PC 20312 Wave Optics Section 3 Interference Interference

PC 20312 Wave Optics Section 3: Interference

Interference fringes I 1 + I 2 Image adapted from Wikipedia

Temporal coherence Phase relationship changes over a characteristic time Coherence 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 • “The Last Man Who Knew Everything “ • Learned 13 languages by age 14 • Comparative study of 400 languages • Translated the Rosetta stone • Ph. D 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. Thomas Young (1773 -1829) 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 1 Young’s original diagram presented to Royal Society in 1803 http: //www. acoustics. salford. ac. uk/feschools/waves/diffract 3. htm Image from Wikipedia

Young’s slits 3 r 2 r 1 a r s s >> a y

Lloyd’s mirror r 1 source l 2 l 1 i y r 2 = l 1+l 2 t image of source Phase change on reflection Rev. Humphrey Lloyd (1800 -1881) Trinity College Dublin

Multiple slits P S 0 a S 1 S 2 S 3 S 4 S 5 r 2 r S 6 3 r s>>a

Interference pattern for multiple slits

Michelson Interferometer Mirror, M 2 d 2 compensator plate light source d 1 beamsplitter d = 2(d 1 - d 2) Mirror, M 1 lens screen Albert Abraham Michelson (1852 -1931) Image from Wikipedia

The compensator plate Rays to M 1 pass thru BS once Without compensator: NB nglass= f( ) • Unequal paths thru glass Rays to M 2 pass thru BS three times • path length diff. = f( ) With compensator: • Equal paths thru glass • path length diff. f( )

Equivalent diagram for Michelson interferometer Images of S in M 1 and M 2 S 1 S S 2 d ( ) s d co f focal plane lens source plane M 1 plane M 2 plane

Fringe patterns White light Sodium lamp Images from http: //hyperphysics. phy-astr. gsu. edu/hbase/phyopt/michel. html#c 1

Fourier Transform Spectroscopy d 2 I(d) compensator plate monochromatic d 1 d beamsplitter I(d) Movable mirror polychromatic lens detector d

Thin films A nt ni i ni source D A t i D B i C C t B s t A s lens C

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 source Er 0 Et 0 Er 1 Et 1 Er 2 Et 2 Er 3 Et 3 Er 4 Et Er 5 Et 5 Er Er 6 lens s lens

Stokes’ relations A) r. E E B) E r. E t. E r 2 E+tt E t. E r. E C) • B) is time-reverse of A) • Comparing B) and C): r 2 + tt =1 r t. E+tr. E t. E Sir George Gabriel Stokes (1819 -1903) r = -r Images from Wikipedia

The Airy function Finesse, F = Free Spectral Range, Resolution, Sir George Biddell Airy (1801 -1892) Image from Wikipedia

Image from Wikipedia

Fabry-Pérot Etalons 1 source s Charles Fabry (1867 -1945) r Outer surfaces are nonparallel lens 2 highly reflecting parallel surfaces Alfred Pérot (1863 -1925) Potrait images from http: //www-obs. cnrs-mrs. fr/tricent/astronomes/fabry. htm f

Fabry-Pérot Etalons 2 Images from Google image Data from D. Binks Ph. D thesis