參考案例講稿optics-chap

1、Chapter 7 InterferenceConditions for interferenceWavefront-splitting interferometersYoungs experimentFresnels double mirror & biprismLloyds mirrorAmplitude-splitting interferometersDielectric filmsMichelson interferometerMach-Zender interferometerSagnac interferometerMultiple beam interference: Fabr

2、y-Perot interferometerSingle & multilayer filmsApplicationsInterference is a kind of rearrangement of energy.General considerationConstructive interference-/2 /2Total constructive interference = 0 2mDestructive interference/2 3/2Total destructive interference = 2mInterference fringes of two point so

3、urcesSpherical wavesIf 1 = 2Max:(r1 - r2) = mMin:(r1 - r2) = m/2Conditions for interferencePolarizationTemporal coherence is a manifestation of spectral purity.Spatial coherenceStable fringes: very nearly the same frequencyClearest fringes: equal or nearly equal amplitude Fresnel-Arago lawsTwo ortho

4、gonal, coherent linear-polarized states cannot interfer.Two parallel, coherent linear-polarized states will interfer.The two constituent orthogonal linear-polarized states of natural light cannot interfer to form a readily observable fringe pattern even if rotated ibto alignment, since these states

5、are incoherent.Interference of independent photon beams“ each photon interferes only with itself. Interference between different photons never occurs.”Principles of Quantum Mechanics, by P.A.M. DiracPfleegor & MandelPhysical Review1967Experimental resultsWavefront-SplittingInterferometersOriginal Yo

6、ungs experimentSpatial coherent,but not temporal coherentDue to symmetry, the primary wavefront arriving at the two slits will be exactly in-phase, and the slits will constitute two coherent secondary sources. Whatever the two waves coming from S1 and S2 overlap, interference will occur (because OPD

7、 coherence length). Analysis ofYoungs experimentFringes pattern of Youngs experimentFresnels double mirrorFresnels double prismLloyds mirrorExample:Using Lloyds mirror, X-ray fringes were observed, the spacing of which was found to be 0.0025 cm. The wavelength used was 8.33 . If the source-screen di

8、stance was 3 m, how high above the mirror plane was the point source of X-ray placed?Light Receiving Fiber123Light Emitting FiberSampleFiber optic equivalent of Lloyds mirrorPropagation of a Gaussian beamE0 : electric field at the original point (x,y,z) = (0,0,0)w0 : beam radius at z=0, w : beam rad

9、ius at zk : wavevector of EM waveR : curvature of wavefrontz0 : Rayleigh range of Gaussian beam Direct- propagation lightRreflected light by the sample surfaceTwo-beam interferometry by splitting wavefrontThe unit of intensity is L2/(E02z02). s-polarization light, =650 nm, z0=75 m, w0=4 m,h=200 m, L

10、=7 mm,n=3.85+0.016i (bare silicon surface)Fringe pattern at the observation plane z = Ls-polarization light, observation plane at z = 7mm(A) = 650nm, n = 3.85+0.016i (bare silicon surface)(B) = 1550nm, n = 3.47 (bare silicon surface)h = 100 mh = 200 mh = 300 m(A)(B)Fringes pattern obtained at differ

11、ent gap distanceAmplitude-SplittingInterferometersDielectric films double-beam interferenceAssumptions:Reflections at the interface are so low that only the first two reflected beams need be considered.The OPL between these two beams is less than the coherence length of the light source.Fringes of e

12、qual inclinationAll rays inclined at the same angle arrive at the same point.Finite aperture & extended sourceHaidinger fringesWhen d is large, the separation between two reflected rays is also large. Then focusing lens is necessary for forming interference fringes.Fringes of equal thicknessEach fri

13、nge is the locus of points in the filmfor which the optical thickness is a constant.i and are small.(nf n1 & nf n1 & nf n2)A wedge-shaped film made of liquid dishwashing soapNewtons ringsThe diameter of the rings vary with m1/2 .(compare with Haidingers fringes)Pictures of Newtons ringsMichelson int

14、erferometerRearrangement of the Michelson interferometerMin. (dark fringes): 2d cosm = m0Michelsons interferometer & displacement measurementMin. (dark fringes): 2d cosm = m0d cosm m Fringes are shrinking toward the center.m = 0, 2d = m00dm - dm-1 = /2 One swept fringe corresponds to a displacement

15、of /2.Mach-Zehnder interferometerScylla IV for studying plasmaSagnac interferometerTypes & localization of interference fringesReal (w/o focusing lens) vs. virtual (w focusing lens)Nonlocalized fringes are real and exist everywhere within an extended region.Localized fringes are observable only over

16、 a particular surface. Real, localizedReal, nonlocalizedRealVirtualMultiple BeamInterferenceGeneral considerationsThe film is nonabsorbing, and n1 = n2.The rays nearly parallel, the scalar theory will suffice.Treatments on reflected beamsTreatments on transmitted beamsViewpoint of conservation of en

17、ergyTwo special casesCase ICase IICoefficient of finesse FAiry functionA (i, r, d, nf)Fabry-Perot interferometerEnclosed gap d is ranging from a few mm km.Used as a laser resonant cavity, also for laser frequency stabilization, phase locking, spectroscopy, etc.Longest Fabry-Perot interferometerin th

18、e worldSignal of Fabry-Perot etalon with absorptionPartially transparent films coated on Fabry-Perot etalon will absorb a fraction A of the energy flux density. T+R+A=150-nm silver film:R=0.94, T=0.01, A=0.05 dropped by 1/36Finesse of Fabry-Perot etalonFabry-Perot SpectroscopyResolving power & free

19、spectral rangeChromaticresolving powerMin. resolvablebandwidthFree spectralrangeApplications ofSingle & Multilayer FilmsFields at the boundary of monolayer film (I)dn1nsn0Fields at the boundary of monolayer film (II)dn1nsn0Fields at the boundary of monolayer film (III)When E / plane-of-incidenceWhen E plane-of-incidenceFields at the boundary of monolayer film (I)dn1nsn0Fields at the boundary of monolayer film (VI)When E / plane-of-inci