PC20312 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 Thomas Young ( ) “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 1 Young’s original diagram presented to Royal Society in 1803 Image from Wikipedia

Young’s slits 3 a y  r2r2 r1r1  rr s s >> a

Lloyd’s mirror ii y r1r1 l1l1 l2l2 Phase change on reflection source image of source r 2 = l 1 +l 2 tt Rev. Humphrey Lloyd ( ) Trinity College Dublin

Multiple slits S0S0 S3S3 S4S4 S5S5 S6S6 S1S1 S2S2 a rr 2r2r 3r3r s>>a P

Interference pattern for multiple slits

Michelson Interferometer Albert Abraham Michelson ( )  d1d1 d2d2 beamsplitter Mirror, M 1 Mirror, M 2 compensator plate lens screen light source d = 2(d 1 - d 2 ) 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 M 1 pass thru BS once Rays to M 2 pass thru BS three times NB n glass = f( )

Equivalent diagram for Michelson interferometer source plane M 1 plane M 2 plane   d d cos(  ) S S1S1 S2S2 Images of S in M 1 and M 2 lens f focal plane

Fringe patterns Sodium lamp Images from White light

Fourier Transform Spectroscopy d1d1 d2d2 beamsplitter compensator plate lens detector Movable mirror d I(d) monochromatic d I(d) polychromatic

Thin films ntnt nini nini B D C A s source lens ii tt A C D ii ii A C B s tt t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 ErEr s source E t0 E t1 E t3 E t2 E t5 E t4 E r0 E r1 E r3 E r2 E r5 E r4 E r6 lens EtEt

Stokes’ relations Sir George Gabriel Stokes ( ) r 2 E+ttE E rE tE E rE tE rE tE rtE+trE A) B) C) B) is time-reverse of A) Comparing B) and C): r 2 + tt=1 r = -r Images from Wikipedia

The Airy function Sir George Biddell Airy ( ) Finesse, F = Free Spectral Range,  Resolution,  Image from Wikipedia  

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

Images from Google imageData from D. Binks PhD thesis Fabry-Pérot Etalons 2