1. Young’s double slit experiment & Spatial coherence of light
Ivana Hamarová 2016
Ladislav Stanke 2017

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. What is actually measured?
Typically we use CCDs, photodiodes, etc.
Thus, intensity/power is measured instead of electric field E
Power is proportional to the square of electric field
Intensity
where
For simplicity we often put:
Impedance of free space
Then we get simple relation

5. wavefronts
Plane wave
Spherical wave

6. Young’s double slit experiment

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

8. Young’s double slit experimentz
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

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

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

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

12. Phase at two points x1, x2 x j1 = 0 …t1 j 1= p/2 …t2 x1 j 1= p …t3z
phase difference between two points j 2 - j 1 = Dj = 0, 0, 0
is constant in time = spatially coherent light

13. Phase at two points x1, x2
Disturbance
(x)
(x,t) x x1 z x2

14. Phase at two points x1, x2 t1 t2 Disturbance (x,t1) x x1 z x2
phase difference between two points j 2 - j 1 = Dj ≠ konst
is not constant in time =spatially incoherent light

15. 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

16. Spatial coherence of lightΔx x1 x2 1 2

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

18. Complex degree of spatial coherence g(Δx)
For experimental setup (far field) y h
rectangular aperture x x2
Disturbance z 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)

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

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

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

22. It works also with electrons and other particles and even molecules…

23. Thank you for your attention