1. Optical Properties
Frequency, wavelength, and energy, trends in spectrum
Optical classifications
How does absorption, A, (or emission) relate to band structure (band gaps, donor/acceptor states)?
Reflection (R)
Refraction
Transmission (T)
Equations for R, A, T
Photoelasticity
Define Phosphorescence and Fluorescence.
Know the principles behind the ruby laser.
Know the principles behind optical data storage (DVDs).

2. Optical Properties

3. Electromagnetic Wave Propagation

4. Electromagnetic Radiation-Waves
EM radiation travels in a vacuum at the speed of light (c=3*108 m/s).
The speed of light is related to dielectric permittivity and magnetic permeability of a vacuum.
The frequency and wavelength are also related to c.
The energy of light (photons) with a given frequency (or wavelength) is related to Planck’s constant (h=6.63*10-34 J*sec).
Radiation can thus be defined in terms of energy, frequency, or wavelength.
E ν λ
? ? ?

5. EM Radiation Spectrum
Spans from gamma rays (radioactive materials) to x-rays, UV, visible, IR, microwave, radio/tv

6. Applications of various waves/photons

7. Optical classification
There are three primary ways to describe the optical quality of a material (color comes later)
Transparent: you can see through it (but color may change).
Glass
Insulators
Some semiconductors
Translucent: light is transmitted diffusely (internal scattering), usually related to defects such as grain boundaries or pores.
Polycrystalline insulators
Opaque: you can’t see through it.
Bulk metals
Adapted from Fig , Callister 6e. (Fig is by J. Telford, with specimen preparation by P.A. Lessing.)

8. Optical Classification
Intensity of the incident beam=Sum of the intensities of the transmitted, absorbed, and reflected beams.
Materials with little absorption and reflection are transparent. You can see through them.
Materials in which light is transmitted diffusely are translucent. Objects are not clearly distinguishable.
Materials where light is absorbed and reflected are opaque.

9. Band structure of materials
Recall back to discussions of band structure:
Based on electron bonding and antibonding orbitals in individual atoms
Orbitals from adjacent atoms overlap in molecules
In a solid, there are so many orbitals that they form a continuous band.
Transitions between bands only allowed for certain energies:
Although a little bit of energy is available to every electron at room temperature (kT=25meV):
they can only conduct current in a metal where there are vacant band states available.
For a semiconductor, a bandgap exists without any available band states within 25meV of the electron. Thus, no conductivity.
Note that photons can transfer their energy to electrons, or vice versa.
Optics can thus tell us about band structure, or band structure about the optical response.

10. Electromagnetic radiation generation
If we can excite electrons in a material (or molecule or atom), as those electrons return to their ground state they may release their energy as light of discrete characteristic wavelengths:
Light bulb
X-ray tube
Sun

11. Electromagnetic radiation absorption
Alternatively, only photons of certain energies can be absorbed by any particular atom (or crystal).
E41, E31, and E21 are also conceivable.
So are E32 and E31.
and E21.
etc.

12. Absorption in Metals • Absorption of photons by electron transition:
Adapted from Fig. 21.4(a), Callister 6e.
• Absorption is usually very small (less than 5%)
• Metals have a fine succession of energy states.
• Near-surface electrons absorb visible light.

13. Absorption in Metals
Most of the absorbed radiation is re-emitted from the surface, less than 0.1 micron. Only very thin films of metals are transparent to visible light.
Metals are only “transparent” to high frequency radiation (x- and gamma-rays).
A bright silvery color when exposed to light indicates that the metal is highly reflective: number & frequency of incoming photons is ~ equal in the incident and reflected beam (Al, Fe, Ti, Ag).
In some metals, short wavelength radiation (green, blue, violet) is not re-emitted. They appear red-orange or yellow (Cu, Au).

14. Absorption in Semiconductors/Insulators
In a metal, just about any visible photon can be absorbed.
But for a semiconductor or insulator, photons must have at least an energy of Eg to be absorbed (to successfully excite an electron into an available band state).

15. More semiconductors/insulators
• Absorption by electron transition occurs if hn > Egap
3.1 eV
1.7 eV
incident photon energy hn
• If Egap < 1.7eV, full visible absorption, black or metallic
• If Egap > 3.1eV, no visible absorption, transparent
• If Egap in between, partial visible absorption, colors

16. Absorption of colored light
Which of the following is true?
If my material absorbs blue, it must also absorb red.
If my material absorbs red, it must also absorb blue.
Think about this at home…

17. Bandgap states
Impurities/dopants cause energy levels in the bandgap (discrete sites and/or very narrow bands).
This allows excitation (or emission) via single or double photon interactions:
Single photons from Ev to Ef, or from Ef to Ec.
Combination of photons, 1st from Ev to Ef and the 2nd from Ef to Ec.

18. Radiation excitation by non-metals
For a system with a band-gap, photons with energies greater than the band gap can be emitted!
Light bulbs
Light Emitting Diodes (LED’s)
Lasers
Generating low energy photons (IR, red) is easy.
Generating blue photons is much harder, as the bandgap must be larger and free of defects.

19. Methods of Photon Absorbtion

20. Refraction
To understand reflection, we first must understand refraction.
The speed of any radiation in any medium (v) is related to the speed of light in a vacuum (c) over the index of refraction of the material.
The speed of radiation in a vacuum (c=vo) is related to the dielectric permittivity and magnetic permeability of a vacuum.
The speed of radiation in any material can also be related to the material dependent dielectric permittivity and magnetic permeability.
The index of refraction (optical property) is thus easily determined if the electronic and magnetic properties are known (r means relative to a vacuum).
Since most materials are only weakly magnetic, the relative dielectric permittivity is often measured based on the optical index of refraction.

21. LIGHT INTERACTION WITH SOLIDS
• Incident light is either reflected, absorbed, or
transmitted:
If photons of a certain color are absorbed, they obviously aren’t being transmitted (or reflected) to your eyes. This will affect the material color.

22. Refraction
Fish use this concept to see you standing on the shore trying to catch them.

23. Reflection
Remember the reflected intensity is proportional to the reflected fraction (R) and the initial intensity.
As ∆n between two bodies increases, so does reflection at the interface.
This is regardless of the quality of the interface, an entirely different term that we don’t cover here.
For light passing between a vacuum (or air) and a solid, the equation simplifies since n=1.
Note that this is strictly true only for photons perfectly normal to the interface.
When there is an angle of incidence, this adds extra, complicating terms to the equations.

24. Absorption
Light traversing a material is absorbed exponentially, depending on the absorption coefficient (β) and the distance traveled (x or l).
Transparent materials have a very small absorption coefficient, while strong absorbers obviously rapidly diminish the transmitted light intensity.
Note that β is technically wavelength dependent.
“Initial beam”
“non-absorbed beam”

25. Light reflected and absorbed going through a material.
“non-reflected beam:”
“non-absorbed beam:”
non-reflected beam 2:

26. COLOR OF NONMETALS in transmission
• Color determined by sum of frequencies of
--transmitted light,
--re-emitted light from electron transitions.
• Ex: Cadmium Sulfide (CdS)
-- Egap = 2.4eV,
-- absorbs higher energy visible light (blue, violet),
-- Red/yellow/orange is transmitted and gives it color.
• Ex: Ruby = Sapphire (Al2O3) + (0.5 to 2) at% Cr2O3
-- Pure sapphire is colorless
(i.e., Egap > 3.1eV)
-- adding Cr2O3 :
• alters the band gap
• blue light is absorbed
• yellow/green is absorbed
• red is transmitted
• Result: Ruby is deep
red in color.

27. Transmission and Absorption
The transmitted intensity is a function of the intensity not already reflected at the surface, the thickness of the material, and a measure of how good of an absorber it is (absorption coefficient, beta).
Large beta = strong absorber.
Remember these terms can vary with the wavelength of incident radiation.

28. Summary of basic optics
Radiation striking an object will reflect, absorb, and/or transmit.
The color of the object depends on the energy dependence of each of these parameters, which depends on the bandstructure (for non-metals).

29. Photoelasticity
The optical properties of some materials change with mechanical loading: photoelasticity.

30. LUMINESCENCE
After electrons are excited across the gap (usually with UV radiation), they may generate new photons by re-emission.
incident
radiation
The radiated light may not have the same wavelength as the incident energy
(but it must always have less E)
UV -> blue
Blue -> red
Never red -> blue
Spontaneous emitted light

31. Luminescence types • Example: fluorescent lamps
Fluorescence: lasts << 1 second
Phosphorescence: 1 second or greater
After the excitation source is turned off:
If the luminescence ends rapidly, then the material is fluorescent (it will luminesce only as long as it is excited).
If the luminescence continues, the material is phosphorescent (light emission persists).

32. LASER Light Amplification by Stimulated Emission of Radiation
Coherent (in phase)
Most other light sources are incoherent—generated by independent, randomly timed optical events.
The Ruby laser is a Al2O3 crystal (sapphire) with .05% Cr3+.
Ruby prepared as a rod with ends polished flat and parallel.
One end is mirrored (silvered), the other end is perfectly parallel and is partially mirrored allowing most light to be internally reflected but some to spill past the mirror (transmission).
Ruby illuminated with ‘flash lamp.’

33. Laser concept
Before the ruby is illuminated with the ‘flash lamp,’ nearly all Cr3+ dopant ions are in their ground states.
Nearly all electrons are in their lowest energy levels.
Photons with 560nm wavelength are at the right energy to excite electrons from the Cr3+ into the conduction band where available energy levels are present.
Decay follows two paths.
A) Fall back directly (like a metal).
B) Most decay into metastable intermediate state, staying there up to 3 ms before falling back to their ground state and emission of a photon in the visible range.
If we can get a lot of these photons, we will have a nicely monochromatic beam (single wavelength, λ).

34. Laser operation
As the metastable intermediate states decay (up to 3 ms), the available time is long on optical scales and thus many Cr3+ states get filled.
Initial spontaneous photon emission stimulates an avalanche of emissions from many metastable Cr3+ ions.
Non-axial Photons decay rapidly.
Most photons generated along the axis of the rod reflect off the mirrored edges, ‘traversing’ from one end to the other and back.
Electrons continue to be excited and then emitted by the flash lamp.
Some electrons transmit through the partially silvered mirror on one side.
Eventually, a collimated (highly parallel), high intensity beam transmits through the laser edge.

35. What to do with a laser? Point Marking
‘burn’ holes (machining), 1um features possible
Cutting (metal, cloth)
Medical applications (cutting and cauterizing=singe tissue after cutting it to seal off blood vessels and stop bleeding)
Heat treatments for very localized and rapid annealing
Localized sintering for 3d manufacture
welding (auto industry)
Distance measurement (to the moon, to your dorm wall)
Barcode scanners
CD’s/DVD’s/etc (data recording and reading)
Communications (via fiber optics)

36. CD and DVD players
Data is stored like a CD, in the form of small regions (bits) with different optical properties than the substrate (disk).
Composed of about 1.2 mm of multilayered, injection molded, clear polycarbonate plastic.
A continuous and very long track of data (7.5 miles), written from the center of the disk and spiraling outward.
Tracks are only 740 nm apart, and data bits are usually < 400 nm on a side.

37. Optical recording Different methods for generating the bits:
Stamping (create ‘craters’).
Coat with metal to enhance reflectivity.
Phase change (crystalline to amorphous transition depending on optical power and time).
No topographic change but a change in the mechanical and optical properties since photoelastic.
Magneto-optical
Domains oriented optically

38. Double sided, double layer
Both sides of the disk can be written on, and then read by turning over the disk or having 2 heads (one on top, the other on the bottom).
Double layer recording is also possible on each side (available in stores, 16 GB, 8 hours of movies).
Focusable, high intensity laser used to read/write at two depths.
Sometimes, 2 lasers with different wavelengths are used (one is reflected by semitransparent layer, the other is transmitted through it to the next layer).

39. SUMMARY Next class: Review
Frequency, wavelength, and energy, trends in spectrum
Optical classifications
How does absorption, A, (or emission) relate to band structure (band gaps, donor/acceptor states, etc)?
Reflection (R)
Refraction
Transmission (T)
Equations for R, A, T
Photoelasticity.
Define Phosphorescence and Fluorescence.
Know the principles behind the ruby laser.
Know the principles behind optical data storage (DVDs).
Next class: Review