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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: [email protected] Office Hours: Tues/Thurs 23PM JDW, ECE Summer 2010 Chapter 8: Laser Oscillations Above Threshold • Laser Gain Saturation • Laser Beam Growth beyond the Saturation Intensity • Optimization of Laser Output Power • Energy Exchange between Upper Laser Level Population and Laser Photons • Laser Output Fluxuations • Laser Amplifiers 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 8 Homework: 1, 2, 3, 4, 11, 8, 10 Laser Gain Saturation • Adding the two equations for upper and lower population states allows one to develop a relation for the lower state in terms of fluxes divided by the lower state decay rate • The upper state can be rewritten as: • Yielding: Population Densities of N u and N l with Beam Present Small – Signal Gain Coefficient • One can define the small signal gain coefficient as the gain at resonance, when no beam is present as: • Where: • This value represents the capability of the gain medium to produce a laser. Thus in order to lase, the smallsignal gain coefficient must be greater than the threshold gain coefficient • Thus the gain: is the amount of gain that would be measured if a low intensity , I o , beam were directed through a gain medium of length L to generate the high power output intensity, I Saturation of the Laser Gain above Threshold • We shall now consider a beam of high intensity, I, with a population difference: • The saturated gain coefficient is then calculated using: Saturation of the Laser Gain above Threshold • We shall now consider a beam of high intensity, I, with a population difference: • Note that the population density above does not depend on the lower level. This can only occur if the additional population flux l u due to stimulated emission is equal to the population flux of absorption ( u l). Thus: • This also requires that above threshold that the gain coefficient goes to zero. This is indeed the solution for an ideal system • However, in real systems only the net gains goes to zero. Mirror transmission losses, absorption losses of the media, and scattering losses in the system always require that the upper level population density is slight larger than the gain ratio multiplied by the lower state: l l u u N g g N > Lasers Above Threshold: Exponential to Linear Growth Lasers Above Threshold: Exponential to Linear Growth • For a two mirror system above threshold: In steady state: Note: Losses associated with the geometry or material properties of the cavity may prevent laser excitation in the center of the...
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 Summer '10
 Williams
 Stimulated emission, Laser Amplifiers

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