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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 4: Radiative Transitions and Emission Linewidth • Decay of Excited States • Emission Broadening and Linewidth due to Radiative Decay • Additional EmissionBroadening Processes • Quantum Description of Radiating Atoms 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 4 Homework: 1, 3, 4, 5, 6, 7, 12, 14 Radiative Decay of Excited States from Isolated Atoms • Start with the following assumptions: • A collection of identical atoms exist in some physical state. All of the atoms present are in their respective ground states. • Assume a pulse of energy is applied to the system excites many of the atoms to a single excited state, u. • We define the populations density of atoms in the system at state u as N u . • If we measure N u over time after the pulse was applied, then we find that Nu decreases exponentially. • Thus, after the pulse is applied, atoms in the system will tend to return to their ground states. Radiative Decay of Excited States from Isolated Atoms • This reduction in energy generally occurs in two ways: – Inelastic scattering of atoms leading to momentum transfer and loss – Isolated atoms that do not scatter but in stead radiate light from into the system in order to reduce their energy states from E u – E 1 • For optical systems we are primarily concerned with radiative energy transfer which we define as spontaneous emission • Each of the photons radiated by spontaneous emission has a frequency and wavelength: • The simplest equation used to model the change in population density is • Where A ul is the inverse of the time constant, τ , associated with the decay Radiative Decay of Excited States from Isolated Atoms • A more general form of the solution in which the u state is allowed to decay to multiple different energy levels can be written as Cd Laser involves the change in quantum number of two electrons (4d 9 5s 2 4d 10 5p) This leads to a much smaller transition probability than a single state change Radiative Decay of Excited States from Isolated Atoms HeNe laser quantum states (2p 5 5s 2p 6 ) Single state transition leads to high probability function and shorter time constant Simplified Equation for Transition Probability • Includes absorption oscillator strength, f lu , wavelength, and statistical degeneracy of the upper and lower states (chapter 3) • The oscillator strength is unique for each spectral transition. In general though: • For most radiative transitions:...
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 Summer '10
 Williams
 Doppler, odd parity, Even Parity, decay rate, Doppler Broadening Processes

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