2 a solid state laser material of refractive index

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2.A solid state laser material of refractive index1.45nhas a spontaneous emission lifetime of150 nsec, a spectral emission bandwidth of 10 THz, and a central wavelength of 1.5m.Thelineshape is Gaussian.In other words the lineshape is described as20221()EEh fEef,whereE0andfare the energies corresponding to the central wavelength and the spectralbandwidth of the lineshape.2(a)What are the Einstein A and B coefficients for this system?(b)What is the gain cross section for this system?The gain at a given energyEis expressed as21()()g EEnn, whereEis the gain cross section, and2nand1nare the populationsin the upper and lower energy states respectively.(c)How big a population inversion is required to amplify a weak 1.5m signal by a factor of 2 in a 1cm length?What are the gain and amplification factor at 1.55m under these conditions?
(d)If there are 1017absorbing ions per cm-3, what is the transmission through 1 cm of this material at1.5m if all the ions are in the ground state?3.A distributed amplifier at1.5 mis built using a doped fiber with the followingcharacteristics:Spontaneous emission lifetime of1500 secA, length2 mL
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Spring
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Photon, Santa Barbara, Department of Electrical and Computer Engineering, University of California

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