Lecture 8: Laser amplifiers

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Rate equations in the absence of amplifier radiation The rates of increase of the population densities of levels 2 and 1 arising from pumping and decay are dN 2 /dt = R 2 –N 2 / 2 dN 1 /dt = -R 1 –N 1 / 1 + N 2 / 21 Steady-state population difference in the absence of amplifier radiation (dN 1 /dt = dN 2 /dt = 0) N 0 = N 2 –N 1 = R 2 2 (1- 1 / 21 ) + R 1 1 A large gain coefficient requires a large population difference ( 0 () = N 0 e ()) 86 86
Rate equations in the absence of amplifier radiation To increase population difference N 0 • Increase pumping and de-pumping rate (R 2 and R 1 ) • Long 2 , but sp must be sufficiently short so as to make the radiative transition rate large • Short 1 (if R 1 < ( 2 / 21 )R 2 ) The physical picture: • the upper level should be pumped strongly and decay slowly so that it retains its population. • The lower level should be de-pumped strongly so that it quickly disposes of its population. Ideally, 21 ≈ sp
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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
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
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: Rate equations 2 R 2 1/ 21 = 1/ sp
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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