Chapter 6. Light Source and Detectors

Chapter 6.
Light Source and Detectors
Quantum- element units of energy
Quantum optics: photoelectric effect
laser emission
blackbody radiation
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.
(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
How tungsten
filaments works
(b) Fluorescent lamps
Fluorescent lamps
High-pressure mercury lamps
High-pressure xenon lamps
(c) Stimulated emission: laser, LED
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
Classical theory failed
 Ultraviolet catastrophe

Quantization of Energy
Max Planck (1858-1947)
Solved the “ultraviolet
catastrophe”

Planck’s hypothesis: An object can only gain
or lose energy by absorbing or emitting
radiant energy in QUANTA.
Electromagnetic Radiation
All waves have:
frequency
and
 symbol: n (Greek letter “nu”)


units:
“cycles per sec” = Hertz
Note: Long wavelength
 small frequency
Short wavelength
 high frequency
wavelength
l (Greek “lambda”)
“distance” (nm)
increasing
frequency
increasing
wavelength
Energy of radiation is proportional to frequency.
E = h•n
where h = Planck’s constant = 6.6262 x 10-34 J•s
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
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.
(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) Plank’s radiation law
M (l  
C1
l5 eC
1
2
/ lT
1
3. Wien's Displacement Law
6.1 Light Sources
plot Planck's law for
different temperatures
lmax
increasing temperature
2.8978  10 3

mK
T
 more energy is emitted
 the peak emission shifts
toward
the
shorter
wavelengths
The temperature and the wavelength of maximum intensity
satisfy
Tlmax=constant
Black-Body Radiation

Hole in a cavity is
a perfect absorber
 a perfect emitter

Called a Black Body
 Wien’s law

lmax
2.898 mm  K

T
Example - Wien’s Law
What is the peak radiation emitted by an
object at 100oC ?
2.898 mm  K 2.898 mm  K
lmax 

 7770 nm
T
373 K
 This is in the far infrared.
 What T required for middle of visible range?

T
2.898 mm  K
lmax
2.898 mm  K

 5000 K
580 nm
Blackbody Radiation: Experimental Results

At 310 Kelvin (=37oC = 98.6oF), only get IR
Intensity
UV
blue
yellow
wavelength
red
IR
Blackbody Radiation:Experimental Results


At much higher temperatures, get visible
look at blue/red ratio to get temperature
Intensity
UV
blue
yellow
wavelength
red
IR
Temperature of the Sun
When we look at the visible spectra of the sun,
we see that it’s intensity peaks at about 500
nm (green light). From the equation:
l = b/T (where b = 2.9 x 10-3m*K)
we get: T = b/l = (2.9 x 10-3m*K) / 500 x 10-9m
 6000 K .
6.1 Light Sources
4. Stefan-Boltzmann's Law
The total energy density inside a blackbody cavity is
given by integration over all wavelengths

M   M (l  dl   T
4
0
W
  5.67 10
m2  K 4
8
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 T=0K is absolute zero,
and T=273K = 0oC (freezing).
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
M  T
4
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.
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.
Let’s see how much radiation you emit when the
temperature is comfortable, say 75oF=24oC=297K,
and pick a surface area, say 1.5m2, that is at a
temperature of 93oF=34oC=307K:
Memitted = AT4 =
(5.67x10-8W/m2K4)*(.97)*(1.5m2)*(307K)4 = 733
Watts emitted!
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:
lpeak = b/T = 2.9x10-3m*K / 307K = 9.5m which
is in the infrared (as expected).
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.
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.
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.
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.
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
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.
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.
Discrete Packets of Energy
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.
Light
eA
V
Variable power
supply
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.
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
When the frequency of the light is increased, the stopping
potential also increases.
The electron photo-current can be stopped by a retarding potential.
Increasing the light intensity do not change the retarding potential.
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.
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 = hn - W
Einstein's photoelectric-effect equation.
hn = W + KE
KE = hn - 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.
Example - Photoelectric Effect

Given that aluminum has a work function of
4.08 eV, what are the threshold frequency
and the cutoff wavelength?

4.08 eV
15
fc  

10
Hz
-15
h 4.14  10 eV  s
hc 1240 eV  nm
lc 

 300 nm

4.08 eV
c
lc 
fc
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
hc
(6.63  10 34 Js )(3  108 m / s ) 1240nmeV
l


19
E
1.6  10
J / eV
E
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/l  3 × 108 m/s / 7 x 10-7 m
= 4.3 x 1014 Hz,

red photon energy = 1.78 eV
blue: l = 400 nm; photon energy = 3.11 eV .
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
Sodium
Potassium
Rubidium
Cesium
Work function (eV)
2.28
2.25
2.13
1.94
Threshold (nm)
543
551
582
639
The Photoelectric Effect on Potassium
Determine the work function W
wavelength nm
stopping potential eV
200
4.11
300
2.05
KE=(hc)(1/l) － W
400
1.03
500
0.41
From the graph:
The plot is essentially KE vs 1/l, so that since
KE=hc/l－W
The intercept when (1/l)=0 give
W=－KE=－(－2eV)=2eV
To obtain Planck’s constant h, we need the slope S
Then h=S/c.
S=(4－(－2))/(5－0) × 10-3=1.2 * 103 eV nm
h = 1.2 × 103 × 1.602 × 10-19×10-9 /(3 × 108) J s
= 6.4× 10-34 J s
cf (6.626 × 10-34 J s)
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.
6.3 Practical Quantum Detectors
The simplest type is
probably the vacuum
phototube, an example of
a photoemissive detector.
Light strikes photocathode (-)
-
+
hv e
Photocathode emits photoelectrons
Photoelectrons accelerate toward anode (+)
flow of electrons = current
current proportional to # photons incident on photocathode
quantum efficiency:the 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
photomultiplier, the efficiency becomes much higher.
form
a
• 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
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.
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.
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.
6.3 Practical Quantum Detectors
image tube:not 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.
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.