WaveOpt_4 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering ECSE 527 Optical Engineering terference Interference Sources: Hecht (Optics), Chapter 9 Andrew Kirk 2010 Interference 1
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E.g. Antireflection coatings ©AGK 2010 Interference 2
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E.g. Interferometric surface profiling fringes ©AGK 2010 Interference 3 Activated (~20V, 30 mrad) MEMS mirror
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E.g. LIGO observatory for gravitational waves 4 km long Michelson terferometer interferometer ©AGK 2010 Interference 4
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©AGK 2010 Interference 5 http://www.lmsal.com/9120/CLAES/mission.html
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E.g. optical modulators ach ender teferometer (Mach Zender inteferometer) ©AGK 2010 Interference 6
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Aspects of interference Different paths (multiple waves) Interference maxima and inima Constructive and destructive interference Coherent wave Split (amplitude/wavefront) Recombine minima – Antireflection coatings, modulators and interference filters Sensitive to optical path difference between interfering waves easurement of distance, refractive index (interferometry) Measurement of distance, refractive index (interferometry) OPD is a function of wavelength – Fabry-Perot etalons and filters ©AGK 2010 Interference 7
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Learning outcomes fter taking this section you should be able to: After taking this section you should be able to: • Explain the basis of optical interference •R e c o gnize the difference between wavefront splitting and amplitude splitting interference • Calculate the fringe pattern observed due to two coincident avefronts wavefronts • Recognize the form and application of Mach-Zender and Michelson-Morely interferometer configurations • Calculate the optical path difference necessary to change an interference pattern ©AGK 2010 Interference 8 • State 3 applications of two-beam interference
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Contents • Basis of interference • Wavefront splitting interference: Young’s slits • Amplitude splitting interfometers – Michelson-Morely – Mach-Zender agnac Sagnac ©AGK 2010 Interference 9
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Basis of interference: Superposition of plane waves E 1 (t) E 01 k k E 02 P ©AGK 2010 Interference 10 2 E 2 (t)
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Interference Equations (2) 2 2 I 1 = E 1 2 , I 2 = E 2 2 For parallel polarization: ©AGK 2010 Interference 12
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Special Case: Equal amplitude plane waves = = I 1 I 2 I 0 I π π π π π π ©AGK 2010 Interference 14 0 π 2 3 4 - π -2 -3 -4
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Linear fringes Projection onto screen at z=0 ©AGK 2010 Interference 16 Wave intensities Projection onto screen at z=-1
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Wavefront splitting: Young’s Experiment Expanding spherical waves in max min max min min max min ©AGK 2010 Interference 17 Fringes
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Single photon source 1 0 1 2 1 2 -10 -5 0 5 10 -2 -1 0 5 0 1 2 Single photon 0 5 0 2 source Sensitive detector 0 5 0 1 ©AGK 2010 Interference 18
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Young’s Experiment: Geometry S 1 y m r 1 r 2 m S 2 a B S m s ©AGK 2010 Interference 19
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Fringe Spacing r 1 r 2 = m r 1 r 2 a Constructive interference when: araxial approximation: m m a Paraxial approximation: Angular location of fringe maxima: y m s a m Position of fringe maxima: y s a Spacing of fringe maxima: ©AGK 2010 Interference 20
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This note was uploaded on 09/28/2010 for the course ECSE ECSE 527 taught by Professor Kirk during the Winter '10 term at McGill.