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MIT 2.71/2.710 Optics 10/18/04 wk7-a-1
Today’s summary
• A new look at propagation and phase delays• Description of plane & spherical waves in terms of phase delay
• Interference• Interferometers –Michelson –Mach-Zehnder –Young
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Optical path delay
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Optical path delay
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Optical path delay
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Optical path delay
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Optical path delay
phasor due to propagation (path delay)
In general,
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Plane wave propagation
path delay increaseslinearly with x
plane of observation
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Plane wave propagation
path delay increaseslinearly with x
plane of observation
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Plane wave propagation
path delay
at fixed
slope
where
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Spherical wave propagation
plane of observation
path delay increaseswith x as
for
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Spherical wave propagation
plane of observation
path delay increaseswith x as
quadraticnear the axis
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Spherical wave propagation
plane of observation
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Spherical wave propagation
path delay
at fixed
where
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Optical path delays matter
path delay inmaterial
ofindex n:
compare withfree space
propagation :
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Optical path delays matter
path path differencedifference
::
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Phase delays matterCan we measure them and how?
• Direct measurement does not work: light waves oscillate too fast for any instrument to follow• We need an indirect method• Solution: interferometersinterferometers “map” phase onto light intensity which can be measured directly
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Interference
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Wave interference
observation screen
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Interference: extreme cases
Waves in-phase
Constructiveinterferenc
e
Waves out-of-phase
Destructiveinterference
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Interference vs phase delay & contrast
Intensity
averageintensity
fringevisibility
akacontrast
Field 1
Field 2
relative phase delay
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Interference vs phase delay & contrast
Intensity perfect contrast imperfect contrastIntensity
Intensityno interferenceHighest contrast /
fringe visibility is obtainedby interfering beams of
equal amplitudes
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Polarization and interference
polarized waves interfere
polarized waves do not interfere
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Michelson interferometer
incominglaser beam
path difference:
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Michelson with variable phase-delay
incominglaser beam
Gas cell
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Mach-Zehnder interferometer
incominglaser beam
brightfringe
(matchedpaths)
interferencepattern
spatialperiod
incominglaser beam
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Young interferometer
incominglaser beam
opaquescreen
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Young interferometer
incomingplane wave
opaquescreen
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Two point sources interfering: math…Paraxial analysis:
Amplitude:
intensity
