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Young ’ s double slit experiment & Spatial coherence of light

Young ’ s double slit experiment & Spatial coherence of light. Ivana Hamarová. Monochromatic plane wave propagating along axis z. Electrical field. Phase j. amplitude. l. l. j = 2 p. Monochromatic plane wave. Electrical field. Phase j. amplitude. l. l. j = 2 p. crests.

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Young ’ s double slit experiment & Spatial coherence of light

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  1. Young’s double slit experiment&Spatial coherence of light Ivana Hamarová

  2. Monochromatic plane wave propagating along axis z Electrical field Phase j amplitude l l j = 2p

  3. Monochromatic plane wave Electrical field Phase j amplitude l l j = 2p crests troughs

  4. wavefronts Spherical wave Plane wave

  5. Young’s double slit experiment Path difference Phase difference x z Constructive interference + Destructive interference +

  6. Young’s double slit experiment x z D >> a, a >> l Dj.. phase difference d… path difference a….distance between slits D…distance between slits and observation plane Period of interference pattern

  7. Effect of slit width on the interference pattern light block

  8. Monochromatic plane wave Electrical field Phase j amplitude l l j = 2p

  9. Monochromatic plane wave Electric field Phase j amplitude E j = 0 …t1,E(z0,t1) j = p/2 …t2,E(z0,t2) j= p…t3,E(z0,t3) z z0

  10. Phase at two pointsx1, x2 x j1 = 0 …t1 j1= p/2 …t2 x1 j1= p…t3 j2 = 0 …t1 j2 = p/2 …t2 x2 j2 = p …t3 z phase difference between two points j 2 - j1 = Dj =0, 0, 0 is constant intime = spatially coherent light

  11. Phase at two pointsx1, x2 Disturbance (x) (x,t) x x1 z x2

  12. Phase at two pointsx1, x2 Disturbance (x,t1) x t1 x1 z x2 Disturbance (x,t2) x t2 x1 z x2 phase difference between two points j 2 - j1 = Dj≠konst is not constant in time=spatially incoherent light

  13. Complex degree of spatial coherence g(Δx) ..describes spatial coherence of light ..a measure of the degree of spatial coherence ..function of distance Dx=x2-x1

  14. Spatial coherence of light Δx x1 x2 2 1

  15. Complex degree of spatial coherence g(Δx) for x1≠ x2 for all points of interest => Fully spatially coherent light => Fully spatially incoherent light

  16. Complex degree of spatial coherence g(Δx) For experimental setup (far field) y h rectangular aperture x x2 z Disturbance Δx x1 R h.. aperture width R...distance between rectangular aperture and the points x1 and x2 coherence distance First minimum of function g (x1,x2)

  17. Effect of the aperture width on the spatial coherence h h ac coherence distance ac increases as aperture width h decreases ac

  18. Effect of the aperture width on the spatial coherence h h a S1 S2 a..distance between S1 and S2 ac ac a = ac => g(a) =0 a < ac => g(a) = 0.55

  19. Visibility of interference fringes (intensity modulation)= |g(Δx)| I(x) a << ac visibility= 1 x ac a |g(Δx)| I(x) a < ac partial visibility ac x a |g(Δx)| I(x) a=ac visibility = 0 ac x a

  20. Thank you for your attention

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