Fraunhofer Diffraction

Geometrical Optics:

…light can’t turn a corner.

IBill Mageors

Physical Optics:

…actually, it can.

IFrancesco Maria Grimaldi

Fraunhofer Diffraction

Huygens-Fresnel Principle

Every point on a wavefront may be regarded as a secondary source of spherical wavelets.

The propagated wave follows the periphery of the wavelets.

Huygens, just add the wavelets considering interference!

Augustin-Jean Fresnel

(That’s a sweet ascot by the way.)

Far-Field Diffraction(a.k.a. Fraunhofer Diffraction)

Far enough that source illumination is a plane wave.

Far enough that diffracted wavelets are plane wave.

b

ds

s

s sin

r

Single Slit Fraunhofer Diffraction

P

Get the amplitudes right!

tkrjoP e

r

dEdE

field amplitude

field

dsEdE Lo

spherical wavelets:

As ds goes to zero, dEo must go to zero:

field amplitude per unit width

tkrjLP e

rdsE

dE

Get the phases right! (just like Young’s Double Slit)

sinkstkrjLP e

rdsE

dE

Integrate over the slit:

2

2

sin2

2

b

b

ksjtkrjL

b

b

P dseerE

dE

2

2

sin

sin

b

b

ksjtkrjL

P jke

erE

E

2sin2sin

sin1

kbjkbjtkrjL

P eejk

erE

E

jjtkrjL

P eejb

erE

E 2

new variable: sin21 kb

tkrjLP e

rbE

E

sin

2

2 Po Ec

I

Calculate irradiance:

2

22sin

2

rbEc

I Lo

field at r

an irradiance

xx

xsin

sinc

“sinc”“sampling function”“sine cardinal”

2sincoII

0

0.2

0.4

0.6

0.8

1

-8 -4 0 4 8

Minima at:2,... 1,m m

sin bm

Maxima at:

tan (graph it!)

Beam spreading