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PC20312 Wave Optics

PC20312 Wave Optics. Section 3: Interference. Interference fringes. I 1 + I 2. Image adapted from Wikipedia. Temporal coherence. Phase relationship changes over a characteristic time. Coherence time:. Image adapted from Wikipedia. Spatial coherence.

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PC20312 Wave Optics

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  1. PC20312 Wave Optics Section 3: Interference

  2. Interference fringes I1 + I2 Image adapted from Wikipedia

  3. Temporal coherence Phase relationship changes over a characteristic time Coherence time: Image adapted from Wikipedia

  4. Spatial coherence Wave with infinite temporal coherence but finite spatial coherence Wave with finite temporal and spatial coherence Wave with infinite temporal and spatial coherence A pinhole isolates part of the wavefront and thus increases spatial coherence. Coherence length is unaffected. Images adapted from Wikipedia

  5. Types of interference Wavefront division Amplitude division e.g. Michelson interferometer e.g. Young’s slits

  6. Thomas Young • “The Last Man Who Knew Everything “ • Learned 13 languages by age 14 • Comparative study of 400 languages • Translated the Rosetta stone • PhD in physics & medical doctor • Young’s slits • Young’s modulus • Founded physiological optics: • colour vision • astigmatism • accommodation of the eye • Seminal work on haemodynamics • Secretary to the Board of Longitude • Superintendent of the HM Nautical Almanac Office. Thomas Young (1773-1829) Image from Wikipedia

  7. Young’s slits 1 Poor spatial coherence Good spatial coherence Single slit isolates part of wavefront To distant screen Double slits act as two coherent sources

  8. Young’s slits 1 Young’s original diagram presented to Royal Society in 1803 http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm Image from Wikipedia

  9. Young’s slits 3  r2 y r1 a  r s s >> a

  10. Lloyd’s mirror r1 source l2 y l1 r2 = l1+l2 i t Phase change on reflection image of source Rev. Humphrey Lloyd (1800-1881) Trinity College Dublin

  11. Multiple slits P S0 S1 a S2 S3 S4 r S5 2r S6 3r s>>a

  12. Interference pattern for multiple slits

  13. Michelson Interferometer d2 Mirror, M2  d1 compensator plate light source beamsplitter Mirror, M1 lens d = 2(d1- d2) Albert Abraham Michelson (1852-1931) screen Image from Wikipedia

  14. The compensator plate Rays to M1 pass thru BS once • Without compensator: • Unequal paths thru glass •  path length diff. = f() NBnglass= f() Rays to M2 pass thru BS three times • With compensator: • Equal paths thru glass • path length diff.  f()

  15. Equivalent diagram for Michelson interferometer Images of S in M1 and M2 S2 S1 d S   d cos() f focal plane lens source plane M2 plane M1 plane

  16. Fringe patterns White light Sodium lamp Images from http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/michel.html#c1

  17. d2 d1 compensator plate beamsplitter Movable mirror lens detector Fourier Transform Spectroscopy I(d) monochromatic d I(d) polychromatic d

  18. A D C Thin films i nt ni ni source A i t D B i C A t t B s lens s C

  19. Thin film applications Dichroic mirrors – high reflectivity for narrow bandwidth only Anti-reflection coatings – reduces glare from lenses Images from Wikipedia

  20. Thin films in nature Oil on water – oil layer thickness varies giving a rainbow effect in white light Soap bubbles – thickness and angle of film varies to give rainbow The tapetum lucidium in a calf’s eye The ‘Tapetum lucidum’ is found behind the retina of many animals (not humans) – it enhances night vision Images from Wikipedia and Google Image

  21. Multibeam interference source Er0 Et0 Er1 Et1 Er2 Et2 Er3 Et3 Er4 Et4 Er5 Er Et Et5 Er6 lens s lens

  22. rE E tE Stokes’ relations A) B) rE E tE r2E+ttE rE C) • B) is time-reverse of A) • Comparing B) and C): • r2 + tt=1 • r = -r Sir George Gabriel Stokes (1819-1903) rtE+trE tE Images from Wikipedia

  23. The Airy function   Finesse, F = Free Spectral Range,  Sir George Biddell Airy (1801-1892) Resolution,  Image from Wikipedia

  24. Image from Wikipedia

  25. Fabry-Pérot Etalons 1 source s Charles Fabry (1867-1945) r Outer surfaces are non-parallel lens f 2 highly reflecting parallel surfaces Alfred Pérot (1863-1925) Potrait images from http://www-obs.cnrs-mrs.fr/tricent/astronomes/fabry.htm &Wikipedia

  26. Fabry-Pérot Etalons 2 Images from Google image Data from D. Binks PhD thesis

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