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MIT 2.71/2.710 Optics 10/18/04 wk7-a-1 Todays summary A new look at propagation and phase delays Description of plane & spherical waves in terms of phase.

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Presentation on theme: "MIT 2.71/2.710 Optics 10/18/04 wk7-a-1 Todays summary A new look at propagation and phase delays Description of plane & spherical waves in terms of phase."— Presentation transcript:

1 MIT 2.71/2.710 Optics 10/18/04 wk7-a-1 Todays 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

2 MIT 2.71/2.710 Optics 10/18/04 wk7-a-2 Optical path delay

3 MIT 2.71/2.710 Optics 10/18/04 wk7-a-3 Optical path delay

4 MIT 2.71/2.710 Optics 10/18/04 wk7-a-4 Optical path delay

5 MIT 2.71/2.710 Optics 10/18/04 wk7-a-5 Optical path delay

6 MIT 2.71/2.710 Optics 10/18/04 wk7-a-6 Optical path delay phasor due to propagation (path delay) In general,

7 MIT 2.71/2.710 Optics 10/18/04 wk7-a-7 Plane wave propagation path delay increases linearly with x plane of observation

8 MIT 2.71/2.710 Optics 10/18/04 wk7-a-8 Plane wave propagation path delay increases linearly with x plane of observation

9 MIT 2.71/2.710 Optics 10/18/04 wk7-a-9 Plane wave propagation path delay at fixed slope where

10 MIT 2.71/2.710 Optics 10/18/04 wk7-a-10 Spherical wave propagation plane of observation path delay increases with x as for

11 MIT 2.71/2.710 Optics 10/18/04 wk7-a-11 Spherical wave propagation plane of observation path delay increases with x as quadratic near the axis

12 MIT 2.71/2.710 Optics 10/18/04 wk7-a-12 Spherical wave propagation plane of observation

13 MIT 2.71/2.710 Optics 10/18/04 wk7-a-13 Spherical wave propagation path delay at fixed where

14 MIT 2.71/2.710 Optics 10/18/04 wk7-a-14 Optical path delays matter path delay in material of ind ex n: compare with free space propagation :

15 MIT 2.71/2.710 Optics 10/18/04 wk7-a-15 Optical path delays matter path difference:

16 MIT 2.71/2.710 Optics 10/18/04 wk7-a-16 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 interferometers Solution: interferometers map phase onto light intensity which can be measured directly

17 MIT 2.71/2.710 Optics 10/18/04 wk7-a-17 Interference

18 MIT 2.71/2.710 Optics 10/18/04 wk7-a-18 Wave interference observation screen

19 MIT 2.71/2.710 Optics 10/18/04 wk7-a-19 Interference: extreme cases Waves in-phase Constructive interferenc e Waves out-of-phase Destructive interference

20 MIT 2.71/2.710 Optics 10/18/04 wk7-a-20 Interference vs phase delay & contrast Intensity average intensity fringe visibility aka contrast Field 1 Field 2 relative phase delay

21 MIT 2.71/2.710 Optics 10/18/04 wk7-a-21 Interference vs phase delay & contrast Intensity perfect contrastimperfect contrast Intensity no interference Highest contrast / fringe visibility is obtained by interfering beams of equal amplitudes

22 MIT 2.71/2.710 Optics 10/18/04 wk7-a-22 Polarization and interference polarized waves interfere polarized waves do not interfere

23 MIT 2.71/2.710 Optics 10/18/04 wk7-a-23 Michelson interferometer incoming laser bea m path difference:

24 MIT 2.71/2.710 Optics 10/18/04 wk7-a-24 Michelson with variable phase-delay incoming laser bea m Gas cell

25 MIT 2.71/2.710 Optics 10/18/04 wk7-a-25 Mach-Zehnder interferometer incoming laser bea m bright fringe (matched paths) interference pattern spatial period incoming laser bea m

26 MIT 2.71/2.710 Optics 10/18/04 wk7-a-26 Young interferometer incoming laser bea m opaque screen

27 MIT 2.71/2.710 Optics 10/18/04 wk7-a-27 Young interferometer incoming plane wave opaque screen

28 MIT 2.71/2.710 Optics 10/18/04 wk7-a-28 Two point sources interfering: math… Paraxial analysis: Amplitude: intensity


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