Transcript optical_sensors_12sept

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.
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
Light from a hot object...
Vibrational motion of particles produces
light
(we call the light “Thermal Radiation”)
The first clue that something was very,
very wrong…Blackbody 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.
Example of a Blackbody
A BLACKBODY
Example of a Blackbody
We measure radiation as a function of frequency (wavelength)
A Thermal Spectrum
How does a thermal
spectrum change when
you change T?
Thermal Radiation
k
T = Temp.
4
 
L  T
in Kelvin
T
MAX
Wavelength where
flux is a maximum
k = 2.898 x 10-3 m.K
Wien’s Law
Total energy emitted
by an object
(or Luminosity W/m2)
 = 5.7 x 10-8 W/(m2.K4)
Stefan’s Law
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
Oscillators
Matter at some temperature T
A BLACKBODY
•
•
•
Problems with wave theory of
light
Not so good here
Take a Blackbody with
a temperature, T
Calculate how the spectrum
would look if light behaved
like a wave (Lord Rayleigh)
Compare with what is
actually observed
F
l
u
x
F
l
u
x
Okay here

Max Plank Solved the
problem in 1900
Max Plank
•
Oscillators cannot have
any energy! They can
be in states with fixed
amounts of energy.
•
The oscillators change
state by
emitting/absorbing
packets with a fixed
amounts of energy
Atomic Physics/Blackbody
Max Planck (1858-1947)
was impressed by the fact
spectrum of a black body
was a universal property.

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 = Planck’s
hypothesis
The birth of the Photon
In 1906, Einstein proved that Planck’s radiation
law could be derived only if the energy of each
oscillator is quantized.
En = nhf ;
n = 0, 1, 2, 3, 4,...
h=Planck’s constant= 6.626x10 -34 J.s
f=frequency in Hz; E=energy in Joules (J).
Einstein introduced the idea that radiation
equals a collection of discrete energy quanta.
 G.N. Lewis in 1926 named quanta “Photons”.

Atomic Physics/Photon
The energy of each photon:
E = hf h=Planck’s constant
f=frequency
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 earth’s
surface is 1000 Watts per square meter, find the number
of photons in sunlight that reach the earth’s surface
per square meter per second.
Ans. 2.5 eV and 2.5 x 10 21
photons / m 2 /s
Shining light onto metals
Light in
Nothing happens
METAL
Shining light onto metals
Different Energy
Light in
electrons
come out
METAL
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
The Photoelectric Effect
Kinetic Energy
of electron
Different
metals
fo
Threshold frequency
Frequency of
Light
Application of Photoelectric
Effect
Soundtrack on
Celluloid film
Metal plate
To speaker
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.
Atomic Physics/Line spectra
(nm) 400
500
600
H
Emission spectrum for hydrogen
The absorption spectrum for hydrogen; dark absorption
lines occur at the same wavelengths as emission lines.
Atomic Physics/Line Spectra
-0.85
-1.51
-3.39
Balmer
Visible
Paschen
IR
n=4
n=3
n=2
-13.6
n=1
Lyman UV
R =Rydberg
1
1
1
Constant =
R(
) 1.09737x10 7m-1
nm2
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!)
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
The spectrum from a blackbody
•Empirically:
(max)T = constant,
Hotter = whiter
wave picture (RayleighJeans) failed to explain the
distribution of the energy
versus wavelength. UV
Catastrophe!!!!
6000K
The
RayleighJeans
Observed
5000K
0
2
4
6
 (10 -7 m)
8
10
Photoelectric Effect
Light
in
e
METAL
Electron
out
The Photoelectric Effect
Photoelectric effect=When 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
Atomic Physics/Photoelectric Effect
hf = KE + 
=work function; minimum
energy needed to extract an
electron.
KE
x
x
x
fo = threshold freq
below which no
photoemission occurs.
x
f0
f, Hz
Atomic Physics/The Photoelectric
Effect-Application
The sound on a
movie film
Sound Track
Phototube
Light Source
speaker
The photoelectric effect
• Photoelectric effect=When 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
The Photoelectric Effect
experiment
Metal surfaces in a vacuum eject electrons when irradiated by
UV light.
PE effect:
5 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.
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.
Quantum Explanation.
• Einstein expanded Planck’s 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 φ, called the work function
of the metal
• φ is the binding energy of the electron to the surface
• This satisfies all 5 experimental observations
Photoelectric effect
• hf = KE + φ
• ( φ =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)
Application: Film soundtracks
Sound Track
Phototube
Light Source
speaker
Example: A GaN based UV
detector
This is a photoconductor
5m
Response Function of UV
detector
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
The structure of a
LED/Photodiode
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
Photomultipliers
hf
e
PE effect
e
e
Secondary
electron
emission
e
e
e
Electron
multiplication
Photomultiplier tube
hf
e
Anode
Dynode
-V
• Combines PE effect with electron
multiplication to provide very high detection
sensitivity
• Can detect single photons.
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
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
http://hea-www.harvard.edu/HRC/mcp/mcp.html
MCP array structure
http://hea-www.harvard.edu/HRC/mcp/mcp.html
MCP fabrication
Disadvantages of Photomultiplers
as sensors
• Need expensive and fiddly high vacuum
equipment
• Expensive
• Fragile
• Bulky
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….
Photoelecric effect with Energy Bands
Evac
Evac
Ec
Ef
Ev
Ef
Metal
Semiconductor
Band gap: Eg=Ec-Ev
Photoconductivity
e
To amplifier
Ec
Evac
Ef
Ev
Semiconductor
Photoconductors
• Eg (~1 eV) can be made smaller than metal
work functions (~5 eV)
• Only photons with Energy E=hf>Eg are
detected
• This puts a lower limit on the frequency
detected
• Broadly speaking, metals work with UV,
semiconductors with optical
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
Example: A GaN based UV
detector
This is a photoconductor
5m
Lecture 13
The photoelectric effect
• Photoelectric effect=When 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
The Photoelectric Effect
experiment
Metal surfaces in a vacuum eject electrons when irradiated by
UV light.
PE effect:
5 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.
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.
Quantum Explanation.
• Einstein expanded Planck’s 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 φ, called the work function
of the metal
• φ is the binding energy of the electron to the surface
• This satisfies all 5 experimental observations
Photoelectric effect
• hf = KE + φ
• ( φ =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)
Application: Film soundtracks
Sound Track
Phototube
Light Source
speaker
Example: A GaN based UV
detector
This is a photoconductor
5m
Response Function of UV
detector
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
The structure of a
LED/Photodiode
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
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….
Photoelecric effect with Energy Bands
Evac
Evac
Ec
Ef
Ev
Ef
Metal
Semiconductor
Band gap: Eg=Ec-Ev
Photoconductivity
e
To amplifier
Ec
Evac
Ef
Ev
Semiconductor
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
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
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 (!)
Atomic Physics/Line Spectra
The absorption spectrum for hydrogen: dark absorption lines occur at
the same wavelengths as emission lines.
Atomic Physics/Line Spectra
Rutherford’s Model
Fatal problems !
Problem 1: From the Classical Maxwell’s
Equation, an accelerating electron emits
radiation, losing energy.
This radiation covers a
continuous range in frequency,
contradicting observed line spectra .
Problem 2: Rutherford’s model failed to
account for the stability of the atom.
+Ze
Bohr’s 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
Transitions between states
hf
E3
E3 - E2 = hf
E2
E1
Nucleus
How big is the Bohr Hydrogen Atom?
Rn=a0n2/Z2
Rn=radius of atomic orbit number n
a0=Bohr radius = 0.0629 nm
Z=atomic numner of element
Exercise: What is the diameter of the hydrogen atom?
What energy Levels are allowed?
Exercise
• A hydrogen atom makes a transition between the n=2 state and the
n=1 state. What is the wavelength of the light emitted?
• Step1: Find out the energy of the photon:
• E1=13.6 eV
E2=13.6/4=3.4 eV
• hence the energy of the emitted photon is 10.2 eV
• Step 2: Convert energy into wavelength.
• E=hf,
hence f=E/h =10.2*1.6x10-19/6.63x10-34 = 2.46x1015 Hz
• Step 3: Convert from frequency into wavelength:
• =c/f =3x108/2.46x1015 = 121.5 nm
Emission versus absorption
Emission
Absorption
Einitial
Efinal
Efinal
Einitial
hf = Efinal - Einitial
hf = Efinal - Einitial
Explains Hydrogen spectra
What happens when we have more than
one electron?
What happens when we have more than
one electron?
Apply rules:
Empty
• 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
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 (E=qV)
X-rays
The X-ray spectrum
consists of two parts:
1. A continuous
spectrum
2. A series of sharp
lines.
0.5 A0

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
25 keV
15 keV
0.5 A0 0.83 A0

Atomic Physics/X-rays
• The characteristic
spectral lines depend
on the target material.
• These Provides a
unique signature of the
target’s atomic
structure
• Bohr’s theory was
used to understand the
origin of these lines
Atomic Physics – X-rays
The K-shell
corresponds to
n=1
The L-shell
corresponds to
n=2
M is n=2, and
so on
Atomic Spectra – X-rays
Example:
Estimate the wavelength of the X-ray emitted from a
tantalum target when an electron from an n=4 state
makes a transition to an empty n=1 state (Ztantalum =73)
Emission from tantalum
Atomic Physics – X-rays
The X-ray is emitted when an e from an n=4 states falls into the
empty n=1 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
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 Bragg’s law
2dsin = n
• We will return to this later in the course when we
discuss sensors of structure
Line Width
• Real
materials emit
or absorb
light over a
small range of
wavelengths
• Example
here is Neon
Stimulated emission
E2 - E1 = hf
E2
E1
Two identical photons
Same
- frequency
- direction
- phase
- polarisation
Lasers
• LASER - acronym for
– Light Amplification by Stimulated Emission of
Radiation
– produce high intensity power at a single frequency (i.e.
monochromatic)
Laser
Globe
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
Population inversion
Lots of atoms in this level
Energy
N2
N1
Few atoms in this level
Want N2 - N1 to be as
large as possible
Population Inversion (3 level System)
E2 (pump state), t2
Pump light
ts >t2
E1 (metastablestate), ts
hfo
Laser output
hf
E1 (Ground state)
Light Amplification
Light amplified by passing light through a medium
with a population inversion.
• Leads to stimulated emission
Laser
Laser
Requires a cavity enclosed by two mirrors.
• Provides amplification
• Improves spectral purity
• Initiated by “spontaneous emission”
Laser Cavity
Cavity possess modes
• Analagous to standing waves on a string
• Correspond to specific wavelengths/frequencies
• These are amplified
Spectral output
Properties of Laser Light.
• Can be monochromatic
• Coherent
•Very intense
•Short pulses can be produced
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)
Lecture 16
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
Molecular Energies
Energy
Classical
Quantum
E4
E3
E2
E1
E0
Molecular Energy Levels
Increasing Energy
Translation
Electronic
orbital
Vibrational
Rotational
Nuclear Spin
Electronic Spin
Rotation
Vibration
etc.
Electronic Orbital
Etotal + Eorbital +
Evibrational + Erotational +…..
Molecular Vibrations
• Longitudinal Vibrations along
molecular axis
• E=(n+1/2)hf
where f is the classical
frequency of the oscillator
•
1
f 
2
k

where k is the ‘spring constant
• Energy Levels equally spaced
• How can we estimate the
spring constant?
r
k
m
M
 = Mm/(M+m)
Atomic mass concentrated
at nucleus
k = f (r)
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)
r
• Evib=(n+1/2)hf  f =0.273eV/(1/2(h))
= 2.07x1013 Hz
• To determine k we need μ
μ=(Mm)/(M+m) =(1.008)2/2(1.008) amu
=(0.504)1.66x10-27kg =0.837x10-27kg
• k= μ(2πf)2 =576 N/m
K
m
M
=
Mm/(M+m)
K = f (r)
Molecular Rotations
• Molecule can also rotate
about its centre of mass
• v1 = wR1 ; v2 = wR2
M1
• L = M1v1R1+ M2v2R2
= (M1R12+ M2R22)w
= Iw
• EKE = 1/2M1v12+1/2M2v22
= 1/2Iw2
M2
R1
R2
Molecular Rotations
• Hence, Erot= L2/2I
• Now in fact L2 is quantized and
L2=l(l+1)h2/42
• Hence Erot=l(l+1)(h2/42)/2I
• Show that Erot=(l+1) h2/42/I. This is not
equally spaced
• Typically Erot=50meV (i.e for H2)
Populations of Energy Levels
ΔE<<kT
ΔE=kT
ΔE>kT
ΔE
(Virtually) all
molecules in ground
state
States almost equally
populated
• Depends on
the relative
size of kT
and E
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
Strong absorption
hv
Weak
emission
2hv
hv
Transition
saturated
hv
General Features of Spectroscopy
• Peak Height or
intensity
• Frequency
• Lineshape or
linewidth
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.
r
K
m
M
f vib= (K/)1/2
 = Mm/(M+m)
K = f(r)
Raman Spectroscopy Cont...
Laser In
Sample
Lens
Monochromator
CCD array
•Incident photons typically
undergo elastic scattering.
•Small fraction undergo
inelastic  energy transferred
to molecule.
•Raman detects change in
vibrational energy of a
molecule.
Raman Microscope
100
Detecting Art Forgery
80
YTI S NET NI
• Ti-white became available
only circa 1920.
Pb white
60
40
• The Roberts painting shows
clear evidence of Ti white but
is dated 1899
20
Ti white
0
0
200
400
600
800
-1
WAVENUMBER (cm )
200
150
YTI S NET NI
100
50
0
0
200
400
600
-1
WAVENUMBER (cm )
800
Tom Roberts, ‘Track To The
Harbour’ dated 1899
Raman Spectroscopy and the Optical
Measurement of Temperature
• Probability that a level is occupied is
proportional to exp(E/kT)
Lecture 17
Optical Fibre Sensors
•
•
•
•
•
•
•
•
Non-Electrical
Explosion-Proof
(Often) Non-contact
Light, small, snakey => “Remotable”
Easy(ish) to install
Immune to most EM noise
Solid-State (no moving parts)
Multiplexing/distributed sensors.
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)
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.
Optical Fibre Principles
•
•
•
•
Snell’s Law: n1sin1=n2sin2
crit = arcsin(n2/n1)
Cladding reduces entry angle
Only some angles (modes) allowed
Optical Fibre Modes
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.
Intensity modulated sensors:
• Axial
displacement:
1/r2 sensitivity
• Radial
Displacement
Microbending (1)
Microbending
– Bent fibers lose energy
– (Incident angle
changes to less than
critical angle)
Microbending (2):
Microbending
– “Jaws” close a bit, less
transmission
– Give jaws period of
light to enhance effect
• Applications:
– Strain gauge
– Traffic counting
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 @514nm
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
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
Phase modulated sensors
Bragg modulators:
– Periodic changes in
refractive index
– Bragg wavelenght (λb)
which satisfies λb=2nD is
reflected
– Separation (D) of same
order as than mode
wavelength
Phase modulated sensors
Period,D
λb=2nD
• Multimode fibre with broad input spectrum
• Strain or heating changes n so reflected wavelength changes
• Suitable for distributed sensing
Phase modulated sensors – distributed sensors
Temperature Sensors
• Reflected phosphorescent signal depends on
Temperature
• Can use BBR, but need sapphire waveguides
since silica/glass absorbs IR
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.
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.
NSOM/AFM Combined
•Optical resolution
determined by
Bent NSOM/AFM
Probe
diffraction limit (~λ)
•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
NSOM Setup
Ideal for thin films or
coatings which are
several hundred nm
thick on transparent
substrates (e.g., a
round, glass cover
slip).
Lecture 12
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.
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
Light from a hot object...
Vibrational motion of particles produces
light
(we call the light “Thermal Radiation”)
The first clue that something was very,
very wrong…Blackbody 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.
Example of a Blackbody
A BLACKBODY
Example of a Blackbody
We measure radiation as a function of frequency (wavelength)
A Thermal Spectrum
How does a thermal
spectrum change when
you change T?
Thermal Radiation
k
T = Temp.
4
 
L  T
in Kelvin
T
MAX
Wavelength where
flux is a maximum
k = 2.898 x 10-3 m.K
Wien’s Law
Total energy emitted
by an object
(or Luminosity W/m2)
 = 5.7 x 10-8 W/(m2.K4)
Stefan’s Law
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
Oscillators
Matter at some temperature T
A BLACKBODY
•
•
•
Problems with wave theory of
light
Not so good here
Take a Blackbody with
a temperature, T
Calculate how the spectrum
would look if light behaved
like a wave (Lord Rayleigh)
Compare with what is
actually observed
F
l
u
x
F
l
u
x
Okay here

Max Plank Solved the
problem in 1900
Max Plank
•
Oscillators cannot have
any energy! They can
be in states with fixed
amounts of energy.
•
The oscillators change
state by
emitting/absorbing
packets with a fixed
amounts of energy
Atomic Physics/Blackbody
Max Planck (1858-1947)
was impressed by the fact
spectrum of a black body
was a universal property.

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 = Planck’s
hypothesis
The birth of the Photon
In 1906, Einstein proved that Planck’s radiation
law could be derived only if the energy of each
oscillator is quantized.
En = nhf ;
n = 0, 1, 2, 3, 4,...
h=Planck’s constant= 6.626x10 -34 J.s
f=frequency in Hz; E=energy in Joules (J).
Einstein introduced the idea that radiation
equals a collection of discrete energy quanta.
 G.N. Lewis in 1926 named quanta “Photons”.

Atomic Physics/Photon
The energy of each photon:
E = hf h=Planck’s constant
f=frequency
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 earth’s
surface is 1000 Watts per square meter, find the number
of photons in sunlight that reach the earth’s surface
per square meter per second.
Ans. 2.5 eV and 2.5 x 10 21
photons / m 2 /s
Shining light onto metals
Light in
Nothing happens
METAL
Shining light onto metals
Different Energy
Light in
electrons
come out
METAL
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
The Photoelectric Effect
Kinetic Energy
of electron
Different
metals
fo
Threshold frequency
Frequency of
Light
Application of Photoelectric
Effect
Soundtrack on
Celluloid film
Metal plate
To speaker
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.
Atomic Physics/Line spectra
(nm) 400
500
600
H
Emission spectrum for hydrogen
The absorption spectrum for hydrogen; dark absorption
lines occur at the same wavelengths as emission lines.
Atomic Physics/Line Spectra
-0.85
-1.51
-3.39
Balmer
Visible
Paschen
IR
n=4
n=3
n=2
-13.6
n=1
Lyman UV
R =Rydberg
1
1
1
Constant =
R(
) 1.09737x10 7m-1
nm2
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!)
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
The spectrum from a blackbody
•Empirically:
(max)T = constant,
Hotter = whiter
wave picture (RayleighJeans) failed to explain the
distribution of the energy
versus wavelength. UV
Catastrophe!!!!
6000K
The
RayleighJeans
Observed
5000K
0
2
4
6
 (10 -7 m)
8
10
Photoelectric Effect
Light
in
e
METAL
Electron
out
The Photoelectric Effect
Photoelectric effect=When 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
Atomic Physics/Photoelectric Effect
hf = KE + 
=work function; minimum
energy needed to extract an
electron.
KE
x
x
x
fo = threshold freq
below which no
photoemission occurs.
x
f0
f, Hz
Atomic Physics/The Photoelectric
Effect-Application
The sound on a
movie film
Sound Track
Phototube
Light Source
speaker
Lecture 13
The photoelectric effect
• Photoelectric effect=When 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
The Photoelectric Effect
experiment
Metal surfaces in a vacuum eject electrons when irradiated by
UV light.
PE effect:
5 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.
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.
Quantum Explanation.
• Einstein expanded Planck’s 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 φ, called the work function
of the metal
• φ is the binding energy of the electron to the surface
• This satisfies all 5 experimental observations
Photoelectric effect
• hf = KE + φ
• ( φ =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)
Application: Film soundtracks
Sound Track
Phototube
Light Source
speaker
Example: A GaN based UV
detector
This is a photoconductor
5m
Response Function of UV
detector
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
The structure of a
LED/Photodiode
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
Photomultipliers
hf
e
PE effect
e
e
Secondary
electron
emission
e
e
e
Electron
multiplication
Photomultiplier tube
hf
e
Anode
Dynode
-V
• Combines PE effect with electron
multiplication to provide very high detection
sensitivity
• Can detect single photons.
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
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
http://hea-www.harvard.edu/HRC/mcp/mcp.html
MCP array structure
http://hea-www.harvard.edu/HRC/mcp/mcp.html
MCP fabrication
Disadvantages of Photomultiplers
as sensors
• Need expensive and fiddly high vacuum
equipment
• Expensive
• Fragile
• Bulky
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….
Photoelecric effect with Energy Bands
Evac
Evac
Ec
Ef
Ev
Ef
Metal
Semiconductor
Band gap: Eg=Ec-Ev
Photoconductivity
e
To amplifier
Ec
Evac
Ef
Ev
Semiconductor
Photoconductors
• Eg (~1 eV) can be made smaller than metal
work functions (~5 eV)
• Only photons with Energy E=hf>Eg are
detected
• This puts a lower limit on the frequency
detected
• Broadly speaking, metals work with UV,
semiconductors with optical
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
Example: A GaN based UV
detector
This is a photoconductor
5m
Response Function of UV
detector
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
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
The structure of a
LED/Photodiode
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
Lecture 15
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
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 (!)
Atomic Physics/Line Spectra
The absorption spectrum for hydrogen: dark absorption lines occur at
the same wavelengths as emission lines.
Atomic Physics/Line Spectra
Rutherford’s Model
Fatal problems !
Problem 1: From the Classical Maxwell’s
Equation, an accelerating electron emits
radiation, losing energy.
This radiation covers a
continuous range in frequency,
contradicting observed line spectra .
Problem 2: Rutherford’s model failed to
account for the stability of the atom.
+Ze
Bohr’s 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
Transitions between states
hf
E3
E3 - E2 = hf
E2
E1
Nucleus
How big is the Bohr Hydrogen Atom?
Rn=a0n2/Z2
Rn=radius of atomic orbit number n
a0=Bohr radius = 0.0629 nm
Z=atomic numner of element
Exercise: What is the diameter of the hydrogen atom?
What energy Levels are allowed?
Exercise
• A hydrogen atom makes a transition between the n=2 state and the
n=1 state. What is the wavelength of the light emitted?
• Step1: Find out the energy of the photon:
• E1=13.6 eV
E2=13.6/4=3.4 eV
• hence the energy of the emitted photon is 10.2 eV
• Step 2: Convert energy into wavelength.
• E=hf,
hence f=E/h =10.2*1.6x10-19/6.63x10-34 = 2.46x1015 Hz
• Step 3: Convert from frequency into wavelength:
• =c/f =3x108/2.46x1015 = 121.5 nm
Emission versus absorption
Emission
Absorption
Einitial
Efinal
Efinal
Einitial
hf = Efinal - Einitial
hf = Efinal - Einitial
Explains Hydrogen spectra
What happens when we have more than
one electron?
What happens when we have more than
one electron?
Apply rules:
Empty
• 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
What happens when we have more than
one electron?
Apply rules:
Empty
• 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
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 (E=qV)
X-rays
The X-ray spectrum
consists of two parts:
1. A continuous
spectrum
2. A series of sharp
lines.
0.5 A0

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
25 keV
15 keV
0.5 A0 0.83 A0

Atomic Physics/X-rays
• The characteristic
spectral lines depend
on the target material.
• These Provides a
unique signature of the
target’s atomic
structure
• Bohr’s theory was
used to understand the
origin of these lines
Atomic Physics – X-rays
The K-shell
corresponds to
n=1
The L-shell
corresponds to
n=2
M is n=2, and
so on
Atomic Spectra – X-rays
Example:
Estimate the wavelength of the X-ray emitted from a
tantalum target when an electron from an n=4 state
makes a transition to an empty n=1 state (Ztantalum =73)
Emission from tantalum
Atomic Physics – X-rays
The X-ray is emitted when an e from an n=4 states falls into the
empty n=1 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
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 Bragg’s law
2dsin = n
• We will return to this later in the course when we
discuss sensors of structure
Line Width
• Real
materials emit
or absorb
light over a
small range of
wavelengths
• Example
here is Neon
Stimulated emission
E2 - E1 = hf
E2
E1
Two identical photons
Same
- frequency
- direction
- phase
- polarisation
Lasers
• LASER - acronym for
– Light Amplification by Stimulated Emission of
Radiation
– produce high intensity power at a single frequency (i.e.
monochromatic)
Laser
Globe
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
Population inversion
Lots of atoms in this level
Energy
N2
N1
Few atoms in this level
Want N2 - N1 to be as
large as possible
Population Inversion (3 level System)
E2 (pump state), t2
Pump light
ts >t2
E1 (metastablestate), ts
hfo
Laser output
hf
E1 (Ground state)
Light Amplification
Light amplified by passing light through a medium
with a population inversion.
• Leads to stimulated emission
Laser
Laser
Requires a cavity enclosed by two mirrors.
• Provides amplification
• Improves spectral purity
• Initiated by “spontaneous emission”
Laser Cavity
Cavity possess modes
• Analagous to standing waves on a string
• Correspond to specific wavelengths/frequencies
• These are amplified
Spectral output
Properties of Laser Light.
• Can be monochromatic
• Coherent
•Very intense
•Short pulses can be produced
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)
Lecture 16
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
Molecular Energies
Energy
Classical
Quantum
E4
E3
E2
E1
E0
Molecular Energy Levels
Increasing Energy
Translation
Electronic
orbital
Vibrational
Rotational
Nuclear Spin
Electronic Spin
Rotation
Vibration
etc.
Electronic Orbital
Etotal + Eorbital +
Evibrational + Erotational +…..
Molecular Vibrations
• Longitudinal Vibrations along
molecular axis
• E=(n+1/2)hf
where f is the classical
frequency of the oscillator
•
1
f 
2
k

where k is the ‘spring constant
• Energy Levels equally spaced
• How can we estimate the
spring constant?
r
k
m
M
 = Mm/(M+m)
Atomic mass concentrated
at nucleus
k = f (r)
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)
r
• Evib=(n+1/2)hf  f =0.273eV/(1/2(h))
= 2.07x1013 Hz
• To determine k we need μ
μ=(Mm)/(M+m) =(1.008)2/2(1.008) amu
=(0.504)1.66x10-27kg =0.837x10-27kg
• k= μ(2πf)2 =576 N/m
K
m
M
=
Mm/(M+m)
K = f (r)
Molecular Rotations
• Molecule can also rotate
about its centre of mass
• v1 = wR1 ; v2 = wR2
M1
• L = M1v1R1+ M2v2R2
= (M1R12+ M2R22)w
= Iw
• EKE = 1/2M1v12+1/2M2v22
= 1/2Iw2
M2
R1
R2
Molecular Rotations
• Hence, Erot= L2/2I
• Now in fact L2 is quantized and
L2=l(l+1)h2/42
• Hence Erot=l(l+1)(h2/42)/2I
• Show that Erot=(l+1) h2/42/I. This is not
equally spaced
• Typically Erot=50meV (i.e for H2)
Populations of Energy Levels
ΔE<<kT
ΔE=kT
ΔE>kT
ΔE
(Virtually) all
molecules in ground
state
States almost equally
populated
• Depends on
the relative
size of kT
and E
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
Strong absorption
hv
Weak
emission
2hv
hv
Transition
saturated
hv
General Features of Spectroscopy
• Peak Height or
intensity
• Frequency
• Lineshape or
linewidth
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.
r
K
m
M
f vib= (K/)1/2
 = Mm/(M+m)
K = f(r)
Raman Spectroscopy Cont...
Laser In
Sample
Lens
Monochromator
CCD array
•Incident photons typically
undergo elastic scattering.
•Small fraction undergo
inelastic  energy transferred
to molecule.
•Raman detects change in
vibrational energy of a
molecule.
Raman Microscope
100
Detecting Art Forgery
80
YTI S NET NI
• Ti-white became available
only circa 1920.
Pb white
60
40
• The Roberts painting shows
clear evidence of Ti white but
is dated 1899
20
Ti white
0
0
200
400
600
800
-1
WAVENUMBER (cm )
200
150
YTI S NET NI
100
50
0
0
200
400
600
-1
WAVENUMBER (cm )
800
Tom Roberts, ‘Track To The
Harbour’ dated 1899
Raman Spectroscopy and the Optical
Measurement of Temperature
• Probability that a level is occupied is
proportional to exp(E/kT)
Population inversion
Lots of atoms in this level
Energy
N2
N1
Few atoms in this level
Want N2 - N1 to be as
large as possible
Population Inversion (3 level System)
E2 (pump state), t2
Pump light
ts >t2
E1 (metastablestate), ts
hfo
Laser output
hf
E1 (Ground state)
Light Amplification
Light amplified by passing light through a medium
with a population inversion.
• Leads to stimulated emission
Laser
Laser
Requires a cavity enclosed by two mirrors.
• Provides amplification
• Improves spectral purity
• Initiated by “spontaneous emission”
Laser Cavity
Cavity possess modes
• Analagous to standing waves on a string
• Correspond to specific wavelengths/frequencies
• These are amplified
Spectral output
Lecture 17
Optical Fibre Sensors
•
•
•
•
•
•
•
•
Non-Electrical
Explosion-Proof
(Often) Non-contact
Light, small, snakey => “Remotable”
Easy(ish) to install
Immune to most EM noise
Solid-State (no moving parts)
Multiplexing/distributed sensors.
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)
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.
Optical Fibre Principles
•
•
•
•
Snell’s Law: n1sin1=n2sin2
crit = arcsin(n2/n1)
Cladding reduces entry angle
Only some angles (modes) allowed
Optical Fibre Modes
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.
Intensity modulated sensors:
• Axial
displacement:
1/r2 sensitivity
• Radial
Displacement
Microbending (1)
Microbending
– Bent fibers lose energy
– (Incident angle
changes to less than
critical angle)
Microbending (2):
Microbending
– “Jaws” close a bit, less
transmission
– Give jaws period of
light to enhance effect
• Applications:
– Strain gauge
– Traffic counting
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 @514nm
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
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
Phase modulated sensors
Bragg modulators:
– Periodic changes in
refractive index
– Bragg wavelenght (λb)
which satisfies λb=2nD is
reflected
– Separation (D) of same
order as than mode
wavelength
Phase modulated sensors
Period,D
λb=2nD
• Multimode fibre with broad input spectrum
• Strain or heating changes n so reflected wavelength changes
• Suitable for distributed sensing
Phase modulated sensors – distributed sensors
Temperature Sensors
• Reflected phosphorescent signal depends on
Temperature
• Can use BBR, but need sapphire waveguides
since silica/glass absorbs IR
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.
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.
NSOM/AFM Combined
•Optical resolution
determined by
Bent NSOM/AFM
Probe
diffraction limit (~λ)
•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
NSOM Setup
Ideal for thin films or
coatings which are
several hundred nm
thick on transparent
substrates (e.g., a
round, glass cover
slip).
Lecture 18
• Not sure what goes here
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 (E=qV)
X-rays
The X-ray spectrum
consists of two parts:
1. A continuous
spectrum
2. A series of sharp
lines.
0.5 A0

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
25 keV
15 keV
0.5 A0 0.83 A0

Atomic Physics/X-rays
• The characteristic
spectral lines depend
on the target material.
• These Provides a
unique signature of the
target’s atomic
structure
• Bohr’s theory was
used to understand the
origin of these lines
Atomic Physics – X-rays
The K-shell
corresponds to
n=1
The L-shell
corresponds to
n=2
M is n=2, and
so on
Atomic Spectra – X-rays
Example:
Estimate the wavelength of the X-ray emitted from a
tantalum target when an electron from an n=4 state
makes a transition to an empty n=1 state (Ztantalum =73)
Emission from tantalum
Atomic Physics – X-rays
The X-ray is emitted when an e from an n=4 states falls into the
empty n=1 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
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 Bragg’s law
2dsin = n
• We will return to this later in the course when we
discuss sensors of structure
Line Width
• Real
materials emit
or absorb
light over a
small range of
wavelengths
• Example
here is Neon
Stimulated emission
E2 - E1 = hf
E2
E1
Two identical photons
Same
- frequency
- direction
- phase
- polarisation
Lasers
• LASER - acronym for
– Light Amplification by Stimulated Emission of
Radiation
– produce high intensity power at a single frequency (i.e.
monochromatic)
Laser
Globe
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
Population inversion
Lots of atoms in this level
Energy
N2
N1
Few atoms in this level
Want N2 - N1 to be as
large as possible
Population Inversion (3 level System)
E2 (pump state), t2
Pump light
ts >t2
E1 (metastablestate), ts
hfo
Laser output
hf
E1 (Ground state)
Light Amplification
Light amplified by passing light through a medium
with a population inversion.
• Leads to stimulated emission
Laser
Laser
Requires a cavity enclosed by two mirrors.
• Provides amplification
• Improves spectral purity
• Initiated by “spontaneous emission”
Laser Cavity
Cavity possess modes
• Analagous to standing waves on a string
• Correspond to specific wavelengths/frequencies
• These are amplified
Spectral output
Lecture 16
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
Molecular Energies
Energy
Classical
Quantum
E4
E3
E2
E1
E0
Molecular Energy Levels
Increasing Energy
Translation
Electronic
orbital
Vibrational
Rotational
Nuclear Spin
Electronic Spin
Rotation
Vibration
etc.
Electronic Orbital
Etotal + Eorbital +
Evibrational + Erotational +…..
Molecular Vibrations
• Longitudinal Vibrations along
molecular axis
• E=(n+1/2)hf
where f is the classical
frequency of the oscillator
•
1
f 
2
k

where k is the ‘spring constant
• Energy Levels equally spaced
• How can we estimate the
spring constant?
r
k
m
M
 = Mm/(M+m)
Atomic mass concentrated
at nucleus
k = f (r)
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)
r
• Evib=(n+1/2)hf  f =0.273eV/(1/2(h))
= 2.07x1013 Hz
• To determine k we need μ
μ=(Mm)/(M+m) =(1.008)2/2(1.008) amu
=(0.504)1.66x10-27kg =0.837x10-27kg
• k= μ(2πf)2 =576 N/m
K
m
M
=
Mm/(M+m)
K = f (r)
Molecular Rotations
• Molecule can also rotate
about its centre of mass
• v1 = wR1 ; v2 = wR2
M1
• L = M1v1R1+ M2v2R2
= (M1R12+ M2R22)w
= Iw
• EKE = 1/2M1v12+1/2M2v22
= 1/2Iw2
M2
R1
R2
Molecular Rotations
• Hence, Erot= L2/2I
• Now in fact L2 is quantized and
L2=l(l+1)h2/42
• Hence Erot=l(l+1)(h2/42)/2I
• Show that Erot=(l+1) h2/42/I. This is not
equally spaced
• Typically Erot=50meV (i.e for H2)
Populations of Energy Levels
ΔE<<kT
ΔE=kT
ΔE>kT
ΔE
(Virtually) all
molecules in ground
state
States almost equally
populated
• Depends on
the relative
size of kT
and E
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
Strong absorption
hv
Weak
emission
2hv
hv
Transition
saturated
hv
General Features of Spectroscopy
• Peak Height or
intensity
• Frequency
• Lineshape or
linewidth
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.
r
K
m
M
f vib= (K/)1/2
 = Mm/(M+m)
K = f(r)
Raman Spectroscopy Cont...
Laser In
Sample
Lens
Monochromator
CCD array
•Incident photons typically
undergo elastic scattering.
•Small fraction undergo
inelastic  energy transferred
to molecule.
•Raman detects change in
vibrational energy of a
molecule.
Raman Microscope
100
Detecting Art Forgery
80
YTI S NET NI
• Ti-white became available
only circa 1920.
Pb white
60
40
• The Roberts painting shows
clear evidence of Ti white but
is dated 1899
20
Ti white
0
0
200
400
600
800
-1
WAVENUMBER (cm )
200
150
YTI S NET NI
100
50
0
0
200
400
600
-1
WAVENUMBER (cm )
800
Tom Roberts, ‘Track To The
Harbour’ dated 1899
Raman Spectroscopy and the Optical
Measurement of Temperature
• Probability that a level is occupied is
proportional to exp(E/kT)
Lecture 17
Optical Fibre Sensors
•
•
•
•
•
•
•
•
Non-Electrical
Explosion-Proof
(Often) Non-contact
Light, small, snakey => “Remotable”
Easy(ish) to install
Immune to most EM noise
Solid-State (no moving parts)
Multiplexing/distributed sensors.
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)
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.
Optical Fibre Principles
•
•
•
•
Snell’s Law: n1sin1=n2sin2
crit = arcsin(n2/n1)
Cladding reduces entry angle
Only some angles (modes) allowed
Optical Fibre Modes
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.
Intensity modulated sensors:
• Axial
displacement:
1/r2 sensitivity
• Radial
Displacement
Microbending (1)
Microbending
– Bent fibers lose energy
– (Incident angle
changes to less than
critical angle)
Microbending (2):
Microbending
– “Jaws” close a bit, less
transmission
– Give jaws period of
light to enhance effect
• Applications:
– Strain gauge
– Traffic counting
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 @514nm
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
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
Phase modulated sensors
Bragg modulators:
– Periodic changes in
refractive index
– Bragg wavelenght (λb)
which satisfies λb=2nD is
reflected
– Separation (D) of same
order as than mode
wavelength
Phase modulated sensors
Period,D
λb=2nD
• Multimode fibre with broad input spectrum
• Strain or heating changes n so reflected wavelength changes
• Suitable for distributed sensing
Phase modulated sensors – distributed sensors
Temperature Sensors
• Reflected phosphorescent signal depends on
Temperature
• Can use BBR, but need sapphire waveguides
since silica/glass absorbs IR
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.
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.
NSOM/AFM Combined
•Optical resolution
determined by
Bent NSOM/AFM
Probe
diffraction limit (~λ)
•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
NSOM Setup
Ideal for thin films or
coatings which are
several hundred nm
thick on transparent
substrates (e.g., a
round, glass cover
slip).
Lecture 18
• Not sure what goes here
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 (E=qV)
X-rays
The X-ray spectrum
consists of two parts:
1. A continuous
spectrum
2. A series of sharp
lines.
0.5 A0

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
25 keV
15 keV
0.5 A0 0.83 A0

Atomic Physics/X-rays
• The characteristic
spectral lines depend
on the target material.
• These Provides a
unique signature of the
target’s atomic
structure
• Bohr’s theory was
used to understand the
origin of these lines
Atomic Physics – X-rays
The K-shell
corresponds to
n=1
The L-shell
corresponds to
n=2
M is n=2, and
so on
Atomic Spectra – X-rays
Example:
Estimate the wavelength of the X-ray emitted from a
tantalum target when an electron from an n=4 state
makes a transition to an empty n=1 state (Ztantalum =73)
Emission from tantalum
Atomic Physics – X-rays
The X-ray is emitted when an e from an n=4 states falls into the
empty n=1 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
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 Bragg’s law
2dsin = n
• We will return to this later in the course when we
discuss sensors of structure
Line Width
• Real
materials emit
or absorb
light over a
small range of
wavelengths
• Example
here is Neon
Stimulated emission
E2 - E1 = hf
E2
E1
Two identical photons
Same
- frequency
- direction
- phase
- polarisation
Lasers
• LASER - acronym for
– Light Amplification by Stimulated Emission of
Radiation
– produce high intensity power at a single frequency (i.e.
monochromatic)
Laser
Globe
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
Properties of Laser Light.
• Can be monochromatic
• Coherent
•Very intense
•Short pulses can be produced
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)
Lecture 16
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
Molecular Energies
Energy
Classical
Quantum
E4
E3
E2
E1
E0
Molecular Energy Levels
Increasing Energy
Translation
Electronic
orbital
Vibrational
Rotational
Nuclear Spin
Electronic Spin
Rotation
Vibration
etc.
Electronic Orbital
Etotal + Eorbital +
Evibrational + Erotational +…..
Molecular Vibrations
• Longitudinal Vibrations along
molecular axis
• E=(n+1/2)hf
where f is the classical
frequency of the oscillator
•
1
f 
2
k

where k is the ‘spring constant
• Energy Levels equally spaced
• How can we estimate the
spring constant?
r
k
m
M
 = Mm/(M+m)
Atomic mass concentrated
at nucleus
k = f (r)
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)
r
• Evib=(n+1/2)hf  f =0.273eV/(1/2(h))
= 2.07x1013 Hz
• To determine k we need μ
μ=(Mm)/(M+m) =(1.008)2/2(1.008) amu
=(0.504)1.66x10-27kg =0.837x10-27kg
• k= μ(2πf)2 =576 N/m
K
m
M
=
Mm/(M+m)
K = f (r)
Molecular Rotations
• Molecule can also rotate
about its centre of mass
• v1 = wR1 ; v2 = wR2
M1
• L = M1v1R1+ M2v2R2
= (M1R12+ M2R22)w
= Iw
• EKE = 1/2M1v12+1/2M2v22
= 1/2Iw2
M2
R1
R2
Molecular Rotations
• Hence, Erot= L2/2I
• Now in fact L2 is quantized and
L2=l(l+1)h2/42
• Hence Erot=l(l+1)(h2/42)/2I
• Show that Erot=(l+1) h2/42/I. This is not
equally spaced
• Typically Erot=50meV (i.e for H2)
Populations of Energy Levels
ΔE<<kT
ΔE=kT
ΔE>kT
ΔE
(Virtually) all
molecules in ground
state
States almost equally
populated
• Depends on
the relative
size of kT
and E
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
Strong absorption
hv
Weak
emission
2hv
hv
Transition
saturated
hv
General Features of Spectroscopy
• Peak Height or
intensity
• Frequency
• Lineshape or
linewidth
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.
r
K
m
M
f vib= (K/)1/2
 = Mm/(M+m)
K = f(r)
Raman Spectroscopy Cont...
Laser In
Sample
Lens
Monochromator
CCD array
•Incident photons typically
undergo elastic scattering.
•Small fraction undergo
inelastic  energy transferred
to molecule.
•Raman detects change in
vibrational energy of a
molecule.
Raman Microscope
100
Detecting Art Forgery
80
YTI S NET NI
• Ti-white became available
only circa 1920.
Pb white
60
40
• The Roberts painting shows
clear evidence of Ti white but
is dated 1899
20
Ti white
0
0
200
400
600
800
-1
WAVENUMBER (cm )
200
150
YTI S NET NI
100
50
0
0
200
400
600
-1
WAVENUMBER (cm )
800
Tom Roberts, ‘Track To The
Harbour’ dated 1899
Raman Spectroscopy and the Optical
Measurement of Temperature
• Probability that a level is occupied is
proportional to exp(E/kT)
Lecture 16
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
Molecular Energies
Energy
Classical
Quantum
E4
E3
E2
E1
E0
Molecular Energy Levels
Increasing Energy
Translation
Electronic
orbital
Vibrational
Rotational
Nuclear Spin
Electronic Spin
Rotation
Vibration
etc.
Electronic Orbital
Etotal + Eorbital +
Evibrational + Erotational +…..
Molecular Vibrations
• Longitudinal Vibrations along
molecular axis
• E=(n+1/2)hf
where f is the classical
frequency of the oscillator
•
1
f 
2
k

where k is the ‘spring constant
• Energy Levels equally spaced
• How can we estimate the
spring constant?
r
k
m
M
 = Mm/(M+m)
Atomic mass concentrated
at nucleus
k = f (r)
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)
r
• Evib=(n+1/2)hf  f =0.273eV/(1/2(h))
= 2.07x1013 Hz
• To determine k we need μ
μ=(Mm)/(M+m) =(1.008)2/2(1.008) amu
=(0.504)1.66x10-27kg =0.837x10-27kg
• k= μ(2πf)2 =576 N/m
K
m
M
=
Mm/(M+m)
K = f (r)
Molecular Rotations
• Molecule can also rotate
about its centre of mass
• v1 = wR1 ; v2 = wR2
M1
• L = M1v1R1+ M2v2R2
= (M1R12+ M2R22)w
= Iw
• EKE = 1/2M1v12+1/2M2v22
= 1/2Iw2
M2
R1
R2
Molecular Rotations
• Hence, Erot= L2/2I
• Now in fact L2 is quantized and
L2=l(l+1)h2/42
• Hence Erot=l(l+1)(h2/42)/2I
• Show that Erot=(l+1) h2/42/I. This is not
equally spaced
• Typically Erot=50meV (i.e for H2)
Populations of Energy Levels
ΔE<<kT
ΔE=kT
ΔE>kT
ΔE
(Virtually) all
molecules in ground
state
States almost equally
populated
• Depends on
the relative
size of kT
and E
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
Strong absorption
hv
Weak
emission
2hv
hv
Transition
saturated
hv
General Features of Spectroscopy
• Peak Height or
intensity
• Frequency
• Lineshape or
linewidth
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.
r
K
m
M
f vib= (K/)1/2
 = Mm/(M+m)
K = f(r)
Raman Spectroscopy Cont...
Laser In
Sample
Lens
Monochromator
CCD array
•Incident photons typically
undergo elastic scattering.
•Small fraction undergo
inelastic  energy transferred
to molecule.
•Raman detects change in
vibrational energy of a
molecule.
Raman Microscope
100
Detecting Art Forgery
80
YTI S NET NI
• Ti-white became available
only circa 1920.
Pb white
60
40
• The Roberts painting shows
clear evidence of Ti white but
is dated 1899
20
Ti white
0
0
200
400
600
800
-1
WAVENUMBER (cm )
200
150
YTI S NET NI
100
50
0
0
200
400
600
-1
WAVENUMBER (cm )
800
Tom Roberts, ‘Track To The
Harbour’ dated 1899
Raman Spectroscopy and the Optical
Measurement of Temperature
• Probability that a level is occupied is
proportional to exp(E/kT)
Lecture 17
Optical Fibre Sensors
•
•
•
•
•
•
•
•
Non-Electrical
Explosion-Proof
(Often) Non-contact
Light, small, snakey => “Remotable”
Easy(ish) to install
Immune to most EM noise
Solid-State (no moving parts)
Multiplexing/distributed sensors.
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)
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.
Optical Fibre Principles
•
•
•
•
Snell’s Law: n1sin1=n2sin2
crit = arcsin(n2/n1)
Cladding reduces entry angle
Only some angles (modes) allowed
Optical Fibre Modes
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.
Intensity modulated sensors:
• Axial
displacement:
1/r2 sensitivity
• Radial
Displacement
Microbending (1)
Microbending
– Bent fibers lose energy
– (Incident angle
changes to less than
critical angle)
Microbending (2):
Microbending
– “Jaws” close a bit, less
transmission
– Give jaws period of
light to enhance effect
• Applications:
– Strain gauge
– Traffic counting
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 @514nm
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
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
Phase modulated sensors
Bragg modulators:
– Periodic changes in
refractive index
– Bragg wavelenght (λb)
which satisfies λb=2nD is
reflected
– Separation (D) of same
order as than mode
wavelength
Phase modulated sensors
Period,D
λb=2nD
• Multimode fibre with broad input spectrum
• Strain or heating changes n so reflected wavelength changes
• Suitable for distributed sensing
Phase modulated sensors – distributed sensors
Temperature Sensors
• Reflected phosphorescent signal depends on
Temperature
• Can use BBR, but need sapphire waveguides
since silica/glass absorbs IR
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.
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.
NSOM/AFM Combined
•Optical resolution
determined by
Bent NSOM/AFM
Probe
diffraction limit (~λ)
•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
NSOM Setup
Ideal for thin films or
coatings which are
several hundred nm
thick on transparent
substrates (e.g., a
round, glass cover
slip).
Lecture 18
• Not sure what goes here