# Lecture 21

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Published on July 11, 2007

Author: luyenkimnet

Source: slideshare.net

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).

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).

Optical Properties

Electromagnetic Wave Propagation

Electromagnetic Radiation-Waves EM radiation travels in a vacuum at the speed of light (c=3*10 8 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 ? ? ? ? ? ?

EM radiation travels in a vacuum at the speed of light (c=3*10 8 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.

Spans from gamma rays (radioactive materials) to x-rays, UV, visible, IR, microwave, radio/tv

Applications of various waves/photons

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 Some semiconductors Adapted from Fig. 21.10, Callister 6e . (Fig. 21.10 is by J. Telford, with specimen preparation by P.A. Lessing.)

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

Some semiconductors

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 .

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.

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.

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 Electromagnetic radiation generation http://www.chemistry.adelaide.edu.au/external/soc-rel/content/at-lvls.htm http://csep10.phys.utk.edu/astr162/lect/light/absorption.html

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

Electromagnetic radiation absorption Alternatively, only photons of certain energies can be absorbed by any particular atom (or crystal). http://csep10.phys.utk.edu/astr162/lect/light/absorption.html E 41 , E 31 , and E 21 are also conceivable. So are E 32 and E 31 . and E 21 . etc.

Alternatively, only photons of certain energies can be absorbed by any particular atom (or crystal).

E 41 , E 31 , and E 21 are also conceivable.

So are E 32 and E 31 .

and E 21 .

etc.

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

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).

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 E g to be absorbed (to successfully excite an electron into an available band state).

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 E g to be absorbed (to successfully excite an electron into an available band state).

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

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…

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 .

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 E v to E f , or from E f to E c . Combination of photons, 1 st from E v to E f and the 2 nd from E f to E c .

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 E v to E f , or from E f to E c .

Combination of photons, 1 st from E v to E f and the 2 nd from E f to E c .

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.

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.

Methods of Photon Absorbtion

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=v o ) 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.

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=v o ) 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.

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.

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

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

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.

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.

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. “non-absorbed beam” “Initial beam”

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.

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

COLOR OF NONMETALS in transmission • Color determined by sum of frequencies of --transmitted light, --re-emitted light from electron transitions. • Ex: Cadmium Sulfide (CdS) -- E gap = 2.4eV, -- absorbs higher energy visible light (blue, violet), -- Red/yellow/orange is transmitted and gives it color. • Ex: Ruby = Sapphire (Al 2 O 3 ) + (0.5 to 2) at% Cr 2 O 3 -- Pure sapphire is colorless (i.e., E gap > 3.1eV) -- adding Cr 2 O 3 : • alters the band gap • blue light is absorbed • yellow/green is absorbed • red is transmitted • Result: Ruby is deep red in color.

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.

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.

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).

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).

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

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

LUMINESCENCE 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 incident radiation After electrons are excited across the gap (usually with UV radiation), they may generate new photons by re-emission. Spontaneous emitted light

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

After electrons are excited across the gap (usually with UV radiation), they may generate new photons by re-emission.

Luminescence types 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). Fluorescence: lasts << 1 second Phosphorescence: 1 second or greater • Example: fluorescent lamps

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).

Fluorescence: lasts << 1 second

Phosphorescence: 1 second or greater

LASER L ight A mplification by S timulated E mission of R adiation Coherent (in phase) Most other light sources are incoherent—generated by independent, randomly timed optical events. The Ruby laser is a Al 2 O 3 crystal (sapphire) with .05% Cr 3+ . 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.’

L ight A mplification by S timulated E mission of R adiation

Coherent (in phase)

Most other light sources are incoherent—generated by independent, randomly timed optical events.

The Ruby laser is a Al 2 O 3 crystal (sapphire) with .05% Cr 3+ .

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.’

Laser concept Before the ruby is illuminated with the ‘flash lamp,’ nearly all Cr 3+ 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 Cr 3+ 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 ).

Before the ruby is illuminated with the ‘flash lamp,’ nearly all Cr 3+ 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 Cr 3+ 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 ).

Laser operation As the metastable intermediate states decay (up to 3 ms), the available time is long on optical scales and thus many Cr 3+ states get filled. Initial spontaneous photon emission stimulates an avalanche of emissions from many metastable Cr 3+ 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.

As the metastable intermediate states decay (up to 3 ms), the available time is long on optical scales and thus many Cr 3+ states get filled.

Initial spontaneous photon emission stimulates an avalanche of emissions from many metastable Cr 3+ 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.

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) http://www.directedlight.com/

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

Communications (via fiber optics)

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. http://www.veeco.com/nanotheatre Tracks are only 740 nm apart, and data bits are usually < 400 nm on a side.

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.

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 http://www.veeco.com/nanotheatre

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

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). http://www6.tomshardware.com/storage/20040827/

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).

SUMMARY 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

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).

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