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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2. Optical path delay
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3. Optical path delay
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4. Optical path delay
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5. Optical path delay
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6. phasor due to propagation (path delay)
Optical path delay
phasor due to propagation (path delay)
In general,
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7. Plane wave propagation
path delay increases
linearly with x
plane of observation
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8. Plane wave propagation
path delay increases
linearly with x
plane of observation
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9. Plane wave propagation
path delay
at fixed
slope
where
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10. Spherical wave propagation
path delay increases
with x as
for
plane of observation
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11. Spherical wave propagation
path delay increases
with x as
quadratic
near the axis
plane of observation
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12. Spherical wave propagation
plane of observation
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13. Spherical wave propagation
path delay
at fixed
where
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14. Optical path delays matter
path delay in
material of
index n:
compare with
free space
propagation :
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15. Optical path delays matter
difference:
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16. Can we measure them and how?
Phase delays matter
Can 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: interferometers “map” phase onto light
intensity which can be measured directly
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17. Interference
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18. Wave interference observation screen
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19. Interference: extreme cases
Waves in-phase
Constructive
interference
Waves out-of-phase
Destructive
interference
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20. Interference vs phase delay & contrast
Intensity
fringe
visibility
aka
contrast
average
intensity
Field 1
Field 2
relative phase delay
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21. Interference vs phase delay & contrast
Intensity
Intensity
perfect contrast
imperfect contrast
Intensity
Highest contrast /
fringe visibility is obtained
by interfering beams of
equal amplitudes
no interference
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22. Polarization and interference
polarized waves interfere
polarized waves do not interfere
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23. Michelson interferometer
incoming
laser beam
path difference:
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24. Michelson with variable phase-delay
Gas cell
incoming
laser beam
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25. Mach-Zehnder interferometer
bright
fringe
(matched
paths)
incoming
laser beam
interference
pattern
incoming
laser beam
spatial
period
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26. Young interferometer incoming laser beam opaque screen
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27. Young interferometer incoming plane wave opaque screen
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28. Two point sources interfering: math…
Paraxial analysis:
Amplitude:
intensity
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