Youngs double slit experiment Spatial coherence of light

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

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 troughs

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: Then we get simple relation Impedance of free space

wavefronts Plane wave Spherical wave

Young’s double slit experiment

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

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

Effect of slit width on the interference pattern light block

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

Monochromatic plane wave Electric field Phase j amplitude E j = 0 …t 1, E(z 0, t 1) j = p/2 …t 2, E(z 0, t 2) j= p …t 3, E(z 0, t 3) z 0 z

Phase at two points x 1, x 2 x j 1 = 0 …t 1 j 1= p/2 …t 2 j 1= p …t 3 x 1 j 2 = 0 …t 1 j 2 = p/2 …t 2 j 2 = p …t 3 x 2 z phase difference between two points j 2 - j 1 = is constant in time = spatially coherent light Dj = 0, 0, 0

Phase at two points x 1, x 2 Disturbance (x) (x, t) x x 1 z x 2

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

Complex degree of spatial coherence g(Δx). . describes spatial coherence of light. . a measure of the degree of spatial coherence. . function of distance Dx=x 2 -x 1

Spatial coherence of light x 1 1 Δx x 2 2

Complex degree of spatial coherence g(Δx) for all points of interest => Fully spatially coherent light for x 1 ≠ x 2 => Fully spatially incoherent light

Complex degree of spatial coherence g(Δx) For experimental setup (far field) Disturbance h y rectangular aperture x x 2 z Δx x 1 R h. . aperture width R. . . distance between rectangular aperture and the points x 1 and x 2 coherence distance First minimum of function g (x 1, x 2)

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

Effect of the aperture width on the spatial coherence h h a a. . distance between S 1 and S 2 a = ac => g(a) =0 a < ac => g(a) = 0. 55 S 1 ac S 2 ac

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 a x

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

Thank you for your attention