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Chapter 7 : Interference of light

Chapter 7 : Interference of light. Chapter 7 : Interference of light. in·ter·fer·ence. 1. Life. Hindrance or imposition in the concerns of others. 2. Sports . Obstruction of an opponent, resulting in penalty. .

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Chapter 7 : Interference of light

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  1. Chapter 7: Interference of light Chapter 7: Interference of light

  2. in·ter·fer·ence 1.Life. Hindrance or imposition in the concerns of others. 2.Sports. Obstruction of an opponent, resulting in penalty. 3. Physics.Superposition of two or more waves, resulting in a new wave pattern. constructive destructive

  3. HeNe laser

  4. Radio City Rockettes, New York, NY

  5. rood blauworanjepaarsoranje blauwgroen rood blauw paars groenroodoranje blauw roodgroen paars oranjerood blauw groenroodblauwpaarsoranjeblauwrood groen paars oranje roodblauw J.R. Stroop "Studies of interference in serial verbal reactions" Journal of Experimental Psychology 18:643-662 (1935).

  6. Peacock

  7. Soap bubbles

  8. 2-beam interference initial phase (at t=0) propagation distance from source of disturbance from superposition principle:

  9. Measuring interference • - Electric fields are rapidly varying (n ~ 1014 Hz) • - Quickly averages to 0 • - Instead of measuring E directly, measure radiant power density • = irradiance, Ee (W/m2) • = time average of the square of the electric field amplitude • - Note: to avoid confusion, Pedotti3 now uses the symbol I instead of Ee

  10. Irradiance at point P I = I1 • + I2 • + I12 - when E1 and E2 are parallel, maximum interference - when orthogonal, dot product = 0; no interference

  11. The interference term I12 dot product of electric fields: simplify by introducing constant phases: use trigonometry: 2cosAcosB = cos(A+B) + cos(B-A) and consider again the time average: w kills it

  12. The interference term I12 simplify by introducing d: to yield the interference term of the irradiance:

  13. Irradiance formula if E1║E2, then -where d is the phase difference -for parallel electric fields

  14. Interference mutually incoherent beams (very short coherence time) mutually coherent beams (long coherence time) maximum when cos d = 1 constructiveinterference d = (2mp) minimum when cos d = -1 destructive interference d = (2m+1)p

  15. Interference fringes maximum when I1 = I2= I0 1 + 1 = 4 !?!

  16. Interference in time and space Young’s experiment wavefront division Michelson interferometer amplitude division

  17. The double slit experiment (first performed in 1803)

  18. Double slit experiment with electrons http://www.youtube.com/watch?v=ZJ-0PBRuthc

  19. Criteria for light and dark bands - approximate arc S1Qto be a straight line - optical path difference D = asinq conditions for interference: constructive destructive m = 0, 1, 2, 3, …

  20. Interference from 1 source: reflection Lloyd’s mirror part of the wavefront is reflected; part goes direct to the screen Fresnel’s mirrors part of the wavefront is reflected off each mirror

  21. Fresnel’s mirrors as solar collectors

  22. Interference from 1 source: refraction Fresnel’s biprism part of the incident light is refracted downward and part upward

  23. Interference via amplitude division - thin films - oil slicks - soap bubbles - dielectric coatings - feathers - insect wings - shells - fish - …

  24. Interference intermezzo Interference intermezzo

  25. The Dancing Couple-1663-Jan Steen

  26. Anatomy of a soap bubble

  27. Soap bubble interference

  28. Thin film interference: normal incidence optical path difference: D = nf(AB + BC) = nf(2t)

  29. Thin film interference: non-normal incidence optical path difference: D=nf(AB + BC) –n0(AD) = 2nf t cosqt D = ml: constructive interference D = (m + ½)l: destructive interference where m = 0,1,2,…

  30. Keep in mind the phase “soft” reflection “hard” reflection Simple version: phase of reflected beam shifted by p if n2 > n1 0 if n1 > n2 Correct version: use Fresnel equations!

  31. Summary of phase shifts on reflection external reflection n1 < n2 TE mode TM mode n1 air n2 glass internal reflection n1 > n2 TE mode TM mode air n1 n2 glass

  32. Back to the bubbles

  33. 180o phase change 0o phase change t n>1 Colors indicate bubble thickness How thick here (red band)? Constructive interference for 2t ~ (m + ½)l At first red band m = 0 t ~ ¼ (700 nm)

  34. pop! Dark, white, and bright bands Bright: Colored “monochromatic” stripes occur at (1/4)l for visible colors White: Multiple, overlapping interferences (higher order) Dark: Super thin; destructive interference for all wavelengths (no reflected light)

  35. Multiple beam interference r, t: external reflection r’, t’ : internal reflection Note: thickness t ! • where d is the phase difference geometric series

  36. Multiple beam interference Introduce Stokes relations: r’=-r and tt’=1-r2and simplify to get: Irradiance:

  37. Multiple beam interference Working through the math, you’ll arrive at: where Ii is the irradiance of the incident beam Likewise for transmission leads to:

  38. This simulation was performed for the two sodium lines described above, with reflectivity                and the separation of the mirrors increasing from 100 microns to 400 microns. Fabry-Perot interferometer (1897) d simulation of two sodium lines: l1 = 0.5890182 mm l2 = 0.5896154 mm mirror reflectivity r = 0.9 mirror separation: 100 - 400 mm

  39. Fabry-Perot interferometer see chapter 8 where F is the coefficient of finesse:

  40. Fabry-Perot interferometer: fringe profiles Michelson d • -transmission maxima occur when d = 2pm • as r approaches 1 (i.e. as Fincreases), the fringes become very narrow • see Chapter 8 for more on Fabry-Perot: • fringe contrast, FWHM, finesse, free spectral range

  41. Fringes of equal thickness Constructive reflection 2d = (m+1/2)λ m=0, 1, 2, 3... Destructive reflection 2d = mλ m=0, 1, 2, 3...

  42. Newton’s rings white-light illumination pattern depends on contact point: goal is concentric rings

  43. Oil slick on pavement Constructive reflection 2d = mλ m=0, 1, 2, 3... Destructive reflection 2d = (m+1/2)λ m=0, 1, 2, 3...

  44. Thin film coatings: anti-reflective Glass: n = 1.5MgF2 coating: n = 1.38To make an AR coating for l = 550 nm, how thick should the MgF2 layer be?

  45. Broadband anti-reflective films

  46. Multilayer mirrors • thin layers with a high refractive index n1,interleaved with thicker layers with a lower refractive index n2 • path lengths lA and lB differ by exactly one wavelength • each film has optical path length D = l/4: all reflected beams in phase • ultra-high reflectivity: 99.999% or better over a narrow wavelength range

  47. Anodized titanium

  48. Natural multi-layer reflectors

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