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Light and Matter

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Light and Matter Quantum electrodynamics Tim Freegarde School of Physics & Astronomy University of Southampton How light interacts with matter Lorentz theory of ... – PowerPoint PPT presentation

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Title: Light and Matter


1
Light and Matter
Quantum electrodynamics
Tim Freegarde
2
How light interacts with matter
  • atoms and molecules are polarized by applied
    fields
  • induced polarization modifies field propagation
    refractive index absorption

3
Lorentz theory of atomic polarization
  • bound or massive nuclei
  • electrons confined in harmonic potential
  • restoring force proportional to displacement
  • Newtonian dynamics
  • dissipation of motion through frictional force

4
Lorentz theory of atomic polarization
  • complex dielectric constant

G0.050
freq
  • real part refractive index
  • imaginary part (absorption)

5
Lorentz theory of atomic polarization
  • complex dielectric constant

G0.050
G0.075
G0.100
G0.125
G0.150
G0.175
G0.200
G0.225
G0.250
G0.275
G0.300
G0.325
G0.350
G0.375
G0.400
G0.425
G0.450
G0.475
G0.500
freq
  • real part refractive index
  • imaginary part absorption

6
Lorentz theory of atomic polarization
  • complex dielectric constant

G0.200
freq
  • real part refractive index
  • imaginary part absorption

strong attenuation even for small G
7
Lorentz theory of atomic polarization
  • complex dielectric constant

G0.050
G0.075
G0.100
G0.125
G0.150
G0.175
G0.200
G0.225
G0.250
G0.275
G0.300
G0.325
G0.350
G0.375
G0.400
G0.425
G0.450
G0.475
G0.500
freq
  • real part refractive index
  • imaginary part absorption
  • stop band from to

strong attenuation even for small G
8
Causality and the dispersion relations
  • causality effect follows cause
  • causality ? must obey

9
the Kramers-Krönig dispersion relations
  • causality effect follows cause
  • Kramers-Krönig relations relate the real and
    imaginary parts of ?(w)

10
Implication for all dielectrics
  • evaluate e1 as w?0
  • if e1 ? 1, there must be frequencies at which e1
    ? 0 (absorption)
  • dielectrics cannot be transparent at all
    wavelengths

11
Application to a single sharp absorption
  • suppose a single absorption at w w0

1
  • Kramers-Krönig then gives

0
freq
12
Quantum description of atomic polarization
  • full time-dependent eigenfunctions therefore
  • any state of the two-level atom may hence be
    written

13
Quantum description of atomic polarization
  • full time-dependent eigenfunctions therefore
  • any state of the two-level atom may hence be
    written

14
Quantum description of atomic polarization
15
Quantum description of atomic polarization
x/a0
x/a0
  • electron density depends upon relative phase of
    superposition components

16
Atomic polarization
  • response of massive electrons to applied electric
    field

G0.050
G0.075
G0.100
G0.125
G0.150
G0.175
G0.200
G0.225
G0.250
G0.275
G0.300
G0.325
G0.350
G0.375
G0.400
G0.425
G0.450
G0.475
G0.500
  • resonant frequency due to confining potential of
    electrons in atom
  • electron displacement leads to atomic polarization

freq
  • frequency-dependent amplitude and phase lag of
    response related by causality
  • Newtonian and quantum mechanical models give same
    result
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