Spectral-domain tandem interferometry to measure the group dispersion of optical samples

A spectral-domain technique based on tandem interferometry is used for measuring the group dispersion of optical samples over a wide wavelength range. The technique utilizes a tandem configuration of a Michelson interferometer and an unbalanced Mach–Zehnder interferometer with a sample inserted into its test arm. First, the theoretical background of the technique is presented and then experiments with individual interferometers and their tandem configuration are specified. In all the experiments the spectral signals are recorded to measure the equalization wavelength as a function of the path length difference, or equivalently the group dispersion. We measure the group refractive index as a function of wavelength for a glass sample of known thickness and for a quartz crystal as well.     

Group index dispersion of holey fibres measured by a white-light spectral interferometric technique

We present a new white-light interferometric technique to measure the group index of holey fibres over a wide wavelength range. The technique utilizes an unbalanced Mach–Zehnder interferometer with a fibre under test of known length placed in one of the interferometer arms and the other arm with adjustable path length. In a first step, the differential group index of the fibre is measured over a wide wavelength range. In a second step, the fibre is replaced by the reference sample of known thickness and group dispersion to determine precisely the group index of the fibre at one specific wavelength. The group index as a function of wavelength is measured for two different holey fibres, one made of pure silica glass and the other made of SK222 glass. For both fibres, the wavelength dependence of the group index of the outer cladding and modes supported by the fibre is measured.     

Dispersion error of a beam splitter cube in white-light spectral interferometry

We revealed that the phase function of a thin-film structure measured by a white-light spectral interferometric technique depends on the path length difference adjusted in a Michelson interferometer. This phenomenon is due to a dispersion error of a beam splitter cube, the effective thickness of which varies with the adjusted path length difference. A technique for eliminating the effect in measurement of the phase function is described. In a first step, the Michelson interferometer with same metallic mirrors is used to measure the effective thickness of the beam splitter cube as a function of the path length difference. In a second step, one of the mirrors of the interferometer is replaced by a thin-film structure and its phase function is measured for the same path length differences as those adjusted in the first step. In both steps, the phase is retrieved from the recorded spectral interferograms by using a windowed Fourier transform applied in the wavelength domain.     

Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry

We present a white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the dispersion of the ordinary and extraordinary group refractive indices of a quartz crystal over the wavelength range approximately from 480 to 860 nm. The technique utilizes a dispersive Michelson interferometer with the quartz crystal of known thickness to record a series of spectral interferograms and to measure the equalization wavelength as a function of the displacement of the interferometer mirror from the reference position, which corresponds to a balanced non-dispersive Michelson interferometer. We confirm that the measured group dispersion agrees well with that described by the dispersion equation proposed by Ghosh. We also show that the measured mirror displacement depends, in accordance with the theory, linearly on the theoretical group refractive index and that the slope of the corresponding straight line gives precisely the thickness of the quartz crystal.     

High angle phase modulated low coherence interferometry for path length resolved Doppler measurements of multiply scattered light

We describe an improved method for coherence domain path length resolved measurements of multiply scattered photons in turbid media. An electro-optic phase modulator sinusoidally modulates the phase in the reference arm of a low coherence fiber optic Mach-Zehnder interferometer, at a high phase modulation angle. For dynamic turbid media this results in Doppler broadened phase modulation interference peaks at the modulation frequency and its multiples. The signal to noise ratio is increased by almost one order or magnitude for large modulation angles and the shape of the spectral peaks resulting from the interference of Doppler shifted sample waves and reference light is not changed. The path length dependent Doppler broadening is compared with the theoretical predictions in the single scattered and diffusive regimes. The experimentally measured optical path lengths are validated with the Monte Carlo technique.     

Dispersive white-light spectral two-beam interference under general measurement conditions

Spectral-domain interference of two beams from a white-light source is analysed theoretically and experimentally when the effects of both dispersion in an interferometer and the response function of a spectrometer are taken into account. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer. The theoretical analysis is accompanied by experiments employing a dispersive Michelson interferometer and a low-resolution spectrometer. Two experiments with different amounts of dispersion in the Michelson interferometer are realized giving rise to the spectral interference fringes resolved only in the vicinity of the so-called equalization wavelength, at which the group optical path difference between interfering beams is zero. The recorded spectral interferograms are in good agreement with the theoretical ones, which are modelled knowing dispersion in the interferometer and the bandpass of the spectrometer.     

白光干涉偏振模耦合分布式光纤传感器分析

分布式光纤传感器能够测量沿光纤长度上连续分布的外界量。用保偏光纤作为传感光纤的分布式光纤传感器,被测外界量引起保偏光纤中传播的两正交偏振模的相互耦合。用迈克尔逊干涉仪两臂光程差来补偿两个偏振模的光程差的方法探测传感信号。为了设计白光干涉偏振模耦合分布式传感器,根据统计光学原理分析了传感器的互相干特性。在此基础上分析了传感器的空间分辨力、光纤耦合点分辨力、最大传感光纤长度。波长1310nm、谱宽36nm的超辐射发光二极管(SLD)作光源．用色散参量为600ps／km,拍长3mm的保偏光纤的分布传感器空间分辨力和光纤耦合点分辨力分别为6cm和3mm。     

群速度色散对于纠缠光场二阶关联函数影响的研究

HBT干涉是量子测量中的一种重要手段, 其通过计算光场的二阶关联函数而得到测量结果. 在长距离测距中, 光场的二阶关联函数会受到光纤中群速度色散的影响而发生展宽和平移, 从而在一定程度上影响测量精度. 本文主要针对二阶关联函数半高宽受群速度色散的影响, 给出了半高宽与测量距离与群速度色散系数的关系.     

All-fiber incoherent frequency-to-time mapping method for microwave signal generation with baseband transmission and multicasting support

We present a proof-of-principle experiment for achieving simultaneous distribution of baseband radio-frequency data and up-conversion with broadcasting support over a passive optical network. The technique is based on an incoherent frequency-to-time mapping method for pulse shaping. Specifically, we synthesize the spectral density function of sliced ASE noise from an EDFA with a periodic Mach–Zehnder fiber interferometer optical filter. By using external intensity modulation combined with propagation in an optical fiber, after photodetection, the resultant averaged temporal pulse profile resembles the shape of the incoherent source. The photodetected signal contains both the baseband data and an up-frequency converted copy with central wavelength for the microwave carrier into the ultra-wideband range and tuning capability by selection of the fiber length.     

Dispersion measurement of liquids with a fiber optic probe based on a bi-functional lensed photonic crystal fiber

We report a fiber optic probe suitable for measuring the wavelength dispersion of liquids. The measuring probe is made from an extrinsic fiber-optic cavity formed by a lensed photonic crystal fiber (PCF) and a micro-mirror. The custom-designed lensed PCF plays a dual role of collimator to help realize a long cavity length of the order of millimeters and as an efficient reflector to form the reference beam. The length of the cavity used in the experiment is about 1620 μm. In this article, we present the analytical method of obtaining dispersion of the liquid sample from the spectral interferogram of a single-arm or common path interferometer. Sodium chloride salt solutions with varied concentrations are used as an example to demonstrate the efficacy of the instrument. The index change with concentration is found to be linear at low concentrations and deviates from linearity as it approaches saturation.     

Increased ranging depth in optical frequency domain imaging by frequency encoding

A technique for increasing the ranging depth in optical frequency domain imaging utilizing frequency encoding is presented. Ranging depth is enhanced by using two interferometer reference arms with different path lengths and independent modulation frequencies (25 and 50 MHz). With this configuration, the sensitivity decreases by 6 dB over a depth range of 7 mm, approximately a threefold improvement over the conventional optical frequency domain imaging technique. We demonstrate that the reference arm frequency separation, tuning speed, center wavelength, and instantaneous coherence length determine the signal-to-cross-talk ratio.     

First step toward a benchtop model of the Laser Interferometer Space Antenna

A technique for simulating large optical path lengths by use of digital delay buffers is presented. This technique is used to generate a synthetic interferometer with one arm having an arbitrary length. The response of the interferometer to phase and frequency modulation is measured and found to be in agreement with predictions. This technique could be used to simulate long-baseline interferometric space missions such as the Laser Interferometer Space Antenna.     

Slightly dispersive white-light spectral interferometry to measure distances and displacements

A new spectral-domain interferometric technique of measuring distances and displacements is realized when the effect of low dispersion in a Michelson interferometer, which comprises two coated plates of a beam splitter and a compensator, is known and the spectral interference fringes are resolved over a wide wavelength range. First, processing the recorded spectral interferograms by an adequate method, the unmodulated spectrum, the spectral fringe visibility function and the unwrapped phase function are obtained. Then, knowing the dispersion relation for the fused-silica plates, the ambiguity of the unwrapped phase function is removed and the thickness of fused silica and the nonlinear phase function due to the effect of the coatings are determined by using a new procedure. It is based on the linear dependence of the overall optical path difference between interferometer beams on the refractive index of fused silica. Once the thickness and the nonlinear phase function are known, the positions of the interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones.     

Electric Voltage Tuning of an All-fiber Mach-Zehnder Interferometer

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Optical Measurement Techniques for Optical Fiber and Waveguide Devices

We describe three major optical characterization methods for fiber and fiber devices. A simple servo controlled scanning fiber-optic confocal microscope is proposed for determining the refractive index profile of an optical fiber. To measure the chromatic dispersion of a short length fiber a Mach-Zehnder fiber interferometer with a novel interferometric distance meter is introduced. At the end, a tomographic method is demonstrated for determining the 2-D stress profile of a fiber.     

Simple method for measurement of surface roughness using spectral interferometry

The phenomenon that correlation between two beams, in a two-beam interferometer, modifies the spectral characteristics of the light field, is used to estimate the average of the roughness of the surfaces. In the case of intensity interferometer, the path difference between the two arms of the interferometer should be less than the coherence length of the light and the light should be quasi-monochromatic. However, the advantage of spectral interferometer is that the light need not be quasi-monochromatic and the path difference could be much more than the coherence length of light. It is found that more the path difference between the two arms of the interferometer, accurate are the measurements of the roughness of the surfaces. This study shows that spectral interferometry enables one to measure average roughness of the surfaces in the subscales of optical wavelengths.     

Continuous-wave measurement of the fiber nonlinear refractive index

We propose a technique for measuring the nonlinear refractive index of fiber based on transmission-coefficient measurements in a fiber Sagnac interferometer. In contrast with traditional methods, the proposed method uses a single optical source operating in cw mode and direct intensity measurement, enabling one to avoid the errors caused by fiber dispersion and uncertainty of spectral peak difference measurements that occur with pulse-based methods. The nonlinear refractive index in 20-mol. % GeO(2) fiber was measured to be (3.1 +/- 0.2) x 10(-16) cm(2) W(-1) at 1064 nm.     

望远镜干涉阵中光程调制的研究

提出了在单模光纤联接的望远镜干涉阵中通过拉伸红外单模光纤实现光程调制的方法。简要分析了该方法的机理及存在的问题，如偏振效应，色散等，用少模光纤和单模光纤分别代替马赫－陈德尔（Ｍａｃｈ－Ｚｅｈｎｄｅｒ）干涉仪的两个臂，并且其中一臂的光纤缠在直径为６ｃｍ的ＰＺＴ圆柱上，给ＰＺＴ圆柱施加三角皮电压后，首次得到干涉条纹，并证明了方法的可行性。     

Long-gauge length embedded fiber optic ultrasonic sensor for large-scale concrete structures

A fiber optic ultrasonic sensor based on Fizeau interferometer has been developed and demonstrated. A helium–neon laser light source with wavelength 0.6328 μm is used in our experiment. A special feature is its Fizeau configuration, which enables one to eliminate much undesirable noise by combining both the reference arm and the sensing arm within the same length of fiber. The dynamic response model of photo-elastic effect of ultrasonic wave and optical fiber is established. The fiber optic ultrasonic sensor experimental results are obtained and compared with the convenient PZT transducer.     

Absolute metrology by phase and frequency modulation for multiwavelength interferometry

A fiber interferometer for absolute distance measurements is presented whereby wavelength variation is achieved via a sinusoidal strain modulation of a fiber Bragg grating to generate a series of beat wavelengths. The interferometer employs fiber laser sources where the design is based on the use of narrow-bandwidth fiber Bragg gratings. The accuracy of the beat wavelengths is improved compared to the use of multiple wavelengths measured with conventional optical spectrum analyzers or available wavemeters. Initial measurements are presented for beat wavelengths of 254.74 mm and 27.4 m over an optical path difference of 200 mm and 3.8 m, respectively. Combined with a two (or three) wavelength interferometer, this technique has the potential for ultrahigh dynamic range metrology ranging over several meters while preserving subfringe resolution and a low system complexity.