Lecture 8: Laser amplifiers

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Spontaneous emission An electron spontaneously falls from a higher energy level E 2 to a lower one E 1 , the emitted photon has frequency = (E 2 –E 1 ) / h |2> This photon is emitted in a random direction with arbitrary polarization. The probability of such a spontaneous jump is given quantitatively by the Einstein coefficient for spontaneous emission (known as the “Einstein A coefficient”) defined as |1> A 21 = “probability” per second of a spontaneous jump from level |2> to level |1>. 8 8
Probability per second of a spontaneous emission For example, if there are N 2 population per unit volume in level |2> then N 2 A 21 per second make jumps to level |1>. The total rate at which jumps are made between the two levels is dN 2 /dt = -N 2 A 21 A negative sign because the population of level 2 is decreasing Generally an electron can make jumps to more than one lower level, unless it is in the first (lowest) excited level. 9 9
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: Three basic photon-matter interacti
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 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
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Population inversion in three-level
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Three-level systems The parameter
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Four-level systems pump h p Nonradi
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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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