Direct measurement of group dispersion of optical components using white-light spectral interferometry

We present a simple white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the group dispersion of optical components over a wide wavelength range. The technique utilizes an unbalanced Mach-Zehnder interferometer with a component under test inserted in one arm and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference. We measure the absolute group refractive index as a function of wavelength for a quartz crystal of known thickness and the relative one for optical fiber. In the latter case we use a microscope objective in front and a lens behind the fiber and subtract their group dispersion, which is measured by a technique of tandem interferometry including also a Michelson interferometer.     

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.     

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.     

pi-shifted Sagnac interferometer for characterization of femtosecond first- and second-order polarization mode dispersion

A novel configuration for measuring femtosecond polarization mode dispersion (PMD) with a pi-shifted Sagnac interferometer is studied. The advantages of this configuration include a response that is independent of the orientation of the device under test. This independence allows characterization of the first-and second-order PMD by measurement of the wavelength dependence of the differential group delay and of the orientation of the device's principal states of polarization. The method provides an extension of the dynamic range of the Sagnac interferometer technique to few-femtosecond PMD measurement.     

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.     

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.     

Linear wavelength sweep of a semiconductor laser and its consequence for dispersion measurements and interference noise in optical fibers

The wavelength shift of a semiconductor laser during triangular pulse modulation has been investigated, using both a Michelson interferometer and direct spectral measurements. This property is used to establish a method for high-resolution dispersion measurements limited to 10 ps, and not affected by material dispersion or detector rise time. A theoretical investigation shows under what conditions the method is equivalent to the standard dispersion measurement setup. The technique is applied to measure polar mode dispersion in single-mode fibers. Examples of polarization noise caused by polarization anisotropy and the variation of source wavelength are presented.     

Linear wavelength sweep of a semiconductor laser and its consequence for dispersion measurements and interference noise in optical fibers

The wavelength shift of a semiconductor laser during triangular pulse modulation has been investigated, using both a Michelson interferometer and direct spectral measurements. This property is used to establish a method for high-resolution dispersion measurements limited to 10 ps, and not affected by material dispersion or detector rise time. A theoretical investigation shows under what conditions the method is equivalent to the standard dispersion measurement setup. The technique is applied to measure polar mode dispersion in single-mode fibers. Examples of polarization noise caused by polarization anisotropy and the variation of source wavelength are presented.     

Low-coherence tandem interferometer for measurement of group refractive index without knowledge of the thickness of the test sample

A new low-coherence interferometric technique is proposed for measuring the group refractive indices of dispersive samples with high accuracy. A tandem configuration of interferometers is used to compensate for the asymmetrical distortion of interferograms that results from the broad spectrum of the light source. The group refractive index can be measured without knowledge of the geometrical thickness of the sample under test. The proposed technique can successfully measure even a thick sample. Computer calculations have shown the effectiveness of the proposed technique, which was verified by preliminary experiments; the difference between the experimental result and the catalog data was 7 x 10(-4).     

Spectral-domain intermodal interference and the effect of a low-resolution spectrometer

Spectral-domain intermodal interference is analysed theoretically at the output of a few-mode optical fibre alone and at the output of the optical fibre in a tandem configuration with a Michelson interferometer. The theoretical analysis is performed under general measurement conditions when a broadband source and a low-resolution spectrometer of a Gaussian response function are considered and when the first- and second-order intermodal dispersion effects in the optical fibre are taken into account. The theoretical analysis is performed for two different examples of dispersion curves of a two-mode optical fibre and the effect of the limiting factors is specified.     

Interferometric determination of refraction and dispersion of a birefringent material: numerical procedure

Air, liquid and solid sample interferometric gaps of the same thickness and simultaneously enclosed in a wedge interferometer are used to produce fringes of equal chromatic order. A mica sample of dimensions 2×5 mm² and an immersion liquid of the same refractive index are used. A single shot interferogram containing fringes in the three gaps is sufficient to deduce the needed experimental data. Locations of fringe maxima are introduced in a numerical procedure to retrieve the sample and liquid refractive indices across the visible spectrum. The numerical procedure is based on a simple dispersion function of wavelength and wavenumber. A modified two-term Sellmeier dispersion formula has been used for fitting the experimental data and deducing the needed dispersion parameters.     

Photothermal modulation of laser diode wavelength: application to sinusoidal phase-modulating interferometer for displacement measurements

In this paper, a novel laser-diode (LD) sinusoidal phase-modulating (SPM) interferometer, which utilizes a photothermal technique for LD wavelength modulation, is proposed to measure displacements with a nanometer accuracy. In conventional LD–SPM interferometers, the LD intensity modulation is concurrent with the wavelength modulation, which increases measurement errors. Using the photothermal technique, the LD wavelength modulation can be accomplished with negligible concomitant intensity modulation, and the measurement errors are thus eliminated. The computer simulations and experiment results verify the usefulness of this novel interferometer.     

Spectral-domain intermodal interference under general measurement conditions

Spectral-domain intermodal interference is analysed theoretically at the output of a few-mode optical fibre alone and at the output of the optical fibre in a tandem configuration with a Michelson interferometer. The theoretical analysis is performed under general measurement conditions when a light source of a given spectral bandwidth and a spectrometer of a given spectral bandpass are considered and when first- and second-order intermodal dispersion effects in the optical fibre are taken into account. Thus, the effect of a variable spectral bandpass of a low-resolution spectrometer on the spectral fringe visibility functions for a two-mode optical fibre of known intermodal dispersion is specified.     

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.     

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.     

非接触二次色散法测量人体血糖的初步研究

提出了一种测量血糖浓度的新方法——二次色散法，此方法采用低相干干涉仪来测量时间相干干涉信号，通过傅里叶变换和多项式拟合获得二次色散。初步测量了三种不同浓度的糖溶液在0．55μm到0．8μm之间的二次色散，实验结果发现随着血糖浓度的增加，二次色散也随之增加。研究证明该方法是一种潜在的无接触、无伤害在线探测人体血糖浓度的方法。为设计一种非接触、无伤害在线探测人体血糖浓度的光学医疗仪器奠定基础。最后讨论了采用本方法尚需改进的问题和进一步的工作。     

A comprehensive study of the chromatic dispersion measurement of the multi-channel fiber Bragg grating based on an asymmetrical Sagnac loop interferometer

A novel all-fiber asymmetrical Sagnac loop interferometer (ASLI) is proposed to measure the chromatic dispersion of a multi-channel fiber Bragg grating (FBG). Theoretical analyses to this proposed approach are presented in details. With this method, the chromatic dispersion and dispersion slope of a 51-channel FBG are simultaneously measured. The experimental results agree well with the ones obtained by using the general phase-shift method (PSM). This method has the advantages of simple configuration, low-cost, and high tolerance for the characteristics of FBG.     

Dispersion of birefringence and differential group delay in polarization-maintaining fiber

We present an interferometric technique for measurement of the dispersion of birefringence in polarization-maintaining fibers. The approach yields measurements over a broad spectral range from analysis of single interferograms obtained in a tandem inteferometer. The technique is demonstrated to measure first-, second-, and third-order dispersion of the differential propagation constant, corresponding to differential group delay (DGD) and its dispersion to second order; measurements are immune to asymmetry in the interferomgram that is being processed. The technique is further applied to measurement of the temperature dependence of DGD and its first-order dispersion.     

An effective optical evaluation technique using visible low-coherence interferometry

An easy and effective path length deviation detection technique is described which uses low-coherent visible light source and Michelson interferometer configuration. This technique uses large-amplitude piezoelectric modulation of a mirror, which probes portions of a complete interferogram. The maximum ambiguity in determining the center position of white light fringes is confined to half the source wavelength. Using this technique, the physical thickness and group index of an optical material are measured with an error around 0.1%. The method of improving the accuracy is also discussed.     

Distributed measurement of birefringence dispersion in polarization-maintaining fibers

A new method to measure the birefringence dispersion in high-birefringence polarization-maintaining fibers is presented using white-light interferometry. By analyzing broadening of low-coherence interferograms obtained in a scanning Michelson interferometer, the birefringence dispersion and its variation along different fiber sections are acquired with high sensitivity and accuracy. Birefringence dispersions of two PANDA fibers at their operation wavelength are measured to be 0.011 ps/(km nm) and 0.018 ps/(km nm), respectively. Distributed measurement capability of the method is also verified experimentally.