Lasers Chapter 11 - Lasers PH 645 OSE 645 EE 613 Summer...

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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: [email protected] Office Hours: Tues/Thurs 2-3PM JDW, ECE Summer 2010
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Chapter 11: Laser Cavity Modes Longitudinal Cavity Modes Fabry-Perot resonator Fabry-Perot cavity modes Longitudinal modes Mode number Transverse Laser Cavity Modes Diffraction integral Plane parallel mirrors Curved mirrors Spatial distributions Gaussian shamed modes Properties of Laser modes Mode characteristics Effects of mode on gain medium profile 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 11 Homework: 2,4,5,6,8,11,12
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Fabry-Perot Resonator Consider two partially reflective mirrors parallel to one another. The mirrors may be nearly entirely reflective, but will always have some transmission value Let us consider light incident on the mirror at an angle θ Light reflecting back and forth between the mirrors is depicted here Mirror plane 1 Mirror plane 2
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Fabry-Perot Resonator Let us consider light incident on the mirror at an angle θ Light reflecting back and forth between the mirrors can be modeled at an angle 2 θ The reflected light follows an additional path length of a+b Mirror plane 1 Mirror plane 2
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Fabry-Perot Resonator The additional path length generates a phase change in the propagating wave. This can be shown by taking an incident plane wave, e ikz , where k is the wave vector and z is the incident propagation direction One can express the phase factor as Furthermore, one can sum all of the transmitted amplitudes as
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Fabry-Perot Resonator The transmitted intensity of the wave is Where the exponential term represents the phase change upon two reflections If we define the reflectivity of the mirror, R, and transmission, T, then one can write Airy Function
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Fabry-Perot Resonator Intensity
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Fabry-Perot Resonator
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