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© Matthias Liepe, 2012
Recap I Lecture 38
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Recap II
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Today: • Lasers
• Stimulated photon emission
• Particle waves
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LASER Light
Amplification by
Stimulated
Emission of
Radiation
Example: He-Ne Laser (red):
100% reflective mirror
99% reflective mirror
optical oscillator
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Special characteristics of laser light:
1. Highly monochromatic (single wavelength).
2. Highly coherent. Individual long waves (wave trains) for
laser light can be several hundred km long. The
corresponding coherence length for wave trains emitted by a
light bulb is typically less than a meter.
3. Highly directional. Spreading of the beam is due to
diffraction at the exit aperture of the laser.
4. Can be sharply focused. Intensity of 1017 W/cm2 can be
readily obtained. (An oxyacetylene flame only has an
intensity of about 103 W/cm2.)
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Coherent vs. Incoherent Light
Polychromatic - incoherent
Monochromatic - incoherent
Monochromatic - coherent
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Laser uses:
Voice & data transmission
over optical fibers.
Read & write CDs, DVDs,
BDs.
Read bar codes.
Surgery.
Laser printing.
Welding. Holography.
Cutting cloth.
Surveying.
Range finding.
Weapons.
Nuclear fusion research.
Spectroscopy.
Interferometry.
Optical trapping.
Microscopy (e.g., confocal,
two-photon).
Photochemistry.
Cutting metal.
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Laser action depends on three processes:
1. Absorption:
Ef
Ei
hf Ef Ei
2. Spontaneous emission:
Ei
Ef
hf Ei Ef
• Emission is not triggered by an outside influence.
• Mean lifetime of excited atoms in ‘normal’ states is 108 s.
• For metastable excited states this can be 105 times longer.
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3. Stimulated emission:
Ei
Ef
hf Ei Ef
New photon
Original photon
• Original & new photons are identical.
• Associated waves have the same: - energy, ()
- direction
- phase
- polarization
• The probability per atom for absorption is the same as the
probability per atom for stimulated emission.
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Two competing processes: Absorption:
Two photons
No photons
Stimulated emission:
• For lasing, need more atoms in the higher energy state than in the lower energy state. This condition is called a population inversion. It must be artificially created by some input of energy.
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Example: Population Inversion Collisions
Simplified energy level diagram of a He-Ne laser:
• Inelastic collision of energetic electrons with ground state helium atoms
• Collisions excite helium atoms from the ground state to higher energy excited states, among them a along-lived metastable state.
• Because of a near coincidence between the energy level of the metastable He state, and an excited state of neon, collisions between these helium metastable atoms and ground state neon atoms results in a selective and efficient transfer of excitation energy from the helium to neon.
-> Population inversion for Ne
Energy
Helium states Neon states
Ground state
Excitation via collisions
metatable
He-Ne collisions
Rapid decay
photon
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Startup of a LASER
• “Pumping” produces a population inversion, i.e. more atoms in are in an excited state then in the ground state.
• Excited atoms emit photons; initially in random directions. Photons cause other exited atom to emit via stimulated emission.
• Photons parallel to axis reflect from mirrors. Reflected photons stimulate further emission by excited atoms. -> amplification in each pass though the laser medium.
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Particle waves λ = h/p : Order of Magnitude Estimate
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An electron’s kinetic energy K is the same as the energy Eph of a photon with 10 nm associated wavelength. How does the electron’s de Broglie wavelength compare with the wavelength associated with the photon (hc = 1240 eV nm; E0,e-=511 keV)?
A. electron photon.
B. electron photon.
C. electron photon.
D. Not enough information.
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Davisson-Germer Experiment (1925): Scattering of low energy electrons by a crystal surface
(1/)
1 Å
Evidence for de Broglie’s Particle Waves:
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G. P. Thompson’s Experiment: Diffraction of 10 – 40 keV electrons by a thin polycrystalline foil
polycrystalline film Bragg condition satisfied for any given reflecting plane concentric circles
0.1 Å=10-11 m
thin foil screen
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Electron diffraction by polycrystalline aluminum
Laue pattern of electron diffraction by a single
crystal
(Courtesy of Prof. Y. Soejima, Dept. of Physics, Kyushu Univ.)
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2-slit Interference of Electrons
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Diffraction of Neutrons
= several Å down to <10-14 m
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The Spallation Neutron Source (SNS) in Oak Ridge, TN
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Why Neutrons?
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Scattering of Alpha Particles
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Crystal Diffraction of Neutral Helium (1930)
1 Å
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Fullerene molecule C60 , consisting of 60 carbon atoms
Interference of Molecules