Chapter 3
Electromagnetic Theory, Photons,and Light
Lecture 6
Photons Radiation Emission of light by atoms
Example problemA laser pointer emits light at 630 nm in xy plane at =450 to axis x(counter clock-wise). The light is polarized along axis z , beam cross-section is A=1 mm2 and its power is P=1 mW.1. Write an equation of E and B components of this EM wave for the region of the beam.
x
y
z trkEE
cos0
Find : c22 Find k: sinˆcosˆ2 jik
Find E0:Irradiance: 2
00
2EcI
AP
00 2 AcPE k̂2 00 AcPE
tcrji
AcPE
2sinˆcosˆ2cosk̂2
0
Electric field:
B
E
Example problem (continued)
tcrji
AcPE
2sinˆcosˆ2cosk̂2
0
x
y
z
B trkBB
cos0Magnetic field:It is in phase with E. Need only find its amplitude and direction.
000
21/AcP
ccEB
cosˆsinˆ21
00 ji
AcP
cB
tcrjiji
AcP
cB
2sinˆcosˆ2coscosˆsinˆ21
0
Example problem (continued)
2. This laser beam is reflected backwards by a mirror. What is the average force on the mirror due to the radiation pressure?
AcP
cIt
T22 PFind average pressure
Find force: N 106.6m/s 103
W1022 128
3
cPAtF
TP
3. How much energy is contained in EM field of 1 m long beam?
Power is amount of energy per unit time. During one second, light travels c meters:
J 103.3m 1m/s 103
J/s 10)1( 128
3
LcPmEnergy
Alternatively can find u using E0 and multiply by volume
Classical EM waves versus photonsThe energy of a single light photon is E=h
The Planck’s constant h = 6.626×10-34 JsVisible light wavelength is ~ 0.5 m J 104 19
1
chhE
Example: laser pointer output power is ~ 1 mWnumber of photons emitted every second:
photons/s 105.2J/photon 104J/s10 15
19
3
1
EP
Conclusion: in many every day situations the quantum nature of light is not pronounced and light could be treated as a classical EM wave
Photons
1900: to explain black body radiation spectrum Max Planck suggested that light is emitted in small indivisible quanta of energy:
E=h (h=6.626×10-34 J.s)
1905: to explain photoelectric effect Einstein stated that EM field itself is quantized
Photons cannot be observed directly, one can only see them through interaction with matter - absorption. Photon is destroyed in the process.
Photons carry energy and momentum (atoms recoil when emit photons)
hp kp
or , where2h
propagation vector
Experimental confirmation:Compton effect
optical power
Energy of a single photon at mean frequency 0 in quasi-monochromatic beam
Energy per unit time crossing some area A
Photon
Mean photon flux:00 h
PhAI
Number of photons emitted every second from a ~1 mW laser pointer is ~1015 photons
Photons strike screen every 1 fs on average.Exact position and time of arrival for each photon cannot be predicted with absolute certainly - we can only predict the probabilities.
no. photons per unit area per unit time
Photon
At any location on a screen, the classical irradiance is proportional to the probability of detecting a photon at that location
photographic film
Light exposurelow medium high
Quantum uncertainty.Example: throw a single coin, it will fall either heads or tails up, unpredictable
but with 1015 coins - can predict result with high precision
Photon statistics
Maxwell-Boltzmann statistics: for distinguishable particles
In quantum physics for indistinguishable particles:* Bose-Einstein statistics for bosons (particles with integer spin)* Fermi-Dirac statistics for fermions (particles with integer+half spins)
Photons are bosons - many photons can simultaneously be in exactly the same state, i.e. have the same energy
When a large number of photons occupy the same state (i.e. have the same energy, polarization and direction), the inherent granularity of the light beam vanishes and the EM field appears as the continuous medium of an electromagnetic wave - monochromatic plane wave.
Different monochromatic plane waves represent different photon states
Photon counter
It is possible to detect single photons
Example: photomultiplier tube (PMT)
Photon kicks an electron out of cathodeThe electron is accelerated by an E-field toward a dynodeThe accelerated electron strikes the dynode and kicks out more electronsMany dynodes are used to get burst of ~105 electrons per single photoelectronThe burst of electron current can be detected electronically
Photon statistics
PMTlow powerlight beam
Photons arrive at random.
Poisson distribution of photons arriving at detector during time T
Radiation: accelerated charges
Electromagnetic pulse can propagate in spaceHow can we initiate such pulse?
Short pulse of transverseelectric field
Field of a moving charge
Radiation: accelerated charges
1. Transverse pulse propagates at speed of light
2. Since E(t) there must be B
3. Direction of v is given by: BE
E
Bv
Electric dipole radiationOscillating charges in dipole create sinusoidal E field and generate EM radiation
Electric dipole radiation
Dipole moment:
t
tddqd
coscos
0
0
pp
p
Electric field of oscillating dipole:
r
tkrkE
cos4
sin
0
20p
2
2
032
420 sin
32 rcI
p
Irradiance:* EM wave is polarized along dipole* I ~ 4 - higher frequency, stronger radiation* No radiation emitted in direction of dipole
Dipole antenna
Example: connect AC generator to ‘dipole’ antenna/Charges will run up and down - dipole moment will be oscillating and radiation will be emitted