Lecture 8: Laser amplifiers

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Spectral lineshape Spread in frequencies Gaussian lineshape The origin of inhomogeneous broadening. The individual Lorentzian emission lines associated with different atomic dipoles are oscillating at multiple distinct frequencies. If a dielectric material is made up of those atoms with such individual lines, its emission line will be the sum of the curves. When the individual lines are densely spaced over a frequency range large compared with their own individual widths, the total lineshape is termed inhomogeneously broadened. Ref: Optical resonance and two-level atoms, L. Allen and J. H. Eberly, pp. 7-10 16
Transition rates The transition rate of a resonant optical process measures the probability per unit time for the process to occur. The transition rate of an induced process is a function of the spectral distribution of the optical radiation and the spectral characteristics of the resonant transition. The spectral distribution of an optical field is characterized by its spectral energy density u() – the energy density of the optical radiation per unit frequency interval at the optical frequency . The total energy density of the radiation The spectral intensity distribution I() = (c/n) u(), n is the refractive index of the medium The total intensity I 0 I()d u 0 u()d 17
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: Inhomogeneous broadening Howeve
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
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
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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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