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1、实验七 法布里珀罗（Fabry Perot）干涉仪测量光波波长十九世纪末由法布里和珀罗首次制出的多光束干涉仪，在近代光学中非常重要。它的特殊价值在于，它除了是一种分辨本领极高的光谱仪器之外，还是基本的激光器谐振腔。 通过本实验，可以了解法布里-伯罗干涉仪的基本功能。实验目的：I、应用光学元件组装法布里一珀罗（Fabry Perot）干涉仪；2、用法布里-珀罗（Fabry Perot）干涉仪测量光波波长； 实验原理：见下页。实验装置和调试：实验装置如下图所示。图中Ml、M2和M3为全反镜，其中 M3固定在一支架上，支架为1: 20的杠杆，通过千分尺可以读出M3移动的距离：L为透镜（f=20mm）
2、 . BSi和BS?为半反镜，透射率分别为 70： 30和50： 50; sc为光屏，光源为 5mWHe Ne激光器。具体调整步骤如下：1、按图1把带有杠杆的有坐标线的小平板放置在大平板上，尽可能能使二者的坐标线重合。2、 按图放置光学元件元件 M1、M2和M3，打开激光器，使得由 Ml、M2到M3的光束和 由M3反射的光束在 M2重合。3、放入半反镜BS2（50: 50），注意镀膜面（与下方的标签同向）朝向 M3。注意，此时应 使由M3反射的光线垂直于光屏。4、 放入半反镜BS1（70 : 30），注意镀膜面（贴有 7:3标签的一面）朝向 M3 .注意M3和 BS1之间距离较近，约 3mm。
3、调整BS1和M3，使得由BS1反射的光束和由 M3反射光束在 屏上基本重合。5、 把透镜L放入光路，小心调整 M3，即可发现干涉图像（圆环）。 实验内容：测量激光的波长。1、按照理论，当干涉环由暗变亮时，共振腔长度d（见图2）的变化量为半个光波波长（-/2），故只要测量一定数量的干涉环的吞吐数n和共振腔长度d的改变量，即可根据公式（10）求出激光波长。d （10）22、 实验时要求测量干涉环吞吐50圈时，共振腔长度d的改变量，求出波长，注意：杠杆 比为1: 20。3、重复测量6次，计算平均值和误差。氦氖激光器波长的理论值为632.8。思考题：试述法布里珀罗干涉仪的优点。按实际的仪器设置绘制光路
4、图。 实验原理:Theory and evaluation。实脸廩理；Theory and evaluation *The Micheison interferonieter (as well as the Mach-Zehnder and Sagnac interferometer) is a hso-beam : In gcnmlT in these ca$e$ two light waves having different frequencies are superimposed with differing a phases.In contrast, the Fabry-Perot
5、interferometer is a multibeam interferometeE An ideal Fabry-Perot interfere) of rwo plan-paraJlel lightMborbing glass plates (mirror) which are separated by di$rance d” Since the ： be neglected, the following is true for the reflection R:R = 1* T (where T = transmittance).The principle of the Fabry-
6、Perot interferometer;The principle of the interferorneter is fHustrakd in Fig. . The input wave has amplitude flp and thus the in( 诸如.Behind the first glass plate, the intensity is:(1 - J?) Zo = T *Accordingly* the amplitude is:轴=Qi _ R 5(2)Fig. i. Mutibeam interferometer attar Fatwy and Perot. Illu
7、stration M thg prinerpte for deriving the individuar amplitudesSemi retLeCtifigiTiirrorFig. sF The transmisskm curve Tt erf a FabryPernt inter* ferameter for Various r时lecfion lectors R at tfie minorFor the subsequent reflections of the wave between (he ghss platc$. the follop 社呂 resuks:禺严RVT-fl段耳In
8、 this case the pariaE beams emerging from the second plate have the following amplitudes：牛=Vi _ R 如=(1 _ /?)闵= 丫 - R 如=(_ R) H 5如=Vl； R 如 N (1 R)R2*aQfln = vrr - aln =(i - R)加 nIf we now consider a time and place-independent oscillation where:E = a cos 3 + kx + )and where E, s the first partial wave
9、 that has passed through the two glass plates, the phase 3 the subsequent partial beams, which are generated by the different path lengths of the ligh interferometer, is as follows:2kdd cos aConsequently, the following equation results for the individual emerging partial beams:& = a】 cos 仙 + Ar x)(3
10、)E2 - a2 - cos (sf + k jc + 5)3 =色 yos (ajt + k9 x + 2 6)n = an cos (a)t + kx + (n - 1) 8)rEn = (1 _ R)用7 do .COS(3/ + 上才 + (n _ 1) 5)The resulting amplitude E is the sum of the individual amplitudes E”n-!with cosa = Re /, the intensity of the resulting light wave is obtained from :(where E* is the
11、conjugated complex)For/? reflections between the plates, the following results for the amplitude according to Equation (3):Re訂十口 ( - 用7 *22The sum is a geometric series炉.歼=m-11 _p /?歼 _ -R 占Thus, the following results for the total field strength E:E = Re (】-刃勺In the formation of the limit,R approaches zero, since R -Perot interfero
