Lasers Chapter 6 - Lasers PH 645/ OSE 645/ EE 613 Summer...

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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) 824-2898 email: williams@eng.uah.edu Office Hours: Tues/Thurs 2-3PM JDW, ECE Summer 2010 Chapter 6: Radiation and Thermal Equilibrium Equilibrium Radiating Bodies Cavity Radiation Absorption and Stimulated Emission Cambridge University Press, 2004 ISBN-13: 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 6 Homework: 5, 6, 7, 8, 9, 10, 12, 13 Thermal Equilibrium Thermal Equilibrium: All individual masses within a closed system have the same temperature Thermal energy is transferred by: Conduction Direct contact of solids Fast heat transfer Convection Transfer through gases/liquids of significant distance Slow heat transfer Radiation Heat transfer by EM field alone Radiator must also be capable of absorption Radiating Bodies Consider a radiating mass The probability distribution that an atom has a discrete energy, E i , is given by the Boltzmann Equation: Where Boltzmann's constant, K B , is The probability is normalized by summing all of the individual atomic energies to 1 The total number of atoms in a particular energy state is therefore: If the material were a solid with continuous bands of energies defined by a Density of States: If the material were a solid with continuous bands of energies defined by a Density of States: Normalization of the various states requires: Allowing one to determine solve for the constant and provide the DoS as: Again, solving for the total number of atoms with continuous energy bands requires that N(E) be normalized such that: Where: Radiating Bodies Advancing on this logic, one can compute the ratio of atoms in two various states, E u and E l where E ul = E u-E l : Note that this solutions holds well for two discrete states similar to that found in gases Or in terms of a dense solid material with continuous energy bands as: It is important to note that this discussion of radiative states requires that thermal equilibrium not only macroscopic temperature dependent but also equilibrium of allowed quantum states within the materials (the vibrational and energies allowed within the atomic structure of the material). Radiating Bodies Determine the temperature required to excite electrons of atoms in a solid to energies capable of producing visible radiation....
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Lasers Chapter 6 - Lasers PH 645/ OSE 645/ EE 613 Summer...

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