Atomic Physics and Lasers

1
Atomic Physics and Lasers

• The idea of a photon
• Black body radiation
• Photoelectric Effect
• The structure of the atom
• How does a Laser work? Interaction of lasers with
  matter
• Laser safety
• Applications
• Spectroscopy, detection of art forgery, flow
  cytometry, eye surgery.

2
The idea of a photon

• What is light?
• A wave?
• Well yes, but.
• The wave picture failed to explain physical
  phenomena including
• the spectrum of a blackbody
• the photoelectric effect
• line spectra emitted by atoms

3
Light from a hot object...
Vibrational motion of particles produces
light(we call the light Thermal Radiation)
4


The first clue that something was very, very
wrongBlackbody radiation

• What is a blackbody?

• An object which emits or absorbs all the
  radiation incident on it.
• Typical black bodies
• A light globe
• A box with a small hole in it.

5
Example of a Blackbody
A BLACKBODY
6
Example of a Blackbody
We measure radiation as a function of frequency
(wavelength)
7
A Thermal Spectrum
How does a thermal spectrum change when you
change T?
8
Thermal Radiation
T Temp. in Kelvin
Total energy emitted by an object (or Luminosity
W/m2)
Wavelength where flux is a maximum
s 5.7 x 10-8 W/(m2.K4)
k 2.898 x 10-3 m.K
Stefans Law
Wiens Law
9
(No Transcript)
10
Light and matter interact

• The spectra we have looked at are for ideal
  objects that are perfect absorbers and emitters
  of light

Light is later emitted
Light is perfectly absorbed
A BLACKBODY
11
Problems with wave theory of light

• Take a Blackbody witha temperature, T
• Calculate how the spectrum would look if light
  behaved like a wave (Lord Rayleigh)
• Compare with what isactually observed

12
Example of a Blackbody
We measure radiation as a function of frequency
(wavelength)
13
Problems with wave theory of light

• Take a Blackbody witha temperature, T
• Calculate how the spectrum would look if light
  behaved like a wave (Lord Rayleigh)
• Compare with what isactually observed

14
Max Plank Solved the problem in 1900

• Oscillators cannot have any energy! They can be
  in states with fixed amounts of energy.
• The oscillators change state by
  emitting/absorbingpackets with a fixed amounts
  of energy

Max Plank
15

Atomic Physics/Blackbody

• Max Planck (1858-1947) was impressed by the
  fact
• spectrum of a black body was a universal
  property.

E nhf

• To get agreement between the experiment and the
  theory, Planck proposed a radical idea Light
  comes in packets of energy called photons, and
  the energy is given by E nhf

The birth of the quantum theory Plancks
hypothesis
16
The birth of the Photon

• In 1906, Einstein proved that Plancks radiation
  law could be derived only if the energy of each
  oscillator is quantized.
• En nhf n 0, 1, 2, 3, 4,...
  
  
• hPlancks constant 6.626x10 -34 J.s
• ffrequency in Hz Eenergy in Joules (J).

• Einstein introduced the idea that radiation
• equals a collection of discrete energy quanta.
• G.N. Lewis in 1926 named quanta Photons.

17
Atomic Physics/Photon

• The energy of each photon
• E hf hPlancks constant
• ffrequency

Ex. 1. Yellow light has a frequency of 6.0 x
1014 Hz. Determine the energy carried by a
quantum of this light. If the energy flux of
sunlight reaching the earths surface is 1000
Watts per square meter, find the number of
photons in sunlight that reach the earths
surface per square meter per second.

Ans. 2.5 eV and 2.5 x 10 21 photons / m 2
/s
18
Lecture 12
19
Shining light onto metals
Light in
Nothing happens
METAL
20
Shining light onto metals
METAL
21
The Photoelectric Effect

• When light is incident on certain metallic
  surfaces, electrons are emitted the
  Photoelectric Effect (Serway and Jewett 28.2)
• Einstein A single photon gives up all its
  energy to a single electron

EPhoton EFree EKinetic
Need at least this much energy to free the
electron
Whatever is left makes it move
22
The Photoelectric Effect
23
Application of Photoelectric Effect
Soundtrack on Celluloid film
To speaker
24
Another Blow for classical physics Line Spectra

• The emission spectrum from a rarefied gas through
  which an electrical discharge passes consists of
  sharp spectral lines.
• Each atom has its own characteristic spectrum.
• Hydrogen has four spectral lines in the visible
  region and many UV and IR lines not visible to
  the human eye.
• The wave picture failed to explain these lines.

25
Atomic Physics/Line spectra
400 500
600
?(nm)

H
Emission spectrum for hydrogen
The absorption spectrum for hydrogen dark
absorption lines occur at the same wavelengths as
emission lines.
26
Atomic Physics/Line Spectra
27
So what is light?

• Both a wave and a particle. It can be both, but
  in any experiment only its wave or its particle
  nature is manifested. (Go figure!)

28
Two revolutions The Nature of light and the
nature of matter

• Light has both a particle and wave nature
• Wave nature
• Diffraction, interference
• Particle nature
• Black body radiation, photoelectric effect, line
  spectra
• Need to revise the nature of matter (it turns out
  that matter also has both a particle and wave
  nature

29

The spectrum from a blackbody

• Empirically
• ?(max)T constant,
• Hotter whiter
• The wave picture (Rayleigh-Jeans) failed to
  explain the distribution of the energy versus
  wavelength. UV Catastrophe!!!!

6000K
Rayleigh- Jeans
Relative Intensity
Observed
5000K
0 2 4 6 8 10
? (10 -7 m)
30
Photoelectric Effect
Light in
e
Electron out
METAL
31
The Photoelectric Effect

• Photoelectric effectWhen light is incident on
  certain metallic surfaces, photoelectrons are
  emitted.
• Einstein applied the idea of light quanta
• In a photoemission process, a single photon
  gives up all its energy to a single electron.

Energy of photon
Energy to free electron


KE of emitted electron
32
Atomic Physics/Photoelectric Effect

?work function minimum energy needed to extract
an electron.
hf KE ?
KE
x
fo threshold freq below which no photoemission
occurs.
x
x
x
f0
f, Hz
33
Atomic Physics/The Photoelectric
Effect-Application
The sound on a movie film
Sound Track

Phototube
Light Source
???speaker
34
The photoelectric effect

• Photoelectric effectWhen light is incident on
  certain metallic surfaces, photoelectrons are
  emitted.
• Einstein applied the idea of light quanta In a
  photoemission process, a single photon gives up
  all its energy to a single electron.

Energy to free electron
Energy of photon
KE of emitted electron


35
The Photoelectric Effect experiment
Metal surfaces in a vacuum eject electrons when
irradiated by UV light.
36
PE effect5 Experimental observations

1. If V is kept constant, the photoelectric current
   ip increases with increasing UV intensity.
2. Photoelectrons are emitted less than 1 nS after
   surface illumination
3. For a given surface material, electrons are
   emitted only if the incident radiation is at or
   above a certain frequency, independent of
   intensity.
4. The maximum kinetic energy, Kmax, of the
   photoelectrons is independent of the light
   intensity I.
5. The maximum kinetic energy, Kmax of the
   photoelectrons depends on the frequency of the
   incident radiation.

37
Failure of Classcial Theory
Observation 1 is in perfect agreement with
classical expectations Observation 2 Cannot
explain this. Very weak intensity should take
longer to accumulate energy to eject
electrons Observation 3 Cannot explain this
either. Classically no relation between frequency
and energy. Observations 4 and 5 Cannot be
explained at all by classical E/M waves.
.
Bottom line Classical explanation fails badly.
38
Quantum Explanation.

• Einstein expanded Plancks hypothesis and
  applied it directly to EM radiation
• EM radiation consists of bundles of energy
  (photons)
• These photons have energy E hf
• If an electron absorbs a photon of energy E hf
  in order to escape the surface it uses up energy
  f, called the work function of the metal
• f is the binding energy of the electron to the
  surface
• This satisfies all 5 experimental observations

.
39
Photoelectric effect

• hf KE f
• ( f work function minimum energy needed to
  extract an electron.)
• fo threshold freq, below which no
  photoemission occurs

KE
x
.
x
x
x
f0
f (Hz)
40
Application Film soundtracks
Sound Track

Phototube
Light Source
???speaker
41
Example A GaN based UV detector
This is a photoconductor
42
Response Function of UV detector
43
Choose the material for the photon energy
required.

• Band-Gap adjustable by adding Al from 3.4 to 6.2
  eV
• Band gap is direct ( efficient)
• Material is robust

44
The structure of a LED/Photodiode
45
Characterization of Detectors

• NEP noise equivalent power
• noise current (A/?Hz)/Radiant
  sensitivity (A/W)
• D detectivity ?area/NEP
• IR cut-off
• maximum current
• maximum reverse voltage
• Field of view
• Junction capacitance

46
Photomultipliers
e
e
e
e
hf
e
e
PE effect
Secondary electron emission
Electron multiplication
47
Photomultiplier tube

• Combines PE effect with electron multiplication
  to provide very high detection sensitivity
• Can detect single photons.

48
Microchannel plates

• The principle of the photomultiplier tube can be
  extended to an array of photomultipliers
• This way one can obtain spatial resolution
• Biggest application is in night vision goggles
  for military and civilian use

49
Microchannel plates

• MCPs consist of arrays of tiny tubes
• Each tube is coated with a photomultiplying film
• The tubes are about 10 microns wide

http//hea-www.harvard.edu/HRC/mcp/mcp.html
50
MCP array structure
http//hea-www.harvard.edu/HRC/mcp/mcp.html
51
MCP fabrication
http//hea-www.harvard.edu/HRC/mcp/mcp.html
52
Disadvantages of Photomultiplers as sensors

• Need expensive and fiddly high vacuum equipment
• Expensive
• Fragile
• Bulky

53
Photoconductors

• As well as liberating electrons from the surface
  of materials, we can excite mobile electrons
  inside materials
• The most useful class of materials to do this
  are semiconductors
• The mobile electrons can be measured as a
  current proportional to the intensity of the
  incident radiation
• Need to understand semiconductors.

54
Photoelecric effect with Energy Bands
Evac
Ef
Semiconductor Band gap EgEc-Ev
55
Photoconductivity
56
Photoconductors

• Eg (1 eV) can be made smaller than metal work
  functions f (5 eV)
• Only photons with Energy EhfgtEg are detected
• This puts a lower limit on the frequency detected
• Broadly speaking, metals work with UV,
  semiconductors with optical

57
Band gap Engineering

• Semiconductors can be made with a band gap
  tailored for a particular frequency, depending on
  the application.
• Wide band gap semiconductors good for UV light
• III-V semiconductors promising new materials

58
Example A GaN based UV detector
This is a photoconductor
59
Lecture 13
60
The photoelectric effect

• Photoelectric effectWhen light is incident on
  certain metallic surfaces, photoelectrons are
  emitted.
• Einstein applied the idea of light quanta In a
  photoemission process, a single photon gives up
  all its energy to a single electron.

Energy to free electron
Energy of photon
KE of emitted electron


61
The Photoelectric Effect experiment
Metal surfaces in a vacuum eject electrons when
irradiated by UV light.
62
PE effect5 Experimental observations

1. If V is kept constant, the photoelectric current
   ip increases with increasing UV intensity.
2. Photoelectrons are emitted less than 1 nS after
   surface illumination
3. For a given surface material, electrons are
   emitted only if the incident radiation is at or
   above a certain frequency, independent of
   intensity.
4. The maximum kinetic energy, Kmax, of the
   photoelectrons is independent of the light
   intensity I.
5. The maximum kinetic energy, Kmax of the
   photoelectrons depends on the frequency of the
   incident radiation.

63
Failure of Classcial Theory
Observation 1 is in perfect agreement with
classical expectations Observation 2 Cannot
explain this. Very weak intensity should take
longer to accumulate energy to eject
electrons Observation 3 Cannot explain this
either. Classically no relation between frequency
and energy. Observations 4 and 5 Cannot be
explained at all by classical E/M waves.
.
Bottom line Classical explanation fails badly.
64
Quantum Explanation.

• Einstein expanded Plancks hypothesis and
  applied it directly to EM radiation
• EM radiation consists of bundles of energy
  (photons)
• These photons have energy E hf
• If an electron absorbs a photon of energy E hf
  in order to escape the surface it uses up energy
  f, called the work function of the metal
• f is the binding energy of the electron to the
  surface
• This satisfies all 5 experimental observations

.
65
Photoelectric effect

• hf KE f
• ( f work function minimum energy needed to
  extract an electron.)
• fo threshold freq, below which no
  photoemission occurs

KE
x
.
x
x
x
f0
f (Hz)
66
Application Film soundtracks
Sound Track

Phototube
Light Source
???speaker
67
Example A GaN based UV detector
This is a photoconductor
68
Response Function of UV detector
69
Choose the material for the photon energy
required.

• Band-Gap adjustable by adding Al from 3.4 to 6.2
  eV
• Band gap is direct ( efficient)
• Material is robust

70
The structure of a LED/Photodiode
71
Characterization of Detectors

• NEP noise equivalent power
• noise current (A/?Hz)/Radiant
  sensitivity (A/W)
• D detectivity ?area/NEP
• IR cut-off
• maximum current
• maximum reverse voltage
• Field of view
• Junction capacitance

72
Photoconductors

• As well as liberating electrons from the surface
  of materials, we can excite mobile electrons
  inside materials
• The most useful class of materials to do this
  are semiconductors
• The mobile electrons can be measured as a
  current proportional to the intensity of the
  incident radiation
• Need to understand semiconductors.

73
Photoelecric effect with Energy Bands
Evac
Ef
Semiconductor Band gap EgEc-Ev
74
Photoconductivity
75
Photodiodes

• Photoconductors are not always sensitive enough
• Use a sandwich of doped semiconductors to create
  a depletion region with an intrinsic electric
  field
• We will return to these once we know more about
  atomic structure

76
Orientation

• Previously, we considered detection of photons.
• Next, we develop our understanding of photon
  generation
• We need to consider atomic structure of atoms
  and molecules

77
Line Emission Spectra

• The emission spectrum from an exited material
  (flame, electric discharge) consists of sharp
  spectral lines
• Each atom has its own characteristic spectrum.
• Hydrogen has four spectral lines in the visible
  region and many UV and IR lines not visible to
  the human eye
• The wave picture of electromagnetic radiation
  completely fails to explain these lines (!)

78
Atomic Physics/Line Spectra
The absorption spectrum for hydrogen dark
absorption lines occur at the same wavelengths as
emission lines.
79
Atomic Physics/Line Spectra
80
Rutherfords Model
81
Fatal problems !

• Problem 1 From the Classical Maxwells Equation,
  an accelerating electron emits radiation, losing
  energy.
• This radiation covers a
• continuous range in frequency,
• contradicting observed line spectra .
• Problem 2 Rutherfords model failed to account
  for the stability of the atom.

82
Bohrs Model

• Assumptions
• Electrons can exist only in stationary states
• Dynamical equilibrium governed by Newtonian
  Mechanics
• Transitions between different stationary states
  are accompanied by emission or absorption of
  radiation with frequency ?E hf

83
Transitions between states
hf
E3
E3 - E2 hf
E2
E1
Nucleus
84
How big is the Bohr Hydrogen Atom?
Rna0n2/Z2 Rnradius of atomic orbit number
n a0Bohr radius 0.0629 nm Zatomic numner of
element
Exercise What is the diameter of the hydrogen
atom?
85
What energy Levels are allowed?
86
Exercise

• A hydrogen atom makes a transition between the
  n2 state and the n1 state. What is the
  wavelength of the light emitted?
• Step1 Find out the energy of the photon
• E113.6 eV E213.6/43.4 eV
• hence the energy of the emitted photon is 10.2
  eV
• Step 2 Convert energy into wavelength.
• Ehf, hence fE/h 10.21.6x10-19/6.63x10-34
  2.46x1015 Hz
• Step 3 Convert from frequency into wavelength
• ?c/f 3x108/2.46x1015 121.5 nm

87
Emission versus absorption
Emission
Absorption
Efinal
Einitial
Efinal
Einitial
hf Efinal - Einitial
hf Efinal - Einitial
Explains Hydrogen spectra
88
What happens when we have more than one electron?
89
What happens when we have more than one electron?

• Apply rules
• Pauli principle only two electrons per energy
  level
• Fill the lowest energy levels first
• In real atoms the energy levels are more
  complicated than suggested by the Bohr theory

Empty
90
Atomic Physics X-rays

• How are X-rays produced?
• High energy electrons are fired at high atomic
  number targets. Electrons will be decelerated
  emitting X-rays.
• Energy of electron given by the applied
  potential (EqV)

91
X-rays

• The X-ray spectrum
• consists of two parts
• 1. A continuous
• spectrum
• 2. A series of sharp
• lines.

Intensity
0.5 A0
?
92

X-rays

• The continuous spectrum depends on the voltage
  across the tube and does not depend on the target
  material.
• This continuous spectrum is explained by the
  decelerating electron as it enters the metal

Intensity
25 keV
15 keV
0.83 A0
0.5 A0
?
93
Atomic Physics/X-rays

• The characteristic spectral lines depend on the
  target material.
• These Provides a unique signature of the
  targets atomic structure
• Bohrs theory was used to understand the origin
  of these lines

94
Atomic Physics X-rays
The K-shell corresponds to n1 The L-shell
corresponds to n2 M is n2, and so on
95
Atomic Spectra X-rays
Example Estimate the wavelength of the X-ray
emitted from a tantalum target when an electron
from an n4 state makes a transition to an empty
n1 state (Ztantalum 73)
96
Emission from tantalum
97
Atomic Physics X-rays
The X-ray is emitted when an e from an n4 states
falls into the empty n1 state
Ei -13.6Z2/n2 -(73)2(13.6 eV)/ 42 -4529
eV Ef -13.6(73)2/12 -72464 eV hf Ei- Ef
72474-4529 67945 eV 67.9 keV What is the
wavelength?
Ans 0.18 Å
98
Using X-rays to probe structure

• X-rays have wavelengths of the order of 0.1 nm.
  Therefore we expect a grating with a periodicity
  of this magnitude to strongly diffract X-rays.
• Crystals have such a spacing! Indeed they do
  diffract X-rays according to Braggs law
• 2dsin?? n?
• We will return to this later in the course when
  we discuss sensors of structure

99
Line Width

• Real materials emit or absorb light over a small
  range of wavelengths
• Example here is Neon

100
Stimulated emission
E2 - E1 hf
E2
E1
Two identical photons
Same - frequency - direction - phase -
polarisation
101
Lasers

• LASER - acronym for
• Light Amplification by Stimulated Emission of
  Radiation
• produce high intensity power at a single
  frequency (i.e. monochromatic)

102
Principles of Lasers

• Usually have more atoms in low(est) energy levels
• Atomic systems can be pumped so that more atoms
  are in a higher energy level.
• Requires input of energy
• Called Population Inversion achieved via
• Electric discharge
• Optically
• Direct current

103
Population inversion
Lots of atoms in this level
N2
Energy
N1
Few atoms in this level
Want N2 - N1 to be as large as possible
104
Population Inversion (3 level System)
E2 (pump state), t2
ts gtt2
E1 (metastable- state), ts
Pump light hfo
Laser output hf
E1 (Ground state)
105
Light Amplification

• Light amplified by passing light through a medium
  with a population inversion.
• Leads to stimulated emission

106
Laser
107
Laser

• Requires a cavity enclosed by two mirrors.
• Provides amplification
• Improves spectral purity
• Initiated by spontaneous emission

108
Laser Cavity

• Cavity possess modes
• Analagous to standing waves on a string
• Correspond to specific wavelengths/frequencies
• These are amplified

109
Spectral output
110
Properties of Laser Light.

• Can be monochromatic
• Coherent
• Very intense
• Short pulses can be produced

111
Types of Lasers

• Large range of wavelengths available
• Ammonia (microwave) MASER
• CO2 (far infrared)
• Semiconductor (near-infrared, visible)
• Helium-Neon (visible)
• ArF excimer (ultraviolet)
• Soft x-ray (free-electron, experimental)

112
Lecture 16
113
Molecular Spectroscopy

• Molecular Energy Levels
• Vibrational Levels
• Rotational levels
• Population of levels
• Intensities of transitions
• General features of spectroscopy
• An example Raman Microscopy
• Detection of art forgery
• Local measurement of temperature

114
Molecular Energies
Quantum
Classical
E4
E3
Energy
E2
E1
E0
115
Molecular Energy Levels
Electronic orbital
Vibrational
Translation Nuclear Spin Electronic Spin Rotation
Vibration Electronic Orbital
Rotational
Increasing Energy
etc.
Etotal Eorbital Evibrational
Erotational ..
116
Molecular Vibrations

• Longitudinal Vibrations along molecular axis
• E(n1/2)hf where f is the
  classical frequency of the oscillator
• 
  where k is the spring constant
• Energy Levels equally spaced
• How can we estimate the spring constant?

r
k
m
M
? Mm/(Mm)
Atomic mass concentrated at nucleus
k f (r)
117
Molecular Vibrations
Hydrogen molecules, H2, have ground state
vibrational energy of 0.273eV. Calculate force
constant for the H2 molecule (mass of H is 1.008
amu)

• Evib(n1/2)hf ? f 0.273eV/(1/2(h))
• 2.07x1013 Hz
• To determine k we need µ
• µ(Mm)/(Mm) (1.008)2/2(1.008) amu
• (0.504)1.66x10-27kg 0.837x10-27kg
• k µ(2pf)2 576 N/m

118
Molecular Rotations

• Molecule can also rotate about its centre of mass
• v1 wR1 v2 wR2
• L M1v1R1 M2v2R2
• (M1R12 M2R22)w
• Iw
• EKE 1/2M1v121/2M2v22
• 1/2Iw2

M2
M1
R2
R1
119
Molecular Rotations

• Hence, Erot L2/2I
• Now in fact L2 is quantized and L2l(l1)h2/4p2
• Hence Erotl(l1)(h2/4p2)/2I
• Show that DErot(l1) h2/4p2/I. This is not
  equally spaced
• Typically DErot50meV (i.e for H2)

120
Populations of Energy Levels

• Depends on the relative size of kT and DE

?EltltkT
?EgtkT
?EkT
?E
(Virtually) all molecules in ground state
States almost equally populated
121
Intensities of Transitions

• Quantum Mechanics predicts the degree to which
  any particular transition is allowed.
• Intensity also depends on the relative population
  of levels

hv
2hv
hv
hv
hv
Strong absorption
Weak emission
Transition saturated
122
General Features of Spectroscopy

• Peak Height or intensity
• Frequency
• Lineshape or linewidth

123
Raman Spectroscopy

• Raman measures the vibrational modes of a solid
• The frequency of vibration depends on the atom
  masses and the forces between them.
• Shorter bond lengths mean stronger forces.

124
Raman Spectroscopy Cont...

• Incident photons typically undergo elastic
  scattering.
• Small fraction undergo inelastic ? energy
  transferred to molecule.
• Raman detects change in vibrational energy of a
  molecule.

Sample
Laser In
Lens
Monochromator
CCD array
125
Raman Microscope
126
Detecting Art Forgery

• Ti-white became available only circa 1920.
• The Roberts painting shows clear evidence of Ti
  white but is dated 1899

Pb white
Ti white
Tom Roberts, Track To The Harbour dated 1899
127
Raman Spectroscopy and the Optical Measurement of
Temperature

• Probability that a level is occupied is
  proportional to exp(DE/kT)

128
Lecture 17
129
Optical Fibre Sensors

• Non-Electrical
• Explosion-Proof
• (Often) Non-contact
• Light, small, snakey gt Remotable
• Easy(ish) to install
• Immune to most EM noise
• Solid-State (no moving parts)
• Multiplexing/distributed sensors.

130
Applications

• Lots of Temp, Pressure, Chemistry
• Automated production lines/processes
• Automotive (T,P,Ch,Flow)
• Avionic (T,P,Disp,rotn,strain,liquid level)
• Climate control (T,P,Flow)
• Appliances (T,P)
• Environmental (Disp, T,P)

131
Optical Fibre Principles

• Cladding glass or Polymer
• Core glass, silica, sapphire
• TIR keeps light in fibre
• Different sorts of cladding graded index, single
  index, step index.

132
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133
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134
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135
Optical Fibre Principles

• Snells Law n1sin?1n2sin?2
• ?crit arcsin(n2/n1)
• Cladding reduces entry angle
• Only some angles (modes) allowed

136
Optical Fibre Modes
137
Phase and Intensity Modulation methods

• Optical fibre sensors fall into two types
• Intensity modulation uses the change in the
  amount of light that reaches a detector, say by
  breaking a fibre.
• Phase Modulation uses the interference between
  two beams to detect tiny differences in path
  length, e.g. by thermal expansion.

138
Intensity modulated sensors

• Axial displacement 1/r2 sensitivity
• Radial Displacement

139
Microbending (1)

• Microbending
• Bent fibers lose energy
• (Incident angle changes to less than critical
  angle)

140
Microbending (2)

• Microbending
• Jaws close a bit, less transmission
• Give jaws period of light to enhance effect
• Applications
• Strain gauge
• Traffic counting

141
More Intensity modulated sensors

• Frustrated Total Internal Reflection
• Evanescent wave bridges small gap and so light
  propagates
• As the fibers move (say car passes), the gap
  increases and light is reflected

Evanescent Field Decay _at_514nm
142
More Intensity modulated sensors

• Frustrated Total Internal Reflection Chemical
  sensing
• Evanescent wave extends into cladding
• Change in refractive index of cladding will
  modify output intensity

143
Disadvantages of intensity modulated sensors

• Light losses can be interpreted as change in
  measured property
• Bends in fibres
• Connecting fibres
• Couplers
• Variation in source power

144
Phase modulated sensors

• Bragg modulators
• Periodic changes in refractive index
• Bragg wavelenght (?b) which satisfies ?b2nD is
  reflected
• Separation (D) of same order as than mode
  wavelength

145
Phase modulated sensors
Period,D
?b2nD

• Multimode fibre with broad input spectrum
• Strain or heating changes n so reflected
  wavelength changes
• Suitable for distributed sensing

146
Phase modulated sensors distributed sensors
147
Temperature Sensors

• Reflected phosphorescent signal depends on
  Temperature
• Can use BBR, but need sapphire waveguides since
  silica/glass absorbs IR

148
Phase modulated sensors

• Fabry-Perot etalons
• Two reflecting surfaces separated by a few
  wavelengths
• Air gap forms part of etalon
• Gap fills with hydrogen, changing refractive
  index of etalon and changing allowed transmitted
  frequencies.

149
Digital switches and counters

• Measure number of air particles in air or water
  gap by drop in intensity
• Environmental monitoring
• Detect thin film thickness in manufacturing
• Quality control
• Counting things
• Production line, traffic.

150
NSOM/AFM Combined
Bent NSOM/AFM Probe

• Optical resolution determined by diffraction
  limit (?)
• Illuminating a sample with the "near-field" of a
  small light source.
• Can construct optical images with resolution
  well beyond usual "diffraction limit", (typically
  50 nm.)

SEM - 70nm aperture
151
NSOM Setup

• Ideal for thin films or coatings which are
  several hundred nm thick on transparent
  substrates (e.g., a round, glass cover slip).

152
Lecture 12
153
Atomic Physics and Lasers

• The idea of a photon
• Black body radiation
• Photoelectric Effect
• The structure of the atom
• How does a Laser work? Interaction of lasers with
  matter
• Laser safety
• Applications
• Spectroscopy, detection of art forgery, flow
  cytometry, eye surgery.

154
The idea of a photon

• What is light?
• A wave?
• Well yes, but.
• The wave picture failed to explain physical
  phenomena including
• the spectrum of a blackbody
• the photoelectric effect
• line spectra emitted by atoms

155
Light from a hot object...
Vibrational motion of particles produces
light(we call the light Thermal Radiation)
156


The first clue that something was very, very
wrongBlackbody radiation

• What is a blackbody?

• An object which emits or absorbs all the
  radiation incident on it.
• Typical black bodies
• A light globe
• A box with a small hole in it.

157
Example of a Blackbody
A BLACKBODY
158
Example of a Blackbody
We measure radiation as a function of frequency
(wavelength)
159
A Thermal Spectrum
How does a thermal spectrum change when you
change T?
160
Thermal Radiation
T Temp. in Kelvin
Total energy emitted by an object (or Luminosity
W/m2)
Wavelength where flux is a maximum
s 5.7 x 10-8 W/(m2.K4)
k 2.898 x 10-3 m.K
Stefans Law
Wiens Law
161
(No Transcript)
162
Light and matter interact

• The spectra we have looked at are for ideal
  objects that are perfect absorbers and emitters
  of light

Light is later emitted
Light is perfectly absorbed
A BLACKBODY
163
Problems with wave theory of light

• Take a Blackbody witha temperature, T
• Calculate how the spectrum would look if light
  behaved like a wave (Lord Rayleigh)
• Compare with what isactually observed

164
Max Plank Solved the problem in 1900

• Oscillators cannot have any energy! They can be
  in states with fixed amounts of energy.
• The oscillators change state by
  emitting/absorbingpackets with a fixed amounts
  of energy

Max Plank
165

Atomic Physics/Blackbody

• Max Planck (1858-1947) was impressed by the
  fact
• spectrum of a black body was a universal
  property.

E nhf

• To get agreement between the experiment and the
  theory, Planck proposed a radical idea Light
  comes in packets of energy called photons, and
  the energy is given by E nhf

The birth of the quantum theory Plancks
hypothesis
166
The birth of the Photon

• In 1906, Einstein proved that Plancks radiation
  law could be derived only if the energy of each
  oscillator is quantized.
• En nhf n 0, 1, 2, 3, 4,...
  
  
• hPlancks constant 6.626x10 -34 J.s
• ffrequency in Hz Eenergy in Joules (J).

• Einstein introduced the idea that radiation
• equals a collection of discrete energy quanta.
• G.N. Lewis in 1926 named quanta Photons.

167
Atomic Physics/Photon

• The energy of each photon
• E hf hPlancks constant
• ffrequency

Ex. 1. Yellow light has a frequency of 6.0 x
1014 Hz. Determine the energy carried by a
quantum of this light. If the energy flux of
sunlight reaching the earths surface is 1000
Watts per square meter, find the number of
photons in sunlight that reach the earths
surface per square meter per second.

Ans. 2.5 eV and 2.5 x 10 21 photons / m 2
/s
168
Shining light onto metals
Light in
Nothing happens
METAL
169
Shining light onto metals
METAL
170
The Photoelectric Effect

• When light is incident on certain metallic
  surfaces, electrons are emitted the
  Photoelectric Effect (Serway and Jewett 28.2)
• Einstein A single photon gives up all its
  energy to a single electron

EPhoton EFree EKinetic
Need at least this much energy to free the
electron
Whatever is left makes it move
171
The Photoelectric Effect
172
Application of Photoelectric Effect
Soundtrack on Celluloid film
To speaker
173
Another Blow for classical physics Line Spectra

• The emission spectrum from a rarefied gas through
  which an electrical discharge passes consists of
  sharp spectral lines.
• Each atom has its own characteristic spectrum.
• Hydrogen has four spectral lines in the visible
  region and many UV and IR lines not visible to
  the human eye.
• The wave picture failed to explain these lines.

174
Atomic Physics/Line spectra
400 500
600
?(nm)

H
Emission spectrum for hydrogen
The absorption spectrum for hydrogen dark
absorption lines occur at the same wavelengths as
emission lines.
175
Atomic Physics/Line Spectra
176
So what is light?

• Both a wave and a particle. It can be both, but
  in any experiment only its wave or its particle
  nature is manifested. (Go figure!)

177
Two revolutions The Nature of light and the
nature of matter

• Light has both a particle and wave nature
• Wave nature
• Diffraction, interference
• Particle nature
• Black body radiation, photoelectric effect, line
  spectra
• Need to revise the nature of matter (it turns out
  that matter also has both a particle and wave
  nature

178

The spectrum from a blackbody

• Empirically
• ?(max)T constant,
• Hotter whiter
• The wave picture (Rayleigh-Jeans) failed to
  explain the distribution of the energy versus
  wavelength. UV Catastrophe!!!!

6000K
Rayleigh- Jeans
Relative Intensity
Observed
5000K
0 2 4 6 8 10
? (10 -7 m)
179
Photoelectric Effect
Light in
e
Electron out
METAL
180
The Photoelectric Effect

• Photoelectric effectWhen light is incident on
  certain metallic surfaces, photoelectrons are
  emitted.
• Einstein applied the idea of light quanta
• In a photoemission process, a single photon
  gives up all its energy to a single electron.

Energy of photon
Energy to free electron


KE of emitted electron
181
Atomic Physics/Photoelectric Effect

?work function minimum energy needed to extract
an electron.
hf KE ?
KE
x
fo threshold freq below which no photoemission
occurs.
x
x
x
f0
f, Hz
182
Atomic Physics/The Photoelectric
Effect-Application
The sound on a movie film
Sound Track

Phototube
Light Source
???speaker
183
Lecture 13
184
The photoelectric effect

• Photoelectric effectWhen light is incident on
  certain metallic surfaces, photoelectrons are
  emitted.
• Einstein applied the idea of light quanta In a
  photoemission process, a single photon gives up
  all its energy to a single electron.

Energy to free electron
Energy of photon
KE of emitted electron


185
The Photoelectric Effect experiment
Metal surfaces in a vacuum eject electrons when
irradiated by UV light.
186
PE effect5 Experimental observations

1. If V is kept constant, the photoelectric current
   ip increases with increasing UV intensity.
2. Photoelectrons are emitted less than 1 nS after
   surface illumination
3. For a given surface material, electrons are
   emitted only if the incident radiation is at or
   above a certain frequency, independent of
   intensity.
4. The maximum kinetic energy, Kmax, of the
   photoelectrons is independent of the light
   intensity I.
5. The maximum kinetic energy, Kmax of the
   photoelectrons depends on the frequency of the
   incident radiation.

187
Failure of Classcial Theory
Observation 1 is in perfect agreement with
classical expectations Observation 2 Cannot
explain this. Very weak intensity should take
longer to accumulate energy to eject
electrons Observation 3 Cannot explain this
either. Classically no relation between frequency
and energy. Observations 4 and 5 Cannot be
explained at all by classical E/M waves.
.
Bottom line Classical explanation fails badly.
188
Quantum Explanation.

• Einstein expanded Plancks hypothesis and
  applied it directly to EM radiation
• EM radiation consists of bundles of energy
  (photons)
• These photons have energy E hf
• If an electron absorbs a photon of energy E hf
  in order to escape the surface it uses up energy
  f, called the work function of the metal
• f is the binding energy of the electron to the
  surface
• This satisfies all 5 experimental observations

.
189
Photoelectric effect

• hf KE f
• ( f work function minimum energy needed to
  extract an electron.)
• fo threshold freq, below which no
  photoemission occurs

KE
x
.
x
x
x
f0
f (Hz)
190
Application Film soundtracks
Sound Track

Phototube
Light Source
???speaker
191
Example A GaN based UV detector
This is a photoconductor
192
Response Function of UV detector
193
Choose the material for the photon energy
required.

• Band-Gap adjustable by adding Al from 3.4 to 6.2
  eV
• Band gap is direct ( efficient)
• Material is robust

194
The structure of a LED/Photodiode
195
Characterization of Detectors

• NEP noise equivalent power
• noise current (A/?Hz)/Radiant
  sensitivity (A/W)
• D detectivity ?area/NEP
• IR cut-off
• maximum current
• maximum reverse voltage
• Field of view
• Junction capacitance

196
Photomultipliers
e
e
e
e
hf
e
e
PE effect
Secondary electron emission
Electron multiplication
197
Photomultiplier tube

• Combines PE effect with electron multiplication
  to provide very high detection sensitivity
• Can detect single photons.

198
Microchannel plates

• The principle of the photomultiplier tube can be
  extended to an array of photomultipliers
• This way one can obtain spatial resolution
• Biggest application is in night vision goggles
  for military and civilian use

199
Microchannel plates

• MCPs consist of arrays of tiny tubes
• Each tube is coated with a photomultiplying film
• The tubes are about 10 microns wide

http//hea-www.harvard.edu/HRC/mcp/mcp.html
200
MCP array structure
http//hea-www.harvard.edu/HRC/mcp/mcp.html
201
MCP fabrication
http//hea-www.harvard.edu/HRC/mcp/mcp.html
202
Disadvantages of Photomultiplers as sensors

• Need expensive and fiddly high vacuum equipment
• Expensive
• Fragile
• Bulky

203
Photoconductors

• As well as liberating electrons from the surface
  of materials, we can excite mobile electrons
  inside materials
• The most useful class of materials to do this
  are semiconductors
• The mobile electrons can be measured as a
  current proportional to the intensity of the
  incident radiation
• Need to understand semiconductors.

204
Photoelecric effect with Energy Bands
Evac
Ef
Semiconductor Band gap EgEc-Ev
205
Photoconductivity
206
Photoconductors

• Eg (1 eV) can be made smaller than metal work
  functions f (5 eV)
• Only photons with Energy EhfgtEg are detected
• This puts a lower limit on the frequency detected
• Broadly speaking, metals work with UV,
  semiconductors with optical

207
Band gap Engineering

• Semiconductors can be made with a band gap
  tailored for a particular frequency, depending on
  the application.
• Wide band gap semiconductors good for UV light
• III-V semiconductors promising new materials

208
Example A GaN based UV detector
This is a photoconductor
209
Response Function of UV detector
210
Choose the material for the photon energy
required.

• Band-Gap adjustable by adding Al from 3.4 to 6.2
  eV
• Band gap is direct ( efficient)
• Material is robust

211
Photodiodes

• Photoconductors are not always sensitive enough
• Use a sandwich of doped semiconductors to create
  a depletion region with an intrinsic electric
  field
• We will return to these once we know more about
  atomic structure

212
The structure of a LED/Photodiode
213
Characterization of Detectors

• NEP noise equivalent power
• noise current (A/?Hz)/Radiant
  sensitivity (A/W)
• D detectivity ?area/NEP
• IR cut-off
• maximum current
• maximum reverse voltage
• Field of view
• Junction capacitance

214
Lecture 15
215
Orientation

• Previously, we considered detection of photons.
• Next, we develop our understanding of photon
  generation
• We need to consider atomic structure of atoms
  and molecules

216
Line Emission Spectra

• The emission spectrum from an exited material
  (flame, electric discharge) consists of sharp
  spectral lines
• Each atom has its own characteristic spectrum.
• Hydrogen has four spectral lines in the visible
  region and many UV and IR lines not visible to
  the human eye
• The wave picture of electromagnetic radiation
  completely fails to explain these lines (!)

217
Atomic Physics/Line Spectra
The absorption spectrum for hydrogen dark
absorption lines occur at the same wavelengths as
emission lines.
218
Atomic Physics/Line Spectra
219
Rutherfords Model
220
Fatal problems !

• Problem 1 From the Classical Maxwells Equation,
  an accelerating electron emits radiation, losing
  energy.
• This radiation covers a
• continuous range in frequency,
• contradicting observed line spectra .
• Problem 2 Rutherfords model failed to account
  for the stability of the atom.

221
Bohrs Model

• Assumptions
• Electrons can exist only in stationary states
• Dynamical equilibrium governed by Newtonian
  Mechanics
• Transitions between different stationary states
  are accompanied by emission or absorption of
  radiation with frequency ?E hf

222
Transitions between states
hf
E3
E3 - E2 hf
E2
E1
Nucleus
223
How big is the Bohr Hydrogen Atom?
Rna0n2/Z2 Rnradius of atomic orbit number
n a0Bohr radius 0.0629 nm Zatomic numner of
element
Exercise What is the diameter of the hydrogen
atom?
224
What energy Levels are allowed?
225
Exercise

• A hydrogen atom makes a transition between the
  n2 state and the n1 state. What is the
  wavelength of the light emitted?
• Step1 Find out the energy of the photon
• E113.6 eV E213.6/43.4 eV
• hence the energy of the emitted photon is 10.2
  eV
• Step 2 Convert energy into wavelength.
• Ehf, hence fE/h 10.21.6x10-19/6.63x10-34
  2.46x1015 Hz
• Step 3 Convert from frequency into wavelength
• ?c/f 3x108/2.46x1015 121.5 nm

226
Emission versus absorption
Emission
Absorption
Efinal
Einitial
Efinal
Einitial
hf Efinal - Einitial
hf Efinal - Einitial
Explains Hydrogen spectra
227
What happens when we have more than one electron?
228
What happens when we have more than one electron?

• Apply rules
• Pauli principle only two electrons per energy
  level
• Fill the lowest energy levels first
• In real atoms the energy levels are more
  complicated than suggested by the Bohr theory

Empty
229
What happens when we have more than one electron?

• Apply rules
• Pauli principle only two electrons per energy
  level
• Fill the lowest energy levels first
• In real atoms the energy levels are more
  complicated than suggested by the Bohr theory

Empty
230
Atomic Physics X-rays

• How are X-rays produced?
• High energy electrons are fired at high atomic
  number targets. Electrons will be decelerated
  emitting X-rays.
• Energy of electron given by the applied
  potential (EqV)

231
X-rays

• The X-ray spectrum
• consists of two parts
• 1. A continuous
• spectrum
• 2. A series of sharp
• lines.

Intensity
0.5 A0
?
232

X-rays

• The continuous spectrum depends on the voltage
  across the tube and does not depend on the target
  material.
• This continuous spectrum is explained by the
  decelerating electron as it enters the metal

Intensity
25 keV
15 keV
0.83 A0
0.5 A0
?
233
Atomic Physics/X-rays

• The characteristic spectral lines depend on the
  target material.
• These Provides a unique signature of the
  targets atomic structure
• Bohrs theory was used to understand the origin
  of these lines

234
Atomic Physics X-rays
The K-shell corresponds to n1 The L-shell
corresponds to n2 M is n2, and so on
235
Atomic Spectra X-rays
Example Estimate the wavelength of the X-ray
emitted from a tantalum target when an electron
from an n4 state makes a transition to an empty
n1 state (Ztantalum 73)
236
Emission from tantalum
237
Atomic Physics X-rays
The X-ray is emitted when an e from an n4 states
falls into the empty n1 state
Ei -13.6Z2/n2 -(73)2(13.6 eV)/ 42 -4529
eV Ef -13.6(73)2/12 -72464 eV hf Ei- Ef
72474-4529 67945 eV 67.9 keV What is the
wavelength?
Ans 0.18 Å
238
Using X-rays to probe structure

• X-rays have wavelengths of the order of 0.1 nm.
  Therefore we expect a grating with a periodicity
  of this magnitude to strongly diffract X-rays.
• Crystals have such a spacing! Indeed they do
  diffract X-rays according to Braggs law
• 2dsin?? n?
• We will return to this later in the course when
  we discuss sensors of structure

239
Line Width

• Real materials emit or absorb light over a small
  range of wavelengths
• Example here is Neon

240
Stimulated emission
E2 - E1 hf
E2
E1
Two identical photons
Same - frequency - direction - phase -
polarisation
241
Lasers

• LASER - acronym for
• Light Amplification by Stimulated Emission of
  Radiation
• produce high intensity power at a single
  frequency (i.e. monochromatic)

242
Principles of Lasers

• Usually have more atoms in low(est) energy levels
• Atomic systems can be pumped so that more atoms
  are in a higher energy level.
• Requires input of energy
• Called Population Inversion achieved via
• Electric discharge
• Optically
• Direct current

243
Population inversion
Lots of atoms in this level
N2
Energy
N1
Few atoms in this level
Want N2 - N1 to be as large as possible
244
Population Inversion (3 level System)
E2 (pump state), t2
ts gtt2
E1 (metastable- state), ts
Pump light hfo
Laser output hf
E1 (Ground state)
245
Light Amplification

• Light amplified by passing light through a medium
  with a population inversion.
• Leads to stimulated emission

246
Laser
247
Laser

• Requires a cavity enclosed by two mirrors.
• Provides amplification
• Improves spectral purity
• Initiated by spontaneous emission

248
Laser Cavity

• Cavity possess modes
• Analagous to standing waves on a string
• Correspond to specific wavelengths/frequencies
• These are amplified

249
Spectral output
250
Properties of Laser Light.

• Can be monochromatic
• Coherent
• Very intense
• Short pulses can be produced

251
Types of Lasers

• Large range of wavelengths available
• Ammonia (microwave) MASER
• CO2 (far infrared)
• Semiconductor (near-infrared, visible)
• Helium-Neon (visible)
• ArF excimer (ultraviolet)
• Soft x-ray (free-electron, experimental)

252
Lecture 16
253
Molecular Spectroscopy

• Molecular Energy Levels
• Vibrational Levels
• Rotational levels
• Population of levels
• Intensities of transitions
• General features of spectroscopy
• An example Raman Microscopy
• Detection of art forgery
• Local measurement of temperature

254
Molecular Energies
Quantum
Classical
E4
E3
Energy
E2
E1
E0
255
Molecular Energy Levels