Chapter 3 Electromagnetic theory, photons and light

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Chapter 3 Electromagnetic theory, photons and
light September 5, 8, 10 Electromagnetic
waves 3.1 Basic laws of electromagnetic
theory Lights are electromagnetic waves. Electric
fields are generated by electric charges or
time-varying magnetic fields. Magnetic fields are
generated by electric currents or time varying
electric fields. Maxwells wave equation are
derived from the following four laws (Maxwells
equations). 3.1.1 Faradays induction law
Electromotive force (old term, actually a
voltage)
A time-varying magnetic field produces an
electric field.
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3.1.2 Gausss Law - electric
Flux of electric field
For point charge , e0 is the
permittivity of free space.
Generally,
For general material, the permittivity
, where KE is the relative permittivity
(dielectric constant).
3.1.3 Gausss Law- magnetic
There is no isolated magnetic monopoles
3.1.4 Amperes circuital law
For electric currents m0 is the permeability of
free space. For general material, the
permeability , where KM is the
relative permeability.
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Moving charges are not the only source for a
magnetic field. Example in a charging capacitor,
there is no current across area A2 (bounded by C).
Amperes law
A time-varying electric field produces a magnetic
field.
3.1.5 Maxwells equations
Gaussians divergence theorem
Stokess theorem
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Maxwells equations in differential
form (integrals in finite regions ? derivatives
at individual points)
In free space,

• Perpendicularity,
• Symmetry,
• Interdependence of E and B.

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3.2 Electromagnetic waves
Applying to free space Maxwells equations, we
have 3D wave equations
3.2.1 Transverse waves
For a plane EM wave propagating in vacuum on the
x direction
For linearly polarized wave
?In free space the plane EM wave is transverse.
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Harmonic waves

• E and B are in phase,
• E and B are mutually perpendicular.
• E B points to the propagation direction.

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Read Ch3 1-2 Homework Ch3 (1-7) 1,3,7 Due
September 12
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September 12, 15 Energy and momentum 3.3 Energy
and momentum 3.3.1 Poynting vector E-filed and
B-filed store energy Energy density (energy per
unit volume) of any E- and B-field in free space
(The first equation can be obtained from a
charging capacitor Eq/e0A, dWEldq).
For light, applying EcB, we have
The energy stream of light is shared equally
between its E-field and B-field. The energy
transport per unit time across per unit
area Assuming energy flows along the light
propagation direction, ?Poynting vector
is the power per unit area
whose normal is parallel to S.
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For a harmonic, linearly polarized plane wave
3.3.2 Irradiance Irradiance (intensity) The
average energy transport per unit area per unit
time.
Time averaging
In a medium
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The inverse square law The irradiance from a
point source is proportional to 1/r2. Total
power I4pr2constant.
3.3.3 Photons The electromagnetic wave theory
explains many things (propagation, interaction
with matter, etc.). However, it cannot explain
the emission and absorption of light by atoms
(black body radiation, photoelectric effect,
etc.). Planks assumption Each oscillator could
absorb and emit energy of hn, where n is the
oscillatory frequency. Einsteins assumption
Light is a stream of photons, each photon has an
energy of
3.3.3 Radiation pressure and momentum Maxwells
theory shows radiation pressure (P) energy
density (WorkPAcDtuAcDt)
For light
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Momentum density of radiation ( pV)
Momentum of a photon (p)
Vector momentum
The energy and momentum of photons have been
confirmed by Compton scattering.
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Read Ch3 3 Homework Ch3 (8-36)
8,14,16,19,27 Due September 19
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September 17,19 Radiation 3.4 Radiation 3.4.1
Linearly accelerating charges
Field lines of a moving charge

• Analogy A train emits smokes at speed c from 8
  chimneys over 360º. What do the trajectories of
  the smoke look like when the train is
• still,
• moving at a constant speed,
• moving at a constant acceleration,
• first accelerated and then moving at a constant
  speed?

Constant speed
With accelerating
Assuming the E-field information propagates at
speed c. Gausss law suggests that the field
lines are curved when the charge is accelerated.
The transverse component of the electric field
will propagate outward. ? A non-uniformly moving
charge produces electromagnetic waves.
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• Examples
• Synchrotron radiation. Electromagnetic radiation
  emitted by relativistic charged particles curving
  in magnetic or electric fields. Energy is mostly
  radiated perpendicular to the acceleration.
• Electric dipole radiation

Far from the dipole (radiation zone)
Irradiance

• Inverse-square-law,
• Angular distribution (toroidal).
• Frequency dependence.

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3.4.4 The emission of light from atoms Bohrs
model of H atom
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Read Ch3 4 Homework Ch3 37 Due September 26
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September 22, 24 Dispersion 3.5 Light in bulk
matter Phase speed in a dielectric
(non-conducting material) Index of refraction
(refractive index)
. KE and KM are the relative
permittivity and relative permeability. For
nonmagnetic materials Dispersion The phenomenon
that the index of refraction is wavelength
dependent. 3.5.1 Dispersion ?
How do we get e (w)?
Lorentz model of determining n (w) The behavior
of a dielectric medium in an external field can
be represented by the averaged contributions of a
large number of molecules. For most materials
Examples Orientational polarization, electronic
polarization, ionic polarization.
Electric polarization The electric dipole
moment per unit volume induced by an external
electric field.
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Atom electron cloud nucleus. How is an atom
polarized ? Restoring force Natural (resonant)
frequency Forced oscillator Damping force
?Newtons second law (equation of
motion) Solution Electric polarization (
dipole moment density)
?Dispersion equation Frequency dependent
frequency dependent n (w)
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Quantum theory w0 is the transition frequency.
For a material with several transition
frequencies Oscillator strength
Normal dispersion n increases with
frequency. Anomalous dispersion n decreases with
frequency.
n' ? Phase velocity n" ? Absorption
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Sellmeier equation An empirical relationship
between refractive index n and wavelength l for a
particular transparent medium
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Read Ch3 5-7 Homework Ch3 (38-)
45,46,48,57 Due October 3