近代光学12Oct22nd剖析课件

1、近代光学12Oct22nd剖析近代光学12Oct22nd剖析Interferometer What is interferometer? Interferometer is the optical setup which split incident light into two beams and then recombines them to create an interference fringe. Typical interferometers Michelson Interferometer Mach-Zehnder interferometer Sagnac interferom

2、eter Fizeau interferometer Twyman-Green interferometer Mirau interferometer Interferometer What is interfeThe Michelson Interferometer In a Michelson interferometer, an incident beam is splitted by a half-reflector (beam splitter) so that one beam strikes a fixed mirror and the other a movable mirro

3、r. The reflected beams are collimated by the half-reflector. Therefore an interference pattern results. The Michelson Interferometer The Michelson InterferometerSide viewDiagram of an Michelson interferometer. BS, beam splitter. C, compensator. Ms, mirrors. BSThe Michelson InterferometerSi = 2 / = 2

4、d dThe Michelson InterferometerWhen one of the two mirrors is moved by l, the optical path length is change by l and the fringe pattern is moved by one fringe. = 2 /dThe Michelson InteInterference FringesM1M2BSScreenM1When M2/M1, Fringes of Equal inclination appardInterference FringesM1M2BSScreEqual

5、 inclination interference Inner rings have higher order and larger angular width. So in the border, fringes are denser. Decreased by /2One ring immerges in the fringe center. The fringe becomes spares. One ring appears from the fringe center. The fringe appear denser.Interference FringesdIncreased b

6、y /2Equal inclination interferenceM1M2BSScreenM1When M2 is not parallel to M1, there are two possibilities. If d0, fringe of equal thickness appears. If d0, Fringes of equal inclination and thickness can be observed.Interference FringesdM1M2BSScreenM1When M2 is not Fringes of equal inclinationEqual

7、inclination +Equal thickness Fringes of Michelson Interferometer Interference FringesFringes of equal inclinationEqMeasuring the Refraction IndexApplication SampleMeasuring the Refraction IndexL = thickness. n = index of refractionNumber of wavelengths in the block (2 times): Nm=2L/n=2Ln/ Number of

8、wavelengths in same distance without block: N=2L/ =2L/ Phase change (in terms of wavelengths):DN=Nm - N=2Ln/l- 2L/l= 2L/l (n-1) Application SampleL = thickness. n = index of re1881The Michelson-Morley Experiment1881The Michelson-Morley ExperWhite light fringesAdjust the mirrors to make the two path

9、has the same path length, one can see white light fringes. White light fringesAdjust the TTM interferometric ObjectiveTTM interferometric ObjectiveGravity Wave DetectionEinstein predicted that accelerated massive objects produce time-dependent gravitational fields, gravity waves, that propagate as “

10、warpages” of spacetime at the speed of light. Very tiny: dL/L of 10-21 for inspiraling binary neutron stars. How to detect the tiny effect?Gravity Wave DetectionEinsteinGravity Wave DetectionLIGO:Laser InterferometricGravitational wave Observatory-Worlds largest interferometers: 4-km -2 in Hanford,

11、WA; 1 in Livingston, LO; - 400 scientists-Projected sensitivity 3 x 10-23 DL 10-19 m (10-9 Ang.) Gravity Wave DetectionLIGO:The LIGO projectThe LIGO projectThe LIGO folks think bigThe longer the interfero-meter arms, the better the sensitivity.So put one in space, of course.The LIGO folks think bigT

12、he lMach-Zehnder interferometerMach-Zehnder interferometerMZI in integrated opticsOptical modulators at tens to hundreds Gb/s MZI in integrated opticsOpticaSagnac interferometerSagnac interferometerAnother version of Sagnac interferometerAnother version of Sagnac inteLaser gyroLight travel time ccwT

13、ravel time cwTime differenceNumber of fringesFringe shift 4 %for 2 rev/secLaser gyroLight travel time ccLaser gyroClosed loopLaser can oscillate both directionsHigh reflectivity mirrors Improve fringe resolutionEarth rotation = 1 rev/day at poles25 ppm of fringeNeed Q 105 or greaterLed to super mirr

14、orspolished to Angstromsion beam machiningConventional mirrorspolished to 100 nanometerslimited by grit sizeLaser gyro developed for aircraft Laser gyroClosed loopLaser gyrFizeau interferometerFizeau interferometerTwyman-Green interferometerTwyman-Green interferometerMirau interferometerMirau interf

15、erometerInterferometric TestingTypical Measurement Results Flatness/Shape Critical Dimensions Roughness Depths and Volumes Film thickness Dynamic Response Typical Parts Measured Optics (flats, spheres, torics, aspheres, prisms, windows) Semiconductor Products (wafers, MEMS) Data Storage (hard disk r

16、ead heads, disks, suspensions) MEMS (pressure sensors, accelerometers, micro-mirrors) Cutting and Grinding Implements Precision Machine Parts Coatings (AR, anti-corrosion coatings)Interferometric TestingTypicalInterferogram ExamplesInterferogram ExamplesAstronomical interferometryvariable delay (B.S

17、)Delay lineBB.SAstronomical interferometryvarAstronomical interferometryAstronomical interferometryCoherenceCoherenceVisibility of interference fringesVisibility(0V1)M1M2BSScreenM1dd increases from 0 to infinity. How does V change with d? Keep constant or ? Visibility of interference friResults in t

18、he Michelson InterferometerMonochromaticSourceResults in the Michelson InterPolychromaticSourceResults in the Michelson InterferometerPolychromaticResults in the MiIntensity of an interferometer The light goes through an interferometer and is splitted into two beams which travel different pathes. On

19、 the screen, the intensity of the interference fringe is given by:here r and t are the reflectance and transmittance of the beam splitter.Intensity of an interferometerCoherence of lightAs for random variables including light, Coherence is definded as the correlation between fields at different time

20、s and/or at different locationsCoherent: g=1V=1Partially coherent: 0g10Vc, the splitted light from the same atom cannot overlap. Pulses from different atoms which are incoherent overlap. No interference happens.Qualitative analysesa1a2dabb2b1aaaa1a2a1a2a1a2a1a2The coherence time The coherence time i

21、s given by:Here Dn is the width of the spectrum. And the coherence length is given by:The coherence time The coheVarying the time delaySince light travels 300 m per ps, 300 m of mirror displacement yields a delay of 2 ps. Moving a mirror backward by a distance L yields a delay of:Translation stageIn

22、put beamE(t)E(tt)MirrorOutput beamVarying the time delaySince liMirror pairs involve tworeflections and displace the return beam in space.Corner cubes involve three reflections and also displace the return beam in space. Even better, they always yield a parallel return beam.Translation stageInputbea

23、mE(t)E(tt)MirrorsOutput beamVarying the time delayMirror pairs involve twoCornerApplication of temporal coherence:Optical coherence tomographyApplication of temporal cohereOCT Principles: Coherence Length & Imaging DepthOCT Principles: Coherence LenSpatial coherenceMeasuring the spatial coherence me

24、ans to determineLet discuss the simplest case: the Youngs double slit setup.Spatial coherenceMeasuring theLet consider the influence of the width of the single slit on the interference pattern. Assume the slit width is b.Spatial CoherenceOPLet consider the influence of Beams from source A have an OP

25、LD ofAssume that da and L, ba, approximatelySo the 0th maximum locates at Spatial CoherenceBeams from source A have an OPFor light from B, the 0th maximum locates at x=Lb/(2a). The two maxima have spatial shift of Lb/a. When the fringe space =Lb/a, the fringe produced by source A is 180o phase out o

26、f the one from B. On the screen there is uniform light. So it must be satisfied:Spatial CoherenceFor light from B, the 0th maxiVfQualitative analysesVfQualitative analysesThe intensity of interference field produced by a extended and uncoherent source is Spatial CoherenceThe complex coherence factor

27、The intensity of interference The spatial coherence depends on the emitter size and its distance away. The van Cittert-Zernike Theorem states that the spatial coherence area Ac is given by:where d is the diameter of the light source and D is the distance away.Basically, wave-fronts smooth out as the

28、y propagate away from the source.Starlight is spatially very coherent because stars are very far away.The spatial coherence depends Experiment of spatial-coherenceFringe pattern observed by Fresnels biprism.In the center, the pattern is clear. But at the boundary, the fringe blurs. Experiment of spa

29、tial-coherencChange the spatial coherenceFrosted glassChange the spatial coherenceFSpatial and Temporal CoherenceBeams can be coherent or only partially coherent (indeed, even incoherent)in both space and time. Spatial andTemporalCoherence:TemporalCoherence;Spatial IncoherenceSpatial Coherence;Tempo

30、ralIncoherenceSpatial andTemporalIncoherenceSpatial and Temporal CoherenceCoherence of other wavesAcoustic wave?Microwave?Elastic wave?Surface wave?Human wave?Influenza wave?.Coherence of other wavesAcoustInterference of waves with different frequenciesInterference of waves with difOptical beatsOpti

31、cal beats What will happen if the two interfering waves have same polarizations, stable original phase difference and different frequencies?Optical beatsOptical beatsHere, Optical beatsHere, Optical beats The intensity of the interference field are temporally modulated, not constants. It is called o

32、ptical beats. kb, b and b are the wave vector, angular frequency and the original phase of the optical beats.Optical beats The intensity of the interOptical beatsOptical beatsHeterodyne technology Phase shift between the two optical beats is , then the light speed is c=b(x1-x2)/. Optical beatsHeterodyne technology PhasLight wave packet Let consider the superposition of wave with rectangle frequency spectrum.Wave packetLight wave packetWave packetFor the point x=0, Wave packetFor the point x=0, Wave packetFor the point x, Wave packetFor the point x, Wave packetAt certain time, light mainl