type Si
p-n junction
light + -
creation of
hole-electron
pair
• Solar powered weather station:
polycrystalline Si
Los Alamos High School weather
station (photo courtesy
P.M. Anderson)

32. Other Applications - Optical Fibers
Schematic diagram showing components of a fiber optic communications system
Fig , Callister & Rethwisch 3e.

33. Optical Fibers (cont.) fibers have diameters of 125 m or less
plastic cladding 60 m thick is applied to fibers
Fig , Callister & Rethwisch 3e. 33 33

34. Optical Fiber Designs Step-index Optical Fiber
Graded-index Optical Fiber
Fig , Callister & Rethwisch 3e.
Fig , Callister & Rethwisch 3e.

35. 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

36. 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

37. ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems: