GeomOpt_Part31

GeomOpt_Part31 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering ECSE 527 Optical Engineering eometric Optics III: Gaussian Beams Geometric Optics III: Gaussian Beams References: Saleh and Teich (Fundamentals of ( Photonics): 3.1 and 3.2 (but these notes should be sufficient) Andrew Kirk 2010 Gaussian beams 1
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Example: Example: Laso Laso-drill drill Inc Inc You have started working for Laso-drill Inc. Your boss asks you to design a laser system to drill 5 m diameter holes through 500 microns of steel, using 1.024 m wavelength light Is it possible? ©AGK 2010 Gaussian beams 2
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Overview The Gaussian beam model is a very useful tool for modelling light at merges om n ptical ber r om ser e ill ee at that emerges from an optical fiber or from a laser. We will see that in this model, we cannot focus light to an infinitely small spot, or collimate it over an infinite distance. We will then use this model to work out the effect that a lens has on a beam. This will allow us to transformbeamsinorderto couplethemintoanotherfiberora particular optical system. ther sources Other resources Newport Optics tutorial: ttp www ewport om/servicesupport/Tutorials/default spx?id= 12 http://www.newport.com/servicesupport/Tutorials/default.aspx?id 112 Melles-Griot collimation and focusing tutorial: http://www.mellesgriot.com/products/lasers/lsrdiode.asp ©AGK 2010 Gaussian beams 3
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Outline • Origins of Gaussian beams • Beam-waist and Rayleigh range • Beam-waist evolution Transformation of beams by lenses ©AGK 2010 Gaussian beams 4
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Learning outcomes After taking this class you will be able to: • Explain the significance of Gaussian beams • Describe a Gaussian beam in terms of beam waist, ayleigh range and wavelength Rayleigh range and wavelength • Calculate the evolution of a Gaussian beam given its initial parameters • Calculate the transformation of a Gaussian beam via lens systems ©AGK 2010 Gaussian beams 5
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Gaussian beams • Wave optics approach • Lasers emit Gaussian beams • Light emitted by a single mode fiber is close to aussian Gaussian • Diffraction limited beams – A Gaussian beam remains Gaussian as it 40 propagates 0 -20 0 20 ©AGK 2010 Gaussian beams 6 0 200 400 600 800 1000 -40
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Example: CD pick Example: CD pick-up up PBS Collimat or Lens Quart er-wave Plat e Disc Laser Diode Diffract ion Grat ing Concave Singlet Object ive Cylindrical How does the beam Photodiode Array evolve through the system? ©AGK 2010 Gaussian beams 7 y
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Plane and sperical waves Spherical waves: mitted from a point Plane waves emitted from a point – maximal divergence infinite extent – zero divergence Both are solutions of the paraxial Helmholz equation for complex amplitude U: 0 2 2 U k U ©AGK 2010 Gaussian beams 8 Gaussian beams have maximum confinement with minimum divergence
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Solution to Helmholz equation • The Gaussian beam is a solution to the paraxial Helmholz equation in cylindrical coordinates, where U is a complex amplitude: 0 2 2 U k U • This solution is of form: ©AGK 2010 Gaussian beams 9
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GeomOpt_Part31 - Department of Electrical and Computer...

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