Chapter 7 : Interference of light

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. http://www.youtube.com/watch?v=qbQ3o0MkK38 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. Kauai, Hawaii

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 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 !?! What about conservation of energy?

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

17. The double slit experiment (first performed in early 1800s)

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 = a sinq conditions for interference: constructive destructive m = 0, 1, 2, 3, …

20. 2-beam 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. 2-beam interference from 1 source: refraction Fresnel’s biprism part of the incident light is refracted downward and part upward

23. Fresnel’s biprism for broadband pulse characterization

24. Interference intermezzo Interference intermezzo

27. Anatomy of a soap bubble

28. Soap bubble interference

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

30. 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,…

31. Keep in mind the phase analogous to wave on a rope “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!

32. 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

33. Colors indicate bubble thickness

34. 180o phase change 0o phase change t n>1 Consider a tapered soap film How thick here (yellow band)? Constructive interference for 2t ~ (m + ½)l At first red band m = 0 t ~ ¼ (700 nm)

35. 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)

36. 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...

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

38. 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...

39. 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?

40. Broadband anti-reflective films

41. 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

42. Anodized titanium

43. Natural multi-layer reflectors

44. Exercises You are encouraged to solve all problems in the textbook (Pedrotti3). The following may be covered in the werkcollege on 29 September 2010: Chapter 7: 1, 2, 7, 9, 15, 16, 24 Next week’s lecture given by Herman Offerhaus