法布里－珀罗干涉仪的原理用途和实验现象
摘要：法布里－珀罗干涉仪也经常称作法布里－珀罗谐振腔，并且当两块玻璃板间用固定长度的空心间隔物来间隔固定时，它也被称作法布里－珀罗标准具或直接简称为标准具（来自法语étalon ， 意为“测量规范”或“标准”，但这些术语在使用时并不严格区分。这一干涉仪的特性为，当入射光的频率满足其共振条件时，其透射频谱会出现很高的峰值，对应着很高的透射率。
关键词：多光束干涉仪，多重反射干涉，光程差，精确测长。 光学中，法布里－珀罗干涉仪（英文：Fabry –P érot interferometer）是一种由两块平行的玻璃板组成的多光束干涉仪，其中两块玻璃板相对的内表面都具有高反射率。法布里－珀罗干涉仪也经常称作法布里－珀罗谐振腔，并且当两块玻璃板间用固定长度的空心间隔物来间隔固定时，它也被称作法布里－珀罗标准具或直接简称为标准具（来自法语étalon ， 意为“测量规范”或“标准”，但这些术语在使用时并不严格区分。这一干涉仪的特性为，当入射光的频率满足其共振条件时，其透射频谱会出现很高的峰值，对应着很高的透射率。法布里－珀罗干涉仪这一名称来自法国物理学家夏尔·法布里和阿尔弗雷德·珀罗
法布里－珀罗干涉仪的共振特性和二项色性滤镜所利用的共振特性是相同的。实质上，二项色性滤镜是由很薄的法布里－珀罗干涉仪组连续排列得到的，从而在设计上它们有着相同的数学处理方法。法布里－珀罗干涉仪还被广泛应用在通信、激光和光谱学领域，它主要用于精确测量和控制光的频率和波长。当代工艺已经能够制造出非常精密且可调谐的法布里－珀罗干涉仪。
对于法布里－珀罗标准具而言，其透射率随波长的显著变化是由于两块反射板之间多重反射光的干涉。当透射光为同相时它们有相长干涉，对应着标准具透射率的峰值；而当透射光反相时则对应着透射率的极小值。多重反射光彼此是否同相，取决于入射光的频率、光线在标准具内传播的折射角、标准具的厚度及其所用材料的折射率。
法布里－珀罗标准具中，两束相邻的反射光之间的光程差
不考虑相移时的相位差为
，在
若两个表面的反射比都为，则标准具的透射率函数由下式给出
其中。
当相邻两束光之间的光程差为波长的整数倍时，透射率函数有最大值1。在介质无吸光的情形下，标准具的反射率满足
当，也就是光程差为波长的半奇数倍时透射率函数有最小值，此时对应着反射率的最大值
在透射率函数上，两个相邻的透射峰值之间的波长间隔被称作标准具的自由光谱范围（FSR ），它由下式给出：
其中是最近峰值的中心波长。
用自由光谱范围除以透射率函数在峰值高度一半时的透射峰宽度（半高宽），得到的值称作细度：
. 对于较高的反射比（），细度通常可近似为
从这个公式可知反射比越高时标准具的细度越高，对应其透射峰越锐利。此外标准具的品质因数等于谐振频率和半高宽的比值，因此细度也正比于品质因数，这意味着细度代表了谐振腔的耗散，细度越高说明谐振腔的耗散越低。
严格意义上的法布里－珀罗干涉仪与标准具的区别在于：干涉仪中两块玻璃板的间隔长度是可调的，从而能够控制不同波长的色光的透射率；并由于透射率还和入射光的倾角有关，通常干涉仪本身也是可旋转的。
干涉条纹
法布里－珀罗干涉仪的完整设置
法布里－珀罗干涉仪的等倾干涉条纹
如前所述，对单色扩展光源，当相邻两束光之间的光程差为波长的整数倍时，透射率函数有最大值1，此时如在透射光的传播方向上垂直放置一透镜，则在其焦平面上会出现等倾干涉的亮条纹：
通常当透镜光轴垂直于屏时，等倾干涉的条纹是一组同心圆，圆心对应着正入射透射光的焦点。此时由于是正入射，，上面的有最大值：
一般情况下不是整数，如将其整数部分设为，小数部分设为
，即，则从中心亮纹数起，外圈第个亮纹的角半径为
从而圆条纹的直径满足
其中是透镜焦距。
法布里－珀罗干涉仪最常见的应用之一是，它是利用相沉积（PVD ）方法将一组标准具薄膜镀在光学器件表面。相比于吸收滤镜，这种光学滤镜往往具有更精确的反射和透射频带，特别是当设计恰当时，它们不会像吸收滤镜那样容易造成升温，因为它们可以反射掉那些不必要的波长的色光。二项色性滤镜被广泛应用在光源、相机及天文器材等光学仪器中。
∙ 在使用技术的通信网络中，包含了成排的由或金刚石制成的微型标准具。这些标准具边长约为2毫米，嵌入到高精度的微型框架中并发出彩虹色的光泽。这类材料能够保持两个反射镜之间距离的高度稳定性，从而使标准具的谐振频率在环境温度变化时也保持高度稳定。金刚石的优越性在于，它具有更好的导热性而仍拥有较低的热膨胀系数。2005年起，有些通信仪器公司开始采用光纤本身作为固态标准具，这种设计的好处是减少了大部分嵌入、准直和冷却带来的困难。
∙ 光学通常可由多至五台法布里－珀罗干涉仪的组合来构成，这些干涉仪的共振频率两两具有10倍的间隔。待测光束被一面圆柱透镜发散后，它在这些法布里－珀罗干涉仪中发生各自的干涉，所产生的亮纹的间距则被一台CCD 相机所记录，由此可以确定入射光的波长。
∙ 当采用平行平面腔的结构时，它可认为是一种法布里－珀罗干涉仪，虽然对于很多激光器而言，其中一面反射镜的反射比可非常接近100%，从而这种谐振腔更像是一种Gires –Tournois 干涉仪。半导体激光器有时会采用法布里－珀罗干涉仪的几何结构。 ∙
法布里－珀罗标准具可用来产生单模激光。在没有标准具的情况下，激光器产生的激光频谱会出现展宽，从而使谐振腔内的激光产生多种模式。使用标准具后，在细度及自由光谱范围都适当的情形下可以抑制其他模式的产生，使谐振腔内的激光工作在单模情形下。
∙ 在中法布里－珀罗标准具可以使的分辨本领得到显著提升，从而可以分辨出波长差极细微的光谱线，例如塞曼效应。
∙ 在中法布里－珀罗标准具可以用来作为一种窄频滤镜，从原子跃迁的多条谱线中过滤出所需的谱线并使之成像，最常见的例子是太阳的H-线以及Ca-K 线。
∙ 在探测中，采用法布里－珀罗谐振腔可以用来在毫秒量级的时间上储存光子，使其在谐振腔的反射镜之间反复振荡。这种做法增加了引力波探测器的干涉臂的有效长度，从而提高了引力波探测器的灵敏度。这种原理被广泛应用在引力波探测器如LIGO 和VIRGO 上，它们的构造都是带有法布里－珀罗谐振腔的等臂迈克耳孙干涉仪，干涉臂长度在几千米的量级。同时这些探测器还采用了小型的谐振腔，这些谐振腔通常被称作模式过滤器，它们可用于参与主激光的频率稳定工作。 ∙
参考文献
1. ^ 牛津英语词典
2. ^ 珀罗的名字原本是没有重音符号的（Perot ），但在科学出版物中他习惯加上重音符号，从而干涉仪的命名也习惯加上重音符号。M étivier, Françoise. Jean-Baptiste Alfred Perot (pdf). Photoniques. 2006.September –October, (no. 25) [2010-02-07] （French ）.Page 2: "Pérot ou Perot?"
3. ^ Lipson, S.G.; Lipson, H.; Tannhauser, D.S. Optical Physics 3rd. London: Cambridge U.P. 1995: 248. ISBN 0521069262.
Max Born; Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Edition) (Hardcover). Cambridge University Press. October 13, 1999: 334. ISBN 0521642221.
∙ Hernandez, G. Fabry–P érot Interferometers. Cambridge: Cambridge University Press. 1986. ISBN 0521322383.
∙ ∙
Fabry-Perot interferometer principle purpose and experimental phenomenon
Summary: Fabry-Cooper Rowe interference instrument also often called law Bree-Cooper Rowe resonant cavity, and Dang two block glass between with fixed length of hollow interval property to interval fixed Shi, it also was called law Bree-Cooper Rowe standard with or directly abbreviation for standard with (from French é Talon, meaning for "measurement specification" or "standard", but these terminology in using Shi does not strictly differentiates. Characteristics of the Interferometer, when the frequency of the incident light when its resonance condition is met, the transmittance Spectra appear very high peaks, corresponding very high transmissivity.
Key words: multiple-beam Interferometer, multiple reflection interference, optical path difference, accurate length measurement.
In optics, Fabry-Perot interferometer (English: Fabry – Pérez-rot Interferometer), composed of two parallel glass plates is a multi-beam Interferometer, that have two glass surfaces with high albedo. Fabry-Cooper Luo interference instrument also often called law Bree-Cooper Luo resonant cavity, and Dang two block glass between with fixed length of hollow interval objects to interval fixed Shi, it also was called law Bree-Cooper Luo standard with or directly referred to for standard with (from French é Talon, means for "measuring specification" or "standard", but these terms in using Shi does not strictly differentiated. Characteristics of the Interferometer, when the frequency of the incident light when its resonance condition is met, the transmittance Spectra appear very high peaks, corresponding very high transmissivity. Fabry-Perot interferometer, a name coming from France and Alfred xiaer·fabuli, a physicist · Perot
Resonance characteristics of Fabry-Perot interferometer and two color filter resonance properties are the same. In essence, two color filters are very thin Fabry-Perot interferometer groups arranged in a row to get, so they shared the same mathematical processing methods in design. Fabry-Perot interferometer is widely used in the field of communications, lasers and spectroscopy, it is mainly used for precise measurement and control of the frequency and wavelength of light. Contemporary craft has been able to make very sophisticated and tunable Fabry-Perot interferometer.
Fabry-Perot etalons are concerned, significant change is due for transmission rates vary with wavelength between two pieces of reflective plate multiple-reflection light interference. When transmitted light for them when there is constructive interference, and corresponds to the peak of Etalon transmission; and when transmitted light transmissivity of reversed-phase, corresponding to the minimum value. Multiple reflection in-phase with each other, depending on the frequency of the incident light, refraction of light inside the Etalon transmission angle, standard thickness and refractive index of the material used.
Fabry-Perot etalons, two neighboring optical path difference between reflected light, without
considering the phase shift phase difference
If the two surface reflectance, Etalon transmission function is given by the following equation
When the optical path difference between two adjacent beams when is an integer multiple of the wavelength, and function has a maximum transmission rate of 1. Media suck-free case, reflectivity
of the Etalon meet
Namely optical path difference to half an odd multiple of the wavelength transmittance function
has a minimum value, at which point value corresponds to the maximum reflectivity
On the transmittance function, two wavelength separation between adjacent transmission peaks is
called the standard with the free spectral range (FSR), it is given by the following equation:
Which is central to the recent peak wavelength.
Using the free spectral range divided by the transmittance function transmission peak width at half
peak height time (full width at half maximum), the resulting value is called fineness:
This formula reflects higher fineness standards when the higher the sharper transmission peaks. In addition of resonant frequency and quality factor is equal to the standard half-height-width ratio of fineness is proportional to the quality factor, which means that the fineness represents the cavity dissipation and fineness higher description cavity dissipation the low.
Fabry-Perot interferometer in the strict sense and the difference between Etalon: interferometer with two pieces of glass in the interval is adjustable in length, is able to control the transmission of different wavelengths of light and due transmission rate and angle of incident light-related, usually Interferometer is rotatable in itself.
Fabry-Perot interferometer full set
Fabry-Perot interferometer equal inclination interference fringes
As previously mentioned, monochrome extended light source, when neighboring optical path difference between the two beams is when an integer multiple of the wavelength, and function has a maximum transmission rate of 1, placed perpendicular to the propagation direction of the light transmission of a lens and its focal plane is in light of equal inclination interference fringes will
appear on:
When the lens axis perpendicular to the screen, usually, equal inclination interference fringes are a set of concentric circles correspond to incident light transmission focus. At this point because it is
the normal incidence, and above the maximum value:
Under normal circumstances is not an integer, such as whose integer part is divided into, fractional
split, that is, from the Central bright fringe, outer sheath of corner radius
Where is the lens focal length.
The Fabry-Perot interferometer II is one of the most common applications of color filters, it is the use of physical vapor deposition (PVD) method adds a set of standard surface with thin-film-coated optical elements. Compared to the absorption filter, the optical filters tend to have a more precise reflection and transmission frequency band, when properly designed, in particular, they will not be as easy as the absorption filter causes warming because they reflect off those unwanted wavelengths of light. Two color filters are widely used in lighting, cameras and astronomical equipment, and other optical instruments.
In a communications network using wavelength division multiplexing technology, collect the multi machine consists of rows of miniature made from fused quartz and diamond etalons. These standards is about 2 mm long, embedded in high-precision micro-framework and issuing of rainbow-colored sheen. These kinds of materials that keep the distance between the two mirrors a high stability, so that the standards of the most resonant frequency changes in the ambient temperature is high and stable. Advantages of diamond is that it still has better heat conductivity and low thermal expansion coefficient. Beginning in 2005, some communications equipment companies began using optical fiber itself as solid etalons, this design has the advantage of reducing the bulk of embedding, alignment and cooling difficulties arising from it.
· An optical wavelength meter typically consists of up to five Fabry-Perot interferometer combined to form these resonance frequencies of the Interferometer 22 has 10 times the interval. Metering is a cylindrical lens after divergence, it occurred in the Fabry-Perot interferometer interference arising out of bright fringe spacing is a CCD camera records, which can determine the wavelength of the incident light
While using parallel plane cavity laser resonant cavity structure, it can be considered as a Fabry-Perot interferometer, although many lasers, one side mirror reflectance can be very close to the 100%, thus the cavity even more like a Gires-Tournois interferometer. Semiconductor lasers are sometimes used geometry of a Fabry-Perot interferometer.
· The Fabry-Perot etalons are used to produce a single-mode laser. In the absence of standard cases, the laser laser spectrum will be broadened so that the resonant cavity lasers produce a variety of models. After using Etalon, in fineness and the free spectral range are appropriate cases can inhibit the other mode, in single-mode resonant cavity laser work situations
· Fabry-Perot Etalon in the spectroscopy allows resolution of the spectrometer has been significantly improved, to distinguish the infinitesimal wavelength difference of spectral lines, such as the Zeeman effect.
· In astronomical Fabry-Perot Etalon can be used as a narrowband filter, from the atom jumps a number of lines needed to filter out the lines and images, the most common example of this is the Sun of the h-Alpha line and the Ca-K line.
· In gravitational wave detection, using Fabry-Perot resonator can be used to store photons on the magnitude of time in milliseconds, which repeated oscillations between the resonator mirrors. This practice increases the interference of gravitational wave detector arm effective length, thereby improving the sensitivity of gravitational wave detectors. This principle is widely used on the gravitational wave detectors such as LIGO and VIRGO, which are constructed with a Fabry-Perot
resonator arm Michelson Interferometer, magnitude of the intervention arm thousands of metres in length. While these probes also incorporates a small resonator, these cavities are often referred to as analog filters, which can be used to participate in the master laser frequency stabilization work. refer to;
1.^ Oxford English Dictionary
2.^ Perot's name was originally not accented (Perot), but he was used in a scientific publication with an accent, thus naming habit with an accent of the Interferometer. Métivier, Françoise. Jean-Baptiste Alfred Perot (pdf). Photoniques. 2006.September–October, (no.
25) [2010-02-07] （French ）.Page 2
3. ^ Lipson, S.G.; Lipson, H.; Tannhauser, D.S. Optical Physics 3rd. London: Cambridge U.P. 1995: 248. ISBN 0521069262.
Max Born; Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Edition) (Hardcover). Cambridge University Press. October 13, 1999: 334. ISBN 0521642221.
Hernandez, G. Fabry–P érot Interferometers. Cambridge: Cambridge University Press. 1986. ISBN 0521322383.