Chapter 6. Light Source and Detectors

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Chapter 6. Light Source and Detectors

• Quantum- element units of energy
• Quantum optics photoelectric effect
• laser emission
• blackbody radiation

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6.1 Light Sources
1. Light Sources

• An object is a source of light.
• A direct source produces light, e.g. the sun,
  light bulb, fire.
• An indirect source does not produce light, e.g.
  an illuminated object.
• An extended object may be regarded as a set of
  point sources.

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• (a) Thermal source sun, wax candle, kerosene
  lanterns, electric light bulb
• light--the consequence of the temperature
• kerosene lanterns carbon freed by the combustion
  process
• electric light bulbs a filament is heated.
  carbon filaments, metal filaments
• Incandescent lamps be heated to incandescence
• ? Refractory metals a high melting point
• ? Tungsten 3410?C evaporates,
• ? Some halogens( iodine), retard the process

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How tungsten filaments works
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• (b) Fluorescent lamps
• Fluorescent lamps
• High-pressure mercury lamps
• High-pressure xenon lamps
• (c) Stimulated emission laser, LED

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2. Blackbody Radiators
6.1 Light Sources

• (a) Black body is an ideal absorber, also a
  perfect emitter
• A good way of making a blackbody is to force
  reflected light to make lots of reflections
  inside a bottle with a small opening

• The spectral distribution of that radiation is a
  function of temperature alone the material as
  such plays no role

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• Classical theory failed
• Ultraviolet catastrophe

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Quantization of Energy
Max Planck (1858-1947) Solved the ultraviolet
catastrophe

• Plancks hypothesis An object can only gain or
  lose energy by absorbing or emitting radiant
  energy in QUANTA.

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Electromagnetic Radiation

• All waves have frequency and
  wavelength
• symbol n (Greek letter nu) l (Greek
  lambda)
• units cycles per sec Hertz distance (nm)

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Energy of radiation is proportional to frequency.
E h n
where h Plancks constant 6.6262 x 10-34 Js
Light with large l (small n) has a small E.
Light with a short l (large n) has a large E.
(b) Photon the oscillators emit energy, as
discrete, elemental units of energy called quanta
or photons
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Photons

• Light also behaves as a stream of particles,
  called photons.
• Light has wave-particle duality , meaning that
  it behaves as waves and as particles.
• This is a concept in quantum mechanics.

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• (c) Black-body radiation is electromagnetic
  radiation that is in thermal equilibrium at a
  temperature T with matter that can absorb and
  emit without favouring any particular wavelength
• (d) Planks radiation law

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3. Wien's Displacement Law
6.1 Light Sources

• plot Planck's law for different temperatures
• increasing temperature
• more energy is emitted
• the peak emission shifts toward the shorter
  wavelengths

The temperature and the wavelength of maximum
intensity satisfy T?maxconstant
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Black-Body Radiation

• Hole in a cavity is
• a perfect absorber
• a perfect emitter
• Called a Black Body
• Wiens law

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Example - Wiens Law

• What is the peak radiation emitted by an object
  at 100oC ?

• This is in the far infrared.
• What T required for middle of visible range?

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Blackbody Radiation Experimental Results

• At 310 Kelvin (37oC 98.6oF), only get IR

Intensity
IR
blue yellow red
UV
wavelength
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Blackbody RadiationExperimental Results

• At much higher temperatures, get visible
• look at blue/red ratio to get temperature

Intensity
IR
blue yellow red
UV
wavelength
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Temperature of the Sun
When we look at the visible spectra of the sun,
we see that its intensity peaks at about 500 nm
(green light). From the equation ? b/T
(where b 2.9 x 10-3mK) we get T b/? (2.9
x 10-3mK) / 500 x 10-9m ? 6000 K .
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4. Stefan-Boltzmann's Law
6.1 Light Sources
The total energy density inside a blackbody
cavity is given by integration over all
wavelengths
Note that Intensity increases with T
Temperature must be in Kelvin, where size of one
Kelvin is same as size of one degree Celsius, but
T0K is absolute zero, and T273K 0oC
(freezing).
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6.1 Light Sources
5. Klrchhoff's Law

• Kirchhoff's law an object that is a good
  radiator at a given wavelength is also a good
  absorber at the same wavelength
• Stefan-Boltzmann's law for gray bodies
• factor ? the emissivity of the surface

• Recall that a good absorber is also a good
  emitter, and a poor absorber is a poor emitter.
  We use the symbol ? to indicate the blackness (?
  0) or the whiteness (?1) of an object.

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Example
If you eat 2,000 calories per day, that is
equivalent to about 100 joules per second or
about 100 Watts - which must be emitted. Lets
see how much radiation you emit when the
temperature is comfortable, say 75oF24oC297K,
and pick a surface area, say 1.5m2, that is at a
temperature of 93oF34oC307K Memitted
??AT4 (5.67x10-8W/m2K4)(.97)(1.5m2)(307K)4
733 Watts emitted!
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Example continued
But this is not the whole story besides
emitting radiation, we receive radiation from the
outside Mabsorbed ??AT4 (5.67x10-8W/m2K4)(
.97)(1.5m2)(297K)4 642 Watts absorbed! Hence,
the net power emitted by the body via radiation
is Mnet 733 Watts - 642 Watts 91 Watts.
The peak of this radiation is at ??peak b/T
2.9x10-3mK / 307K 9.5?m which is in the
infrared (as expected).
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6.2 Detectors

• thermal detectors
• based on absorption and heating
• If the absorbing material is black, they are
  independent of wavelength.
• quantum detectors.
• based on photoelectric effect
• Quantum detectors are of particular interest,
  both theoretical and practical some of them are
  so sensitive they respond to individual quanta.

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6.2 Detectors

• 1. Thermal Detectors
• slow to respond
• Golay cell
• a thin black membrane placed over a small,
  gas-filled chamber. Heat absorbed by the membrane
  causes the gas to expand, which in turn can be
  measured, either optically (by a movable mirror)
  or electrically (by a change in capacitance).
• used in the infrared.

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6.2 Detectors

• Thermocouple
• a junction between two dissimilar metals. As
  the junction is heated, the potential difference
  changes. In practice, two junctions are used in
  series, a hot junction exposed to the radiation,
  and a cold junction shielded from it. The two
  voltages are opposite to each other thus the
  detector, which without this precaution would
  show the absolute temperature, now measures the
  temperature differential.
• thermopile
• contains several thermocouples and, therefore,
  is more sensitive.

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6.2 Detectors

• bolometer
• contains a metal element whose electrical
  resistance changes as a function of temperature
  if instead of the metal a semiconductor is used,
  it is called a thermistor.
• Unlike a thermocouple, a bolometer or
  thermistor does not generate a voltage they must
  be connected to a voltage source.

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6.2 Detectors

• 2. Quantum Detectors
• the wavelength of the light plays an important
  role
• there is a certain threshold above which there
  is no effect at all, no matter what the intensity
  
• intense light and dim light cause same of an
  effect

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Photoelectric Effect
Albert Einstein (1879-1955)
Photoelectric effect demonstrates the particle
nature of light
No e- observed until light of a certain minimum E
is used.
Number of e- ejected does NOT depend on
frequency, rather it depends on light intensity.
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Photoelectric Effect (2)

• Classical theory said that E of ejected
• electron should increase with increase
• in light intensity not observed!

• Experimental observations can be explained if
  light consists of particles called PHOTONS of
  discrete energy.

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Discrete Packets of Energy
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6.2 Detectors

• plate M(photocathode)
• when irradiated, releases electrons (called
  photoelectrons)
• collector plate C(anode)
• photoelectrons released by M are attracted
  by, and travel to C.

As the potential V, read on an high-impedance
voltmeter, is increased, the current, I, read on
an ammeter, increases too, but only up to a given
saturation level, because then all of the
electrons emitted by M are collected by C.
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6.2 Detectors
if C is made negative, some photocurrent will
still exist, provided the electrons ejected from
M have enough kinetic energy to overcome the
repulsive field at C. But as C is made more
negative, a point is reached where no electrons
reach C and the current drops to zero. This
occurs at the stopping potential, V0. In short
A significant amount of photocurrent is present
only if the collector, C, is made positive
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When the frequency of the light is increased, the
stopping potential also increases.
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The electron photo-current can be stopped by a
retarding potential. Increasing the light
intensity do not change the retarding potential.
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6.2 Detectors

• If more intense light falls on the photocathode,
  it will release more electrons but their
  energies, and their velocities, will remain the
  same.
• The energy of the photoelectrons depends on the
  frequency of the light blue light produces more
  energetic photo-electrons than red light.
• The response of a quantum detector is all but
  instantaneous there is no time lag, at least not
  more than 10-8 s, between the receipt of the
  irradiation and the resulting current.

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6.2 Detectors

• The light is received in the form of discrete
  quanta.
• Part of the energy contained in a quantum is
  needed to make the electron escape from the
  surface that part is called the work function,
  W.
• Only the excess energy, beyond the work
  function, appears as kinetic energy of the
  electron. The maximum kinetic energy with which
  the electron can escape, therefore, is
• KEmax h? - W
• Einstein's photoelectric-effect equation.

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h? W KE KE h? - W

• Einstein suggested that the linear behaviour is
  simply a Conservation of Energy.
• Energy of Light Energy needed to get out
  Kinetic Energy of electron.

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Example - Photoelectric Effect

• Given that aluminum has a work function of 4.08
  eV, what are the threshold frequency and the
  cutoff wavelength?

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6.2 Detectors
It is often convenient to measure energies on an
atomic scale not in joule but in electron volt,
eV. 1 eV (1e)(1V) 1.60 6 ? 10-19 J
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Photons and Colors

• Electron volts are useful size units of energy
• 1 eV 1.6 x 10-19 Coul 1V 1.6 x 10-19 J.
• radio photon hf 6.63 x 10-34 Js 1 x 106 /s
  6.63 x 10-28 J 4 x 10-15 eV
• red photon f c/????3 108 m/s / 7 x 10-7 m
  4.3 x 1014 Hz, red photon energy 1.78
  eV
• blue ?? 400 nm photon energy 3.11 eV .

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6.2 Detectors
The work function determines the longest
wavelength to which a detector can respond the
lower the work function, the longer the
wavelength. The lowest work functions are found
among the alkali metals. Photoelectric Properties
Of Some Alkali Metals Alkali Work
function (eV) Threshold (nm) Sodium
2.28
543 Potassium 2.25
551 Rubidium
2.13 582 Cesium
1.94
639
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The Photoelectric Effect on Potassium
Determine the work function W
KE(hc)(1/?) - W
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From the graph The plot is essentially KE vs
1/?, so that since KEhc/?-W The intercept when
(1/?)0 give W-KE-(-2eV)2eV
To obtain Plancks constant h, we need the slope
S Then hS/c. S(4-(-2))/(5-0) 10-31.2 103
eV nm h 1.2 103 1.602 10-1910-9 /(3
108) J s 6.4 10-34 J s cf (6.626 10-34
J s)
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6-3. Practical Quantum Detectors
In contrast to thermal detectors, quantum
detectors respond to the number of quanta, rather
than to the energy contained in them.
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6.3 Practical Quantum Detectors

• The simplest type is probably the vacuum
  phototube, an example of a photoemissive
  detector.

• Light strikes photocathode (-)
• Photocathode emits photoelectrons
• Photoelectrons accelerate toward anode ()
• flow of electrons current
• current proportional to photons incident on
  photocathode

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• quantum efficiencythe ratio of the number of
  photoelectrons released to the number of photons
  received.
• Ordinarily, this efficiency is no higher than a
  few percent.
• Several diodes are combined in series to form a
  photomultiplier, the efficiency becomes much
  higher.

• Light strikes photocathode (-)
• Photocathode emits photoelectrons
• Photoelectrons accelerate toward series of
  increasingly positive anodes () at which
  photoelectrons and secondary electrons are
  emitted (dynodes)
• Electrons accelerated toward collection anode

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6.3 Practical Quantum Detectors

• A photocell is the solid-state equivalent of the
  vacuum photodiode most often it is a
  semiconductor.
• A semiconductor conducts electricity better than
  an insulator but not as well as a conductor.
• In an insulator, the electrons are tightly bound
  to their respective atoms.
• In a metal, the electrons can move freely hence,
  even a small voltage applied to the conductor
  will cause a current.

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6.3 Practical Quantum Detectors

• photoconductive detectors semiconductor, such
  as cadmium sulfide (CdS), gallium arsenide, and
  silicon, conduct electricity poorly only in the
  dark when exposed to light, they conduct very
  well.

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6.3 Practical Quantum Detectors

• photo-voltaic detectors
• made from two semiconductors, one of them
  transparent to light, for instance a layer of CdS
  deposited on selenium. When light is incident on
  the junction, the electrons start moving, but
  only in one direction producing a current in
  other words, the junction converts light energy
  into electrical energy.
• used as solar cells and as exposure meters in
  photographic cameras.

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6.3 Practical Quantum Detectors

• image tubenot only detects light but also
  preserves the spatial characteristics of an image.

• contain an array of photoconductors, one for each
  pixel. When exposed to light, the elements from a
  latent image that can be read by an electron beam
  scanning across them.

• the photoelectrons emitted by the cathode can be
  focused by an electron lens and made visible on a
  phosphor screen mounted in the same tube.

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6.3 Practical Quantum Detectors

• image intensifier
• the image is merely amplified.
• image converter
• the image is formed in the IR, the UV or the
  X-ray range and converted into the visible
• microchannel image intensifier
• the system is built around an array of many short
  fibers or capillaries, fused into a wafer.