Analytical model for low finesse, external cavity, fiber Fabry-Perot interferometers including multiple reflections and angular misalignment

We present an analytical model for single mode, multiply reflected, external cavity, optical fiber Fabry-Perot interferometers in the low finesse regime using simple geometry and the Gaussian beam approximation. The multiple reflection model predicts attenuation of the peak-to-peak interference as the fiber to mirror distance approaches zero, as well as fringe asymmetry in the presence of nonabsorbing mirrors. A series of experiments are conducted in which a series of fiber Fabry-Perot cavities are constructed using uncoated, single mode glass fibers, and mirrors of varying reflectivity. The cavity length is swept, and the predictions of the model are found to be in good agreement with the experimental interferograms.     

保偏微结构光纤光栅 F-P腔折射率传感特性分析

针对提高光纤光栅折射率传感器抗干扰能力以及增加反射率的需求,本文提出了一种基于Fabry-Perot腔的保偏微结构光纤(PM-MOF)布拉格光栅折射率传感器.根据传榆矩阵法和有限元方法,分析了微结构光纤光栅F-P腔中被测物折射率与F-P腔反射谱中两个偏振模谐振波长差的关系,在此基础上讨论了中心孔直径、F-P腔长度等参数对传输特性的影响.研究结果表明,随着空气孔中填充物折射率的增加,保偏微结构光纤光栅F-P腔的两个偏振态的谐振波长差将逐渐减小;F-P腔的干涉作用使反射率较单个光栅有很大提高,便于长距离传输和实时解调;两个偏振模对外界干扰具有相似的响应,因此该传感器具有更强的抗干扰能力.本文研究结果为保偏微结构光纤光栅在折射率传感器及其生物传感器方面的应用提供了理论依据.     

Miniature all-fiber Fabry-Perot sensor for simultaneous measurement of pressure and temperature

This article presents a miniature, high-sensitivity, all-silica Fabry-Perot fiber-optic sensor suitable for simultaneous measurements of pressure and temperature. The proposed sensor diameter does not exceed 125 μm and consists of two low-finesse Fabry-Perot resonators created at the tip of an optical fiber. The first resonator is embodied in the form of a short air cavity positioned at the tip of the fiber. This resonator utilizes a thin silica diaphragm to achieve the sensor's pressure response. The second resonator exploits the refractive index dependence of silica fiber in order to provide the proposed sensor's temperature measurement function. Both resonators have substantially different lengths that permit straightforward spectrally resolved signal processing and unambiguous determination of the applied pressure and temperature.     

Measuring optical fiber length by use of a short-pulse optical fiber ring laser in a self-injection seeding scheme

A method for measuring the length of an optical fiber by use of an optical fiber ring laser pulse source is proposed and demonstrated. The key element of the optical fiber ring laser is a gain-switched Fabry-Perot laser diode operated in a self-injection seeding scheme. This method is especially suitable for measuring a medium or long fiber, and a resolution of 0.1 m is experimentally achieved. The measurement is implemented by accurately determining the pulse frequency that can maximize the output power of the fiber ring laser. The measurement results depend only on the refractive index of the fiber corresponding to this single wavelength, instead of the group index of the fiber, which represents a great advantage over both optical time-domain reflectometry and optical low-coherence reflectometry methods.     

Reflectometry measuring refractive index and thickness of polymer samples simultaneously

It is proposed and demonstrated that a novel reflectometry based on the Michelson interference measures simultaneously group refractive index and thickness of polymer samples. Such a reflectometry is a contactless measurement technique, and no damage occurs to the sample measured. Moreover, the measurement error of refractive index decreases linearly with the increasing measured sample's thickness. The ingenious planar polymer sample fabricated acts as not only the measured sample but also the fixed mirror that is necessary in other Michelson interference systems, which simplify the measurement configuration. Our reflectometry exhibits some advantages, such as simple measurement configuration, straightforward principle, easy operation, contactless measurement and high measurement precision.     

Transparent thin-film characterization by using differential optical sectioning interference microscopy

We propose an optical thin-film characterization technique, differential optical sectioning interference microscopy (DOSIM), for simultaneously measuring the refractive indices and thicknesses of transparent thin films with submicrometer lateral resolution. DOSIM obtains the depth and optical phase information of a thin film by using a dual-scan concept in differential optical sectioning microscopy combined with the Fabry-Perot interferometric effect and allows the solution of refractive index and thickness without the 2pi phase-wrapping ambiguity. Because DOSIM uses a microscope objective as the probe, its lateral resolution achieves the diffraction limit. As a demonstration, we measure the refractive indices and thicknesses of SiO2 thin films grown on Si substrate and indium-tin-oxide thin films grown on a glass substrate. We also compare the measurement results of DOSIM with those of a conventional ellipsometer and an atomic force microscope.     

一种基于梳状滤波器的固体腔厚度测量方法

针对密集波分复用(DWDM)技术中所使用的梳状滤波器,对固体腔研磨厚度指标要求极高△v=200 GHz,△d≤13.37 nm,本文提出运用法布里-珀罗干涉理论(Fabry-Perot),研究设计了一种针对固体腔厚度的现场检测方法.该方法根据被测元件等效为系统干涉腔的间接测量方法,以通过被测元件后的法珀相邻能量极值特性,作为检测厚度合格的判定依据,实现了对超窄带梳状滤波器组成元件--未镀膜层固体腔(SiO_2)的高精度厚度检测.实验结果表明,该测量方法适用于对透光介质的厚度检测.     

Digital Hilbert transformation for separation measurement of thicknesses and refractive indices of layered objects by use of a wavelength-scanning heterodyne interference confocal microscope

A wavelength-scanning heterodyne interference confocal microscope quickly accomplishes the simultaneous measurement of the thickness and the refractive index of a sample by detection of the amplitude and the phase of the interference signal during a sample scan. However, the measurement range of the optical path difference (OPD) that is obtained from the phase changes is limited by the time response of the phase-locked loop circuit in the FM demodulator. To overcome this limitation and to improve the accuracy of the separation measurement, we propose an OPD detection using digital signal processing with a Hilbert transform. The measurement range is extended approximately five times, and the resolution of the OPD is improved to 5.5 from 9 microm without the electrical noise of the FM demodulator circuit. By applying this method for simultaneous measurement of thickness and the refractive index, we can measure samples 20-30-microm thick with refractive indices between 1 and 1.5.     

任意偏折法测量玻璃折射率

提出了一种高精度测量玻璃折射率的方法。它克服了传统的最小偏向角方法的缺点，即需要反复调节样品棱镜直到准确位于最小偏向角位置上才能测量。该方法测量精度高、速度快，适用于光电对准式测角仪器，是标准玻璃样块折射率标定的较好方法。同时，它也适用于不可见光波段的折射率标定测量。     

Nondestructive measurement of an optical fiber refractive-index profile by a transmitted-light differential interference contact microscope

A novel transmitted-light differential interference contrast (DIC) system is used for nondestructive measurement of the refractive-index profile (RIP) of an optical fiber. By means of this system the phase of a measured light beam can be modulated with an analyzer, and the phase distribution of a fiber is obtained by calculation of the various interference patterns. The measurement theory and structure and some typical applications of this system are demonstrated. The results of measuring RIPs in graded-index fiber are presented. Both the experimental results and theoretical analysis show that the system takes the advantage of high index resolution and of sufficient measurement accuracy for measuring the refractive index of the optical fiber. The system has strong ability to overcome environmental disturbance because of its common-path design. Moreover, one can use the system to measure the RIP along the fiber axis and acquire an image of the three-dimensional RIP of the fiber.     

折叠腔法布里—珀罗干涉及其透射光相位变化的研究

利用折叠腔法-珀干涉仪实现了高精度位移测量,使干涉级次的当量缩小了一倍,而且扩大了法-珀干涉仪的测量范围。但折叠腔法-珀干涉仪透射光的相位在经立体棱镜反射时发生了变化,本文对折叠腔法-珀干涉仪及其透射光相位的变化进行了分析研究。     

Vibration: history and measurement with an extrinsic Fabry-Perot sensor with solid-state laser interferometry

We have studied the history of vibration and demonstrate a laser-based noncontact interferometric vibration sensor. The sensor promises the measurement of microdisplacement by using a Fabry-Perot cavity formed between a partially coated gradient-index lens and a movable reflector. Displacement is determined by the detection of interference fringes caused by phase modulation within the cavity. The sensor was tested in conjunction with both multimode and single-mode fiber transmission. Calibration with multimode fiber produced a fringe-contrast function that decreased monotonically with displacement. This calibration allowed at least 30 fringes to be discriminated, giving a displacement resolution of 0.034 mum across a range of 10.2 mum. Dynamic tests demonstrated a working range of at least 3.74 mum at frequencies as high as 2 kHz. Similar tests in which single-mode fiber was used indicated a dynamic working range of at least 4.29 mum.     

Roughened glass slides and a spectrophotometer for the detection of the wavelength-dependent refractive index of transparent liquids

We describe a method to determine the wavelength-dependent refractive index of liquids by measurement of light transmittance with a spectrophotometer. The method is based on using roughened glass slides with different a priori known refractive indices and immersing the slides into the transparent liquid with unknown refractive index. Using the dispersion data on the glass material it is possible to find the index match between the liquid and the glass slide, and hence the refractive index of the liquid.     

Measurement of CO2-laser-irradiation-induced refractive index modulation in single-mode fiber toward long-period fiber grating design and fabrication

We report a new method to measure the CO(2)-laser-irradiation-induced refractive index modulation in the core of a single-mode optical fiber for the purpose of design and fabrication of long-period fiber gratings (LPFGs) without applying tension. Using an optical fiber Fabry-Perot interferometer, the laser-induced axial refractive index perturbation was measured. We found that the CO(2)-laser-irradiation-induced refractive index change in the fiber core had a negative value and that the magnitude was a sensitive function of the laser exposure time following almost a linear relation. Under the assumption of a Gaussian-shaped refractive index modulation profile and based on the first two terms of Fourier series approximation, the measured refractive index perturbations were used to simulate the LPFG transmission spectra. LPFGs with the same laser exposure parameters were fabricated without applying tension, and their spectra were compared with those obtained by simulations.     

Interplay Between Physics and Statistics for Modeling Optical Fiber Bandwidth

In multimode optical fiber, the refractive index of the glass is varied radially in such a way that a light pulse propagates through multiple modes, or paths, as it travels. We investigate the prediction of fiber transmission capacity, specifically bandwidth, by using refractive index profiles of glass preform rods measured in a manufacturing environment before the rods are drawn into optical fiber. By closely linking empirical and theoretical approaches to modeling, we demonstrate the feasibility of predicting bandwidth despite the finding that profile measurements are grossly inaccurate. Empirical components of the modeling involve extensive preprocessing of raw measurements that approximate continuous functions, followed by spline fitting and specialized cross-validation for model assessment. Modeling from physical theory is based on solutions of Maxwell's equations. This article shows how a blending of physics with statistics provides conclusions that could not be obtained separately from either approach—namely, good predictions are possible, but profiling equipment needs to be upgraded to remove substantial measurement biases.     

Fabry-Perot metrology for displacements up to 50 mm

A system designed to apply Fabry-Perot interferometry to the measurement of displacements is described. Two adjacent modes of a Fabry-Perot cavity are probed, and both the absolute optical frequencies and their difference are used to determine displacements via changes in cavity length. Light is coupled to the cavity via an optical fiber, making the system ideal for remote sensing applications. Continuous interrogation is not necessary, as the cavity length is encoded in the free spectral range. The absolute uncertainty is determined to be below 10 pm, which for the largest displacement measured corresponds to a relative uncertainty of 4 x 10(-10). To my knowledge this is the smallest relative uncertainty in a displacement measurement ever demonstrated.     

Linearly polarized er(3+)-doped fiber laser by use of a fiber loop polarizer and a wavelength-selective fiber loop reflector

We demonstrate a novel single-polarization Er(3+)-doped fiber Fabry-Perot laser. The all-fiber Fabry-Perot cavity is simple inasmuch as it is formed by only two fiber-based components, a fiber loop polarizer and a wavelength-selective fiber loop reflector. The threshold power is 6.5 mW, the slope efficiency is 12.2%, and the extinction ratio is approximately 25 dB.     

Use of analyte-modulated modal power distribution in multimode optical fibers for simultaneous single-wavelength evanescent-wave refractometry and spectrometry

A new method is described for the simultaneous determination of absorbance and refractive index of a sample medium. The method is based on measurement of the analyte-modulated modal power distribution (MPD) in a multimode waveguide. In turn, the MPD is quantified by the far-field spatial pattern and intensity of light, i.e., the Fraunhofer diffraction pattern (registered on a CCD camera), that emerges from a multimode optical fiber. Operationally, light that is sent down the fiber interacts with the surrounding analyte-containing medium by means of the evanescent wave at the fiber boundary. The light flux in the propagating beam and the internal reflection angles within the fiber are both affected by optical absorption connected with the analyte and by the refractive index of the analyte-containing medium. In turn, these angles are reflected in the angular divergence of the beam as it leaves the fiber. As a result, the Fraunhofer diffraction pattern of that beam yields two parameters that can, together, be used to deduce refractive index and absorbance. This MPD based detection offers important advantages over traditional evanescent-wave detection strategies which rely on recording only the total transmitted optical power or its lost fraction. First, simultaneous determination of sample refractive index and absorbance is possible at a single probe wavelength. Second, the sensitivity of refractometric and absorption measurements can be controlled simply, either by adjusting the distance between the end face of the fiber and the CCD detector or by monitoring selected modal groups at the fiber output. As a demonstration of these capabilities, several weakly absorbing solutions were examined, with refractive indices in the range from 1.3330 to 1.4553 and with absorption coefficients in the range 0-16 cm-1. The new detection strategy is likely to be important in applications in which sample coloration varies and when it is necessary to compensate for variations in the refractive index of a sample.     

Fabrication of a graded-index polymer optical fiber preform without a cavity by inclusion of an additional monomer under a centrifugal force field

When two or more monomers with different densities and refractive indices are polymerized under a centrifugal force field, a radially varying refractive index is generated owing to the difference in density of the monomers. After the polymerization is completed, a cavity is generated about the rotational axis as a result of inherent volume shrinkage during bulk radical polymerization. Therefore it is necessary to feed an additional monomer into the cavity to compensate for the undesirable volume shrinkage. We have successfully fabricated a preform with graded indices for polymer optical fiber without a cavity by adding another monomer during rotation of the reactor. One can control the overall refractive-index profile by changing the rotation speed. Furthermore, the refractive-index profile can be predicted as a function of rotating speed by use of a simple mathematical model.     

Absolute refractometry of dry gas to ±3 parts in 10⁹

We present a method of measuring the refractive index of dry gases absolutely at 632.8 nm wavelength using a Fabry-Perot cavity with an expanded uncertainty of <3×10?? (coverage factor k=2). The main contribution to this uncertainty is how well vacuum-to-atmosphere compression effects (physical length variation) in the cavities can be corrected. This paper describes the technique and reports reference values for the refractive indices of nitrogen and argon gases at 100 kPa and 20 °C with an expanded uncertainty of <9×10?? (coverage factor k=2), with the additional and larger part of this uncertainty coming from the pressure and temperature measurement.