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
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Causality and the dispersion relations

• causality effect follows cause

• causality ? must obey

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the Kramers-Krönig dispersion relations

• causality effect follows cause

• Kramers-Krönig relations relate the real and
  imaginary parts of ?(w)

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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

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Application to a single sharp absorption

• suppose a single absorption at w w0

1

• Kramers-Krönig then gives

0
freq
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Quantum description of atomic polarization

• full time-dependent eigenfunctions therefore

• any state of the two-level atom may hence be
  written

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Quantum description of atomic polarization

• full time-dependent eigenfunctions therefore

• any state of the two-level atom may hence be
  written

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Quantum description of atomic polarization
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Quantum description of atomic polarization
x/a0
x/a0

• electron density depends upon relative phase of
  superposition components

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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