Lecture 8: Laser amplifiers

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Four-level pumping This is not always the case because the population densities of the ground state and level 3, N g and N 3 , are related to N 1 and N 2 by N g N 1 N 2 N 3 N a where the total atomic density in the system, N a , is a constant. If the pumping involves a transition between the ground state and level 3 with transition probability W, then R (N g N 3 )W If levels 1 and 3 are short-lived, then N 1 ≈ N 3 ≈ 0, N g + N 2 ≈ N a s.t. N g ≈ N a -N 2 ≈ N a - N 94 94
Four-level pumping Under these conditions, the pumping rate can be approximated as R ( Na N) W which reveals that the pumping rate is a linearly decreasing function of the population difference N and is thus not independent of it. This arises because the population inversion established between levels 2 and 1 reduces the number of atoms available to be pumped. We obtain N sp N a W 1 sp W sp W i 95 95
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Lecture 8: Laser amplifiers Opt
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Optical transitions 3
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Photon-matter interaction processes
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Three basic photon-matter interacti
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Probability per second of a spontan
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Spectral lineshape The spectra
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Homogeneous broadening If all o
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Inhomogeneous broadening Howeve
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Transition rates The transiti
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Transition rates For the upward tr
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Transition rates The total induce
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Blackbody radiation A system und
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Planck’s law of blackbody radiati
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Transition rates In thermal equili
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Boltzmann distribution Energy E E 2
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Transition rates Therefore, the s
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Transition cross section For the
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Optical absorption and amplificatio
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Optical absorption and amplificatio
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Resonant optical susceptibility Fo
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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
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: Four-level pumping In most four-le
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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