Lecture 8: Laser amplifiers

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Transition rates The induced and the spontaneous transition rates for a given system are directly proportional to one another. The relationship can be obtained by considering the interaction of blackbody radiation with an ensemble of identical atomic systems in thermal equilibrium. The spectral energy density of the blackbody radiation at a temperature T (known as thermal radiation or blackbody radiation) is given by Planck’s formula: u() 8n3 h 3 c 3 1 e h /k BT 1 where k B is the Boltzmann constant, k B T is the thermal energy (k B T = 26 meV @ T = 300 K) 22
Blackbody radiation A system under thermal equilibrium produces a radiation energy density u()(J Hz -1 m -3 ) which is identical to blackbody radiation. A blackbody absorbs 100% all the radiation falling on it, irrespective of the radiation frequency. If the inside of this body is in thermal equilibrium it must radiate as much energy as it absorbs and the emission from the body is therefore characteristic of the equilibrium temperature T inside the body => this type of radiation is often called “thermal” radiation or blackbody radiation Thermal radiation 23 23
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 and 18: Transition rates The transiti
Page 19 and 20: Transition rates For the upward tr
Page 21: Transition rates The total induce
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
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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
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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