PC20312 Wave Optics

Section 3:

Interference

Interference fringes

212 II

212 III1 + I2

Image adapted from Wikipedia

Temporal coherence

Phase relationship changes over a characteristic time

1

cCoherence time:Image adapted from Wikipedia

Spatial coherence

Wave with infinite temporal and spatial coherence

Wave with infinite temporal coherence but finite spatial

coherence

Wave with finite temporal and spatial coherence

A pinhole isolates part of the wavefront and thus

increases spatial coherence. Coherence

length is unaffected.

Images adapted from Wikipedia

Types of interference

Wavefront division

e.g. Young’s slits

Amplitude division

e.g. Michelson interferometer

Thomas Young

Thomas Young (1773-1829)

• “The Last Man Who Knew Everything “

• Learned 13 languages by age 14

• Comparative study of 400 languages

• Translated the Rosetta stone

• PhD in physics & medical doctor

• Young’s slits

• Young’s modulus

• Founded physiological optics:

• colour vision

• astigmatism

• accommodation of the eye

• Seminal work on haemodynamics

• Secretary to the Board of Longitude

• Superintendent of the HM Nautical Almanac Office. Image from Wikipedia

Young’s slits 1

Poor spatial coherence

Good spatial coherence

Single slit isolates part of wavefront

Double slits act as two coherent

sources

To distant screen

Young’s slits 1Young’s original diagram presented to Royal Society in 1803

Image from Wikipedia

http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm

Young’s slits 3

a

y

r2

r1

r

s

s >> a

Lloyd’s mirror

i

y

r1

l1l2

Phase change on reflection

source

image of source

r2 = l1+l2

t

Rev. Humphrey Lloyd (1800-1881) Trinity College Dublin

Multiple slits

S0

S3

S4

S5

S6

S1

S2

a

r

2r

3r

s>>a

P

Interference pattern for multiple slits

Inte

nsity

, I

N=10N=3N=5

ka2

Michelson Interferometer

Albert Abraham Michelson (1852-1931)

d1

d2

beamsplitter

Mirror, M1

Mirror, M2

compensator plate

lens

screen

light source

d = 2(d1- d2)

Image from Wikipedia

The compensator plate

Without compensator:

• Unequal paths thru glass

• path length diff. = f()

With compensator:

• Equal paths thru glass

path length diff. f()

Rays to M1 pass thru BS once

Rays to M2 pass thru BS three

times

NB nglass= f()

Equivalent diagram for Michelson interferometer

source plane M1 plane M2 plane

d

d cos()

S S1 S2

Images of S in M1 and M2

lens

f

focal plane

Fringe patterns

Sodium lamp

Images from http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/michel.html#c1

White light

Fourier Transform Spectroscopy

d1

d2

beamsplitter

compensator plate

lens

detector

Movable mirror

0 2 4 6 8 10 12 140

0.5

1

1.5

2

d

I(d) monochromatic

d

I(d) polychromatic

Thin films

nt nini

BD

C

A

s

source

lens

i

t

A

C

D

i

i

A

C

B st

t

Thin film applications

Dichroic mirrors – high reflectivity for narrow bandwidth only Anti-reflection coatings –

reduces glare from lenses

Images from Wikipedia

Thin films in nature

Oil on water – oil layer thickness varies giving a rainbow effect in white light

Soap bubbles – thickness and angle of film varies to give rainbow

The ‘Tapetum lucidum’ is found behind the retina of many animals (not humans) – it enhances night vision

The tapetum lucidium in a

calf’s eye

Images from Wikipedia and Google Image

Multibeam interference

Er

s

source

Et0

Et1

Et3

Et2

Et5

Et4

Er0

Er1

Er3

Er2

Er5

Er4

Er6

lenslens

Et

Stokes’ relations

Sir George Gabriel Stokes (1819-1903)

r2E+ttE

E rE

tE

E rE

tE

rE

tErtE+trE

A) B)

C) • B) is time-reverse of A)

• Comparing B) and C):

r2 + tt=1

r = -r

Images from Wikipedia

The Airy function

Sir George Biddell Airy (1801-1892)

Finesse, F = Free Spectral Range, Resolution,

Image from Wikipedia

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Frequency

Tra

nsm

issi

on

F=2F=10F=50

RRF

12

Image from Wikipedia

Fabry-Pérot Etalons 1

Potrait images from http://www-obs.cnrs-mrs.fr/tricent/astronomes/fabry.htm &Wikipedia

Charles Fabry (1867-1945)

Alfred Pérot (1863-1925)

s

r

source

lens

f2 highly reflecting parallel surfaces

Outer surfaces are non-parallel

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 5 10 15 20 25 30

Frequency (GHz)

Inte

nsi

ty (

Arb

. u

nit

s)

FSR

Images from Google image Data from D. Binks PhD thesis

Fabry-Pérot Etalons 2