Lecture 8: Laser amplifiers

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Three basic photon-matter interaction processes Absorption – when the quantum energy h equals the energy difference between the two energy levels (a resonant condition); the atom gains a quantum of energy Stimulated emission – the emission of a photon is triggered by the arrival of another, resonant photon Spontaneous emission – when an atom emits a photon, losing a quantum of energy in the process Einstein in 1917 first pointed out that stimulated emission is essential in the overall balance between emission and absorption, about reaching thermal equilibrium for a system of atoms. (Einstein Relations) Stimulated emission was demonstrated in 1953 in the microwave frequency by Basov, Prokhorov and Townes (Nobel 1964) 6
Three basic photon-matter interaction processes A photon emitted by stimulated emission has the same frequency, phase, polarization and propagation direction as the optical radiation that induces the process. Spontaneously emitted photons are random in phase and polarization and are emitted in all directions, though their frequencies are still dictated by the separation between the two energy levels, subject to a degree of uncertainty determined by the linewidth of the transition. Therefore, stimulated emission results in the amplification of an optical signal, whereas spontaneous emission adds noise to an optical signal. Absorption leads to the attenuation of an optical signal. 7
Page 1 and 2: Lecture 8: Laser amplifiers Opt
Page 3 and 4: Optical transitions 3
Page 5: Photon-matter interaction processes
Page 9 and 10: Probability per second of a spontan
Page 11 and 12: Spectral lineshape The spectra
Page 13 and 14: Homogeneous broadening If all o
Page 15 and 16: Inhomogeneous broadening Howeve
Page 17 and 18: Transition rates The transiti
Page 19 and 20: Transition rates For the upward tr
Page 21 and 22: Transition rates The total induce
Page 23 and 24: Blackbody radiation A system und
Page 25 and 26: Planck’s law of blackbody radiati
Page 27 and 28: Transition rates In thermal equili
Page 29 and 30: Boltzmann distribution Energy E E 2
Page 31 and 32: Transition rates Therefore, the s
Page 33 and 34: Transition cross section For the
Page 35 and 36: Optical absorption and amplificatio
Page 37 and 38: Optical absorption and amplificatio
Page 39 and 40: Resonant optical susceptibility Fo
Page 41 and 42: Resonant optical susceptibility Th
Page 43 and 44: Population inversion 43
Page 45 and 46: Population inversion A nonequilibr
Page 47 and 48: Rate equations The net rate of chan
Page 49 and 50: Population inversion Population in
Page 51 and 52: Two-level systems No matter how a
Page 53 and 54: Two-level systems Take the upward
Page 55 and 56: Two-level systems Intuitively, th
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Quasi-two-level systems By pumpi
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Population inversion in three-level
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Three-level systems The parameter
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Four-level systems pump h p Nonradi
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Neodymium-doped glass Nd 3+ :glass
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Coherent optical amplifiers Gain, n
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Coherent light amplification As
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Population inversion Light tran
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Real coherent amplifiers Real
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Gain and bandwidth The wave is am
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Gain coefficient As the incident
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Gain coefficient The coefficient
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Gain bandwidth The dependence
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Phase‐shift coefficient The las
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Rate equations 2 R 2 1/ 21 = 1/ sp
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Rate equations in the absence of am
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Rate equations in the presence of a
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Four-level pumping Pump R Laser W i
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Four-level pumping In most four-le
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Four-level pumping Under these c
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Three-level pumping Rapid decay S
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Three-level pumping The population
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Three-level pumping The dependence
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Saturated gain in homogeneously bro
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Gain coefficients This represents t
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Amplified spontaneous emission T
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Amplifier noise The ASE of a la
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Lecture 8: Laser amplifiers

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