15'1 Monochromatic Plane Waves

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15.1 Monochromatic Plane Waves
So long as we restrict ourselves to linear media,
we can understand the properties of any EM waves
by studying a single frequency (monochromatic)
plane waves.
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• Last lecture we de-coupled the set of mixed
  differential equations to produce two wave
  equations, one for the E field, and one for the B
  field.
• The result was in the form of a transverse plane
  wave the E and B fields vary in the and
  directions, while the wave progresses in the
  direction.
• In de-coupling the equations we lost one piece of
  information the phase relation between the
  different fields.

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15.2 Energy and Momentum of E/M Waves Two
lectures ago we found an expression for the
energy stored in an E/M field In the case of
an E/M plane wave we can directly relate the
amplitude of the B field to that of the E
field (equally we could do the reverse but it is
traditional to write the result in terms of
E) This, in-turn, allows us to construct a
simple expression for the Poynting vector
associated with an E/M plane wave
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We are not going into the details here (see G
p352-355 if youre interested) but we can also
write down an expression for the momentum carried
by an E/M wave For optical measurements the
wavelength will be very short and we will
typically be averaging over many cycles of the
wave.
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Example (G 9.10) The intensity of sunlight
hitting the earth is about 1300 W/m2. If
sunlight strikes a perfect absorber, what
pressure does it exert? How about a perfect
reflector? What fraction of atmospheric pressure
does this amount to?
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15.3 E/M Waves in Insulators The if there are no
free charges or currents (and the material is
linear) then Maxwells Equations
become Where i.e. the fields inside the
matter are
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15.4 Absorption and Dispersion E/M Waves in
Conductors For the case of E/M waves propagating
in a vacuum and through and insulator we clearly
had no free charge or any currents. For a
conductor this is certainly not the case! To
understand what will happen to our E/M wave in a
conductor we first need to look at what happens
if we introduce a charge density into a conductor
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So once we have waited for any transient
accumulated free charge to dissipate then we
have Clearly there is only one term that
is different in this case. Applying the curl to
each of the right-hand equations, as we did for
the vacuum case, we get the modified wave
equations
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These equations still produce plane wave
solutions but the wave number k is complex
now The imaginary part of results
in an attenuation of the wave (decreasing
amplitude with increasing z)