WaveOpt_41 - 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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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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Basis of interference: Superposition of plane waves     10 1 1 1 ,c o s . cos rt t tt   EE k r E k r Conditions: Same polarization     20 2 2 1 2 , . r I E Coherent Same frequency Same location E 1 (t) E 01  * 2 12 2 .  E E E k 1 22 1 2 121 2 2. II I E E k 2 E 02 P . E ©AGK 2010 Interference 11 E 2 (t) 12 1 2 c o s I 1 2 ..  kr kr
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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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Interference Equations (2) 2 2 s I 1 = E 1 2 , I 2 = E 2 2 For parallel polarization: I 12 =2 I 1 I 2 cos 0 π π : = 0, ±2 , ±4 : Maximum constructive interference I max = I 1 + I 2 +2 I 1 I 2 = ± π , ±3 π : Maximum destructive interference I min = I 1 + I 2 – 2 I 1 I 2 ©AGK 2010 Interference 13
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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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Special Case: Equal amplitude plane waves = = I 1 I 2 I 0 I =2 I 0 1 + cos =4 I 0 cos 2 2 I min =0,
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WaveOpt_41 - Department of Electrical and Computer...

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