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Unformatted text preview: Lasers PH 645/ OSE 645/ EE 613 Summer 2010 Section 1: T/Th 2:45 4:45 PM Engineering Building 240 John D. Williams, Ph.D. Department of Electrical and Computer Engineering 406 Optics Building  UAHuntsville, Huntsville, AL 35899 Ph. (256) 8242898 email: williams@eng.uah.edu Office Hours: Tues/Thurs 23PM JDW, ECE Summer 2010 Chapter 9: Requirements for Obtaining Population Inversions Inversion of two level systems Radiative vs. collisional decay rates Steadystate inversions in 3 and 4 level systems Transient population inversions Processes that inhibit or destroy inversions Cambridge University Press, 2004 ISBN13: 9780521541053 All figures presented from this point on were taken directly from (unless otherwise cited): W.T. Silfvast, laser Fundamentals 2 nd ed., Cambridge University Press, 2004. Chapter 9 Homework: 1 (bonus), 6,8,10, 12 Simplistic Model of a 2 Level System Consider a two level system Let atoms in the cell be at room temperature so that nearly all of the electrons are in the lower level (ground state) This requirements stipulates that thermal population to the upper state is prohibited and thus the upper state can only be obtained through a pumping flux Furthermore by defining a two state system, the degeneracy ratio of upper to lower state transitions must be 1 Thus we can stipulate that prior to pumping the system behaves as When applying a pumping flux, one drives a few electrons excited to the upper level that decay back to the lower level at rate, ul The number of atoms in the upper state can then be equated by Allowing one to rewrite the gain equations as We can easily note here that as the population of Nu increases, that the ratio of lower states to the total number of states decreases When it reaches a value of 0.5, no more energy will be absorbed because the exponent will go to zero This rather simplistic approach provides a key bit of information for one to consider. If the number of upper states is equal to the number of lower states, then no further absorption can occur, b/c N u can never exceed N l . While radiative decay will always reduce the population of N u , it can never exceed the value of N l and thus there can be no population inversion We therefore conclude that it is impossible a laser from a simple two level system Simplistic Model of a 2 Level System Before we move on to more complex systems that do allow population inversions, let us review two basic decay processes From Chapter 4, we learned that radiative decay from and upper to a lower state is proportional to ul 2 We intend to show later in this chapter that collisional (vibrational) decays respond as: Thus we present the following relation decay rates in terms of energy and time. This relation provides a guide for analyzing for multistate population inversions Radiative vs. Collisional Decay Rates Energy Level Arrangements for Pumping 3 and 4 level Systems...
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This note was uploaded on 12/15/2011 for the course OSE 2000 taught by Professor Williams during the Summer '10 term at University of Alabama  Huntsville.
 Summer '10
 Williams

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