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7/27/2019 Lecture6 Ch3 Photons
http://slidepdf.com/reader/full/lecture6-ch3-photons 1/17
Chapter 3
Electromagnetic theory, Photons.and Light
Lecture 6
Pointing vector and Irradiance
Photons
Radiation Electromagnetic spectrum
7/27/2019 Lecture6 Ch3 Photons
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Energy of EM wave
It was shown (in Phys 272) that field
energy densities are:
20
2 E u E
2
02
1
Bu B
Since E=cB and c=( 0 0)-1/2:
B E uu - the energy in EM wave is shared equally
between electric and magnetic fields
Total energy:2
0
2
0
1 B E uuu B E
(W/m2)
7/27/2019 Lecture6 Ch3 Photons
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The Poynting vector
EM field contains energy that propagates
through space at speed c
Energy transported through area A in timet : uAct
EB EBcB E c E cuct A
t uAcS
0
0
00
0
2
0
11
Energy S transported by a wave through
unit area in unit time: E c2
The Poynting vector:
B E S
0
1
power flow per unit area for a
wave, direction of propagation
is direction of S .
(units: W/m2)
John Henry Poynting
(1852-1914)
7/27/2019 Lecture6 Ch3 Photons
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The Poynting vector: polarized harmonic wave
B E S 0
1
Polarized EM wave:
t r k E E
cos0
t r k B B
cos0
Poynting vector:
t r k B E S
2
00
0cos
1
This is instantaneous value: S is oscillating
Light field oscillates at ~10 15 Hz -most detectors will see average value of S .
7/27/2019 Lecture6 Ch3 Photons
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Irradiance
t r k B E S
2
00
0
cos1Average value for periodic function:
need to average one period only.
It can be shown that average of cos2
is: 21cos
2
T t 2
00
00
0 22
1 E
c B E S
T
And average power flow per unit time:
Irradiance:2
00
2 E
cS I
T
Alternative eq-ns:
T T B
c E c I
2
0
2
0
Usually mostly E-field component interacts with matter, and we
will refer to E as optical field and use energy eq-ns with E
Irradiance is proportional to the square of the amplitude of the E field
For linear isotropic
dielectric:
T E I 2
v
Optical power radiant flux total power falling on some area (Watts)
7/27/2019 Lecture6 Ch3 Photons
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Spherical wave: inverse square law
Spherical waves are produced by point sources.As you move away from the source light intensity
drops
t r k r
t r vcos, A
Spherical wave eq-n:
t r k
r
E E
cos0 t r k
r
B B
cos0
t r k r
B
r
E S
200
0
cos1
2
02
0 1
2 E
r
cS I
T
Inverse square law: the irradiance from a point source drops as 1/r 2
7/27/2019 Lecture6 Ch3 Photons
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Classical EM waves versus photons
The energy of a single light photon is E=h
The Planck’s constant h = 6.626×10-34 Js
Visible light wavelength is ~ 0.5 mJ104 19
1
c
hh E
Example: laser pointer output power is ~ 1 mW
number of photons emitted every second:
photons/s105.2J/photon104
J/s10 15
19
3
1
E
P
Conclusion: in many every day situations the quantum nature of
light is not pronounced and light could be treated as a classical
EM wave
7/27/2019 Lecture6 Ch3 Photons
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Photon counter
It is possible to detect single photons
Example: photomultiplier tube (PMT)
Photon kicks an electron out of cathode
The electron is accelerated by an
E-field toward a dynode
The accelerated electron strikes
the dynode and kicks out more
electrons
Many dynodes are used to get
burst of ~105 electrons per single
photoelectron
The burst of electron current can
be detected electronically
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Radiation pressure
Using classical EM theory Maxwell showed that radiation pressure
equals the energy density of the EM waves:
2
0
20
2
1
2 B E u
P
ucS
c
t S t P
This is the instantaneous pressure that would be exerted on a
perfectly absorbing surface by a normally incident beam
Average pressure:
c
I
c
t S t T
T P (N/m2)
* for reflecting surface pressure doubles* in quantum picture each photon has a momentum:
h p k p
or , where
2
h
propagation vector
Experimental confirmation:
Compton effect
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Example problem (continued)
t
cr ji
Ac
P E
2sinˆcosˆ2
cosk ˆ2
0
x
y
z
B
t r k B B
cos0Magnetic field:It is in phase with E .
Need only find its amplitude and direction.
0
00
21/ Ac
P
cc E B
cosˆsinˆ21
0
0 ji Ac
P
c B
t
cr ji ji
Ac
P
c B
2sinˆcosˆ2
coscosˆsinˆ21
0
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Radiation: accelerated charges
Electromagnetic pulse can propagate in space
How can we initiate such pulse?
Short pulse of transverse
electric field
Field of a moving charge
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Radiation: accelerated charges
1. Transverse pulse
propagates at speed of
light2. Since E(t) there must
be B
3. Direction of v is given
by:
E
Bv
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Electric dipole radiation
Oscillating charges in dipole create sinusoidal E
field and generate EM radiation
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Electric dipole radiation
Dipole moment:
t
t d d
qd
cos
cos
0
0
p p
p
Electric field of oscillating dipole:
r
t kr k E
cos
4
sin
0
2
0 p
2
2
0
32
42
0 sin
32 r c I
p
Irradiance:
* EM wave is polarized along dipole
* I ~ 4 - higher frequency, stronger radiation
* No radiation emitted in direction of dipole
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