Optical polarimetry for noninvasive glucose sensing enabled by Sagnac interferometry

Optical polarimetry is used in pharmaceutical drug testing and quality control for saccharide-containing products (juice, honey). More recently, it has been proposed as a method for noninvasive glucose sensing for diabetic patients. Sagnac interferometry is commonly used in optical gyroscopes, measuring minute Doppler shifts resulting from mechanical rotation. In this work, we demonstrate that Sagnac interferometers are also sensitive to optical rotation, or the rotation of linearly polarized light, and are therefore useful in optical polarimetry. Results from simulation and experiment show that Sagnac interferometers are advantageous in optical polarimetry as they are insensitive to net linear birefringence and alignment of polarization components.     

Noncontact detection of ultrasonic waves using fiber optic Sagnac interferometer

This paper describes a fiber optic sensor suitable for noncontact detection of ultrasonic waves. This sensor is based on the fiber optic Sagnac interferometer, which has a path-matched configuration and does not require active stabilization. Quadrature phase bias between two interfering laser beams in the Sagnac loop is applied by controlling the birefringence using a fiber polarization controller. A stable quadrature phase bias can be confirmed by observing the interferometer output according to the change of phase bias. Additional signal processing is not needed for the detection of ultrasonic waves using the Sagnac interferometer. Ultrasonic oscillations produced by conventional ultrasonic piezoelectric transducers were successfully detected, and the performance of this interferometer was investigated by a power spectrum analysis of the output signal. Based on the validation of the fiber optic Sagnac interferometer, noncontact detection of laser-generated surface waves was performed. The configured Sagnac interferometer is very effective for the detection of small displacement with high frequency, such as ultrasonic waves used in conventional nondestructive testing (NDT)     

Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer

A principal scheme for an external cavity technique for changing the polarization of a laser beam based on a modified Sagnac interferometer is proposed. The modified Sagnac interferometer includes standard optical components: a displacement polarizing beam splitter, an angle reflector, and a Dove prism. The radially polarized beams, obtained with the help of the developed scheme, allow the generation of a longitudinally polarized electric field by sharp focusing. The phase correction of radially polarized modes of higher orders leads to increasing the longitudinal field in the focus of the beam.     

High-visibility interferometric measurement of the diffraction phase

We obtain the absolute phase in Fresnel diffraction for Gaussian beams by using a modified polarization Sagnac interferometer in which counterpropagating paths are spatially separated and labeled according to polarization. By erasing the polarization "which-path" information with an analyzing polarizer situated after the modified interferometer, we are able to regain interference and to precisely control the relative intensities of the diffracted and the reference beams. The resulting optimized visibility allows for a precise phase determination. This setup is very stable, requiring no active elements.     

New interferometric fiber-optic gyroscope with amplified optical feedback

A novel interferometric fiber-optic gyroscope with amplified optical feedback by an Er-doped fiber amplifier (EDFA) is proposed and theoretically investigated (the proposed gyroscope is named the feedback EDFA-FOG, FE-FOG in what follows). The FE-FOG functions like a resonant fiber-optic gyro (R-FOG) because of its multiple utilization of the Sagnac loop; however, it is completely different because a low-coherence light source is used. In addition, the gyro output signal is pulsed because the modulation frequency of the phase modulator placed in the Sagnac loop is selected to match the total round-trip time delay of the light, which includes the Sagnac-loop delay plus that of the feedback loop of the fiber amplifier. The sharpness of the output pulse can be adjusted by both the gain of an EDFA and the modulation depth of the phase modulator. When rotation occurs the peak position of the output pulse is shifted as a result of the Sagnac effect. The resolution of the rotation measurement depends on the sharpness of the output pulse. The techniques of both the open-loop and closed-loop methods are described in detail, which shows the great advantage of the proposed gyroscope over the to the conventional interferometric fiber-optical gyroscope (I-FOG).     

The sagnac effect in optically active media

The propagation of a plane, homogeneous and transverse electromagnetic wave through an optically active medium, at rest in an inertial frame or on a uniformly rotating disc, is studied here. This problem is associated with the well known Sagnac effect. The shift of fringe order one in an interferometer due to the rotation is calculated. The solution of the resulting eigenvalue problem is based on a perturbation technique in which only terms up to the first order in the rotation and the optical activity coefficient are retained.     

A Passive Phase Recovery Technique for Sagnac Interferometers Based on Controlled Loop Birefringence

We analyse the polarization and phase properties of the birefringent Sagnac interferometer in the case of a polarized source. We show that control of loop birefringence allows an arbitrary phase difference to be imposed upon the counter-propagating beams for any source polarization state, with control over the relative states of polarization of the recombining beams. We show how this may be achieved using one half-wave and two quarter-wave plates. We discuss the application of this method in fibre-optic sensors.     

Rotation sensing based on a slow-light resonating structure with high group dispersion

The concept of the Sagnac effect in a slow-light medium and resonator structure with a high group dispersion is investigated. It is found that a slow-light medium can be utilized for relative motion sensing, and a slow-light resonator structure is suitable to detect absolute rotation for navigation purposes. It is noted that the high group dispersion leads to a huge enhancement of the rotation sensor's sensitivity in a resonating structure, and an approach to evaluate and design resonator devices with slow-light property is proposed. Moreover, a folded loop-lattice-based structure is numerically simulated to verify the concept.     

Rotational spin Hall effect in a uniaxial crystal

We have considered the propagation process of the phase-matched array of singular beams through a uniaxial crystal. We have revealed that local beams in the array are rotated when propagating. However the right and left rotations are unequal. There are at least two processes responsible for the array rotation: the interference of local beams and the spatial depolarization. The interference takes place in the vortex birth and annihilation events forming the symmetrical part of the rotation. The depolarization process contributes to the asymmetry of the rotation that is called the rotational spin Hall effect. It can be brought to light due to the difference between the envelopes of the dependences of the angular displacement on the inclination angle of the local beams or the crystal length reaching the value of some angular degree. The direction of the additional array rotation is exclusively defined by the handedness of the circular polarization in the initial beam array.     

Slip effects in reinforced concrete beams with mechanically fastened FRP strip

This investigation concerns the flexural behavior of reinforced concrete (RC) beams strengthened with a mechanically fastened pultruded FRP strip (MF-FRP beams). Twelve small size MF-FRP beams and two control RC beams were tested under flexural loading. The main failure mode observed in this experimental program was nail rotation and bearing damage under increasing flexural load, which resulted in FRP slip with respect to the soffit of the RC-beam and loss of stress transfer. Strain gage data and visual observations obtained during the experiments provided useful insight for developing a new procedure for estimating the nominal moment capacity of the MF-FRP beams. The proposed method is guided by experimental evidence pointing to the significance of nail rotation associated with flexural cracking in RC beams. The developed procedure, based on a “strain reduction factor” of 24%, is able to estimate the nominal moment capacity of the MF-FRP beams with good accuracy.     

Effects of approximations in analyses of beams of open thin‐walled cross‐section—part I: Flexural–torsional stability

In formulating a finite element model for the flexural–torsional stability and 3‐D non‐linear analyses of thin‐walled beams, a rotation matrix is usually used to obtain the non‐linear strain–displacement relationships. Because of the coupling between displacements, twist rotations and their derivatives, the components of the rotation matrix are both lengthy and complicated. To facilitate the formulation, approximations have been used to simplify the rotation matrix. A simplified small rotation matrix is often used in the formulation of finite element models for the flexural–torsional stability analysis of thin‐walled beams of open cross‐section. However, the approximations in the small rotation matrix may lead to the loss of some significant terms in the stability stiffness matrix. Without these terms, a finite element line model may predict the incorrect flexural–torsional buckling load of a beam. This paper investigates the effects of approximations in the elastic flexural–torsional stability analysis of thin‐walled beams, while a companion paper investigates the effects of approximations in the 3‐D non‐linear analysis. It is found that a finite element line model based on a small rotation matrix may predict incorrect elastic flexural–torsional buckling loads of beams. To perform a correct flexural–torsional stability analysis of thin‐walled beams, modification of the model is needed, or a finite element model based on a second‐order rotation matrix can be used. Copyright © 2001 John Wiley & Sons, Ltd.     

Design and initial operation of a 367-m2 rectangular ring laser

The design and operation of a proof-of-principle rectangular He-Ne ring laser resonator with a cavity perimeter of 77.0 m and an area of approximately 367 m2 are described. With unevacuated beam lines this device gave an Earth-induced Sagnac frequency of 1513 Hz, with a relative Allan deviation over 1000 s down to 3 parts per million. The Earth's rotation provided a bias that eliminated the lock-in susceptibility. The use of increased pressure in the plasma tube facilitated single-mode operation by increasing the homogeneous pressure-broadened linewidth.     

Full investigation of the resonant frequency servo loop for resonator fiber-optic gyro

Resonator fiber-optic gyro (RFOG) is a high-accuracy inertial rotation sensor based on the Sagnac effect. A high-accuracy resonant frequency servo loop is indispensable for a high-performance RFOG. It is composed of a frequency discriminator, a loop filter, and a laser actuator. Influences of the loop parameters are fully developed. Optimized loop parameters are obtained by considering the noise reduction and wide dynamic performance of the RFOG. As a result, with the integration time of 10?s, the accuracy of the resonant frequency loop is increased to 0.02?Hz (1σ). It is equivalent to a rotation rate of 0.067°/h, which is close to the shot noise limit for the RFOG, while a minimum rotation of ±0.05°/s has been carried out simultaneously. These are the best results reported to date, to the best of our knowledge, for an RFOG using the miniature semiconductor laser that benefits from the optimization of the resonant frequency servo-loop parameters.     

Effects of approximations in analyses of beams of open thin‐walled cross‐section—part II: 3‐D non‐linear behaviour

In a companion paper, the effects of approximations in the flexural‐torsional stability analysis of beams was studied, and it was shown that a second‐order rotation matrix was sufficiently accurate for a flexural‐torsional stability analysis. However, the second‐order rotation matrix is not necessarily accurate in formulating finite element model for a 3‐D non‐linear analysis of thin‐walled beams of open cross‐section. The approximations in the second‐order rotation matrix may introduce ‘self‐straining’ due to superimposed rigid‐body motions, which may lead to physically incorrect predictions of the 3‐D non‐linear behaviour of beams. In a 3‐D non‐linear elastic–plastic analysis, numerical integration over the cross‐section is usually used to check the yield criterion and to calculate the stress increments, the stress resultants, the elastic–plastic stress–strain matrix and the tangent modulus matrix. A scheme of the arrangement of sampling points over the cross‐section that is not consistent with the strain distributions may lead to incorrect predictions of the 3‐D non‐linear elastic–plastic behaviour of beams. This paper investigates the effects of approximations on the 3‐D non‐linear analysis of beams. It is found that a finite element model for 3‐D non‐linear analysis based on the second‐order rotation matrix leads to over‐stiff predictions of the flexural‐torsional buckling and postbuckling response and to an overestimate of the maximum load‐carrying capacities of beams in some cases. To perform a correct 3‐D non‐linear analysis of beams, an accurate model of the rotations must be used. A scheme of the arrangement of sampling points over the cross‐section that is consistent with both the longitudinal normal and shear strain distributions is needed to predict the correct 3‐D non‐linear elastic–plastic behaviour of beams. Copyright © 2001 John Wiley & Sons, Ltd.     

Measuring the rotation rates of superpositions of higher-order Bessel beams

Experimental measurements are reported of the rotation rates of superpositions of higher-order Bessel beams. Digitally generated phase masks of two annular rings, were imprinted on a spatial light modulator and used to obtain superpositions of higher-order Bessel beams of the same order but of opposite topological charge. Such a superposition field carries on average zero orbital angular momentum, yet exhibits a rotation in the intensity pattern: the resultant field rotates at a constant rate about the optical axis as it propagates. The rotation rates of the generated fields were measured for different orders and for various values of the difference between the wave-vectors of the superimposing beams, and are shown to be in good agreement with that predicted theoretically.     

Michelson interferometer for precision angle measurement

An angle-measuring technique based on an optical interferometer is reported. The technique exploits a Michelson interferometric configuration in which a right-angle prism and a glass strip are introduced into a probe beam. Simultaneous rotation of both components along an axis results in an optical path difference between the reference and the probe beams. In a second arrangement two right-angle prisms and glass strips are introduced into two beams of a Michelson interferometer. The prisms and the strips are rotated simultaneously to introduce an optical path difference between the two beams. In our arrangement, optimization of various parameters makes the net optical path difference between the two beams approximately linear for a rotation as great as +/-20 degrees . Results are simulated that show an improvement of 2-3 orders of magnitude in error and nonlinearity compared with a previously reported technique.     

Experiments on the impact bending of continuous and notched steel beams

The results of quasi-static four-point bend tests and dynamic bend tests free-free beams, both continuous and notched, are reported. Angles of bend and rotation are measured as a function of time after impact, where the angle of bend is defined as the angle of deflection of one part of the beam relative to a neighbouring segment of the beam, and the angle of rotation is the angle of deflection relative to a datum line through the initial axis of the beam. The effect of notches is to change the strain profile in the beams, localize plastic formation and provides sites for fracture initiation. The influence of the notch depends on its position and depth; however, the responses of beams in terms of angles of bend and rotation are similar for notched and unnotched cases and are also insensitive to notch depth, being governed primarily by inertia of the rotating sections rather than the strength of the joint. Elastic deformation and wave propagation are shown to be important. Comparisons of angles of bend and rotation as functions of time are made with a rigid-plastic solution and with two-dimensional finite-element computations, both of which slightly underestimate the angle of bend at any time after impact.     

A new approach to the finite element modelling of beams with warping effect

As a first step toward developing a finite element formulation that can model coupling among extensional, bending and torsional behaviour of beams, a new method is proposed to properly represent the warping of arbitrary cross-sections. The basic approach is to introduce a small warping displacement superimposed over flat cross-sections of a shear-flexible beam in a deformed configuration. Numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach. The present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rotation.     

Vibration of shear-deformable beams using a spline-function approach

B-spline functions are used as trial functions in a Rayleigh-Ritz analysis of the free vibration of shear-deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross-sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear-locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B-spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear-locking difficulty is completely eliminated. This has clear significance for the analysis of shear-deformable plates and shells when using B-spline functions.