Lecture 8: Laser amplifiers

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Two-level systems In a true two-level system, the energy levels |2> and |1> can each be degenerate with degeneracies g 2 and g 1 , but the population densities in both levels are evenly distributed among the respective degenerate states. In this situation, p = ep / ap = g 1 /g 2 = e / a N 2 e –N 1 a = - a N t [1+( e + a )(I/hW p / a ) 2 ] -1 < 0 No matter how a true two-level system is pumped, it is clearly not possible to attain population inversion for an optical gain in the steady state. 54
Two-level systems Intuitively, the pump for a two-level system has to be in resonance with the transition between the two levels, thus inducing downward transitions and upward transitions. In the steady state, the two-level system would reach thermal equilibrium with the pump at a finite temperature T, resulting in a Boltzmann population distribution N 2 /N 1 = (g 2 /g 1 ) exp(-h/k B T) without population inversion. 55
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Lecture 8: Laser amplifiers Opt
Page 3 and 4: Optical transitions 3
Page 5 and 6: Photon-matter interaction processes
Page 7 and 8: Three basic photon-matter interacti
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: Two-level systems Take the upward
Page 57 and 58: Quasi-two-level systems By pumpi
Page 59 and 60: Population inversion in three-level
Page 61 and 62: Three-level systems The parameter
Page 63 and 64: Four-level systems pump h p Nonradi
Page 65 and 66: Neodymium-doped glass Nd 3+ :glass
Page 67 and 68: Coherent optical amplifiers Gain, n
Page 69 and 70: Coherent light amplification As
Page 71 and 72: Population inversion Light tran
Page 73 and 74: Real coherent amplifiers Real
Page 75 and 76: Gain and bandwidth The wave is am
Page 77 and 78: Gain coefficient As the incident
Page 79 and 80: Gain coefficient The coefficient
Page 81 and 82: Gain bandwidth The dependence
Page 83 and 84: Phase‐shift coefficient The las
Page 85 and 86: Rate equations 2 R 2 1/ 21 = 1/ sp
Page 87 and 88: Rate equations in the absence of am
Page 89 and 90: Rate equations in the presence of a
Page 91 and 92: Four-level pumping Pump R Laser W i
Page 93 and 94: Four-level pumping In most four-le
Page 95 and 96: Four-level pumping Under these c
Page 97 and 98: Three-level pumping Rapid decay S
Page 99 and 100: Three-level pumping The population
Page 101 and 102: Three-level pumping The dependence
Page 103 and 104: Saturated gain in homogeneously bro
Page 105 and 106:
Gain coefficients This represents t
Page 107 and 108:
Amplified spontaneous emission T
Page 109:
Amplifier noise The ASE of a la
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Lecture 8: Laser amplifiers

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