Lecture 8: Laser amplifiers

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Spectral energy density The energy density of a radiation field u() (joules per unit volume per unit frequency interval) can be simply related to the intensity of a plane electromagnetic wave. If the intensity of the wave is I() (watts per unit area per frequency interval) u() c = I() where c is the velocity of light in free space (in the medium of refractive index n, u() c/n = I()) V A Length c in a second 18 18
Transition rates For the upward transition from |1> to |2> associated with absorption in the frequency range between and +d is W 12 ()d B 12 u()ĝ()d (s -1 ) For the downward transition from |2> to |1> associated with stimulated emission W 21 ()d B 21 u()ĝ()d (s -1 ) The spontaneous emission rate is independent of the energy density of the radiation and is solely determined by the transition lineshape function W sp ()d A 21 ĝ()d (s -1 ) The A and B constants are the Einstein A and B coefficients. 19
Page 1 and 2: 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: Transition rates The transiti
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
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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