A Direct Kinematical Derivation of the Relativistic Sagnac Effect for Light or Matter Beams

The Sagnac time delay and the corresponding Sagnac phase shift, for relativistic matter and electromagnetic beams counter-propagating in a rotating interferometer, are deduced on the ground of relativistic kinematics. This purely kinematical approach allows to explain the universality of the effect, namely the fact that the Sagnac time difference does not depend on the physical nature of the interfering beams. The only prime requirement is that the counter-propagating beams have the same velocity with respect to any Einstein synchronized local co-moving inertial frame.     

Relativistic Sagnac Effect and Ehrenfest Paradox

There seems to exist a dilemma in the literature as to the correct relativistic formula for the Sagnac phase-shift. The paper addresses this issue in the light of a novel, kinematically equivalent linear Sagnac-type thought experiment, which provides a vantage point from which the effect of rotation in the usual Sagnac effect can be analyzed. The question is shown to be related to the so-called rotating disc problem known as the Ehrenfest paradox. The relativistic formula for the Sagnac phase-shift seems to depend on the way the paradox is resolved. Kinematic resolution of the Ehrenfest paradox proposed by some authors predicts the usually quoted formula for the Sagnac delay but the resolution itself is shown to be based upon some implicit assumptions regarding the behaviour of solid bodies under acceleration. In order to have a greater insight into the problem, a second version of the thought experiment involving linear motion of a special type of a non-rigid frame of reference is discussed. It is shown by analogy that the usually quoted special relativistic formula for the Sagnac delay follows, provided the material of the disc matches the special type.     

The Sagnac Vortex Optical Effect

It is shown that the Sagnac phenomenon observed experimentally is in conflict with special (and also general) relativity. The calculation of the magnitude of the Sagnac effect within the framework of a relativistic theory results in a paradox. Thus, for the moving relativistic observer, the simultaneous events of meeting of ± rays with the radiant are nonsimultaneous for the events of meeting of the radiant with ± rays. Here, the index + denotes a ray propagating in the direction of motion of the observer, while the index – denotes a ray propagating against the motion. The paradox is resolved within the framework of the theory of a luminiferous ether at rest.     

Anandan quantum phase for a neutral particle with Fermi–Walker reference frame in the cosmic string background

We study geometric quantum phases in the relativistic and non-relativistic quantum dynamics of a neutral particle with a permanent magnetic dipole moment interacting with two distinct field configurations in a cosmic string spacetime. We consider the local reference frames of the observers are transported via Fermi–Walker transport and study the influence of the non-inertial effects on the phase shift of the wave function of the neutral particle due to the choice of this local frame. We show that the wave function of the neutral particle acquires non-dispersive relativistic and non-relativistic quantum geometric phases due to the topology of the spacetime, the interaction between the magnetic dipole moment with external fields and the spin–rotation coupling. However, due to the Fermi–Walker reference frame, no phase shift associated to the Sagnac effect appears in the quantum dynamics of a neutral particle. We show that in the absence of topological defect, the contribution to the quantum phase due to the spin–rotation coupling is equivalent to the Mashhoon effect in non-relativistic dynamics.     

一种新型Sagnac式光纤电流传感器

为了消除震动对Sagnac式电流传感器测量结果的影响,提出一种光路改进方法来消除传感器对震动的敏感性,其基本原理是抵消Sagnac效应而不影响法拉第磁光效应。利用琼斯矩阵对改进后的光路结构进行了偏振态分析,理论分析和实验结果吻合,表明改进后的传感器其输出与震动无关。耦合半波片后Sagnac式光纤电流传感器的震动敏感性被消除了,为Sagnac式光纤电流传感器的工程化实现提供了一种可行的方法。     

A scheme for Sagnac-effect quantum enhancement with Fock state light input

Sagnac effect enhancement can improve optical gyro precision. For a certain input intensity, we suggest that the other input port of beam splitter(BS) should be fed with some quantum light to break through shot noise limit(SNL) to improve Sagnac effect without increasing radiation-pressure noise(NRP). We design a Sagnac effect quantum enhancement criterion(SQEC) to judge whether some quantum light can enhance Sagnac effect and present a Sagnac effect enhancement scheme that utilizing Fock state light and parity measurement technique to extract the output phase. The results of the theoretical analysis show that the maximum sensitivity can be reached at θ = 0, and the phase precision can break through SNL and even achieve Heisenberg limit(HL). When the Fock state average photon number n is far less than coherent state, the minimum measurable angular rate is improved with (2n+1)~(1/2) times, which can deduce shot noise and increase NRP little.     

Electron Sagnac gyroscope in an array of mesoscopic quantum rings

The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations with respect to an inertial frame are measured in the interference pattern. We analyze the Sagnac effect in a serial array of mesoscopic ring shaped electron interferometers comprised of rings with half-circumferences comparable to the mean free path. The entire array is, however, much larger than the phase coherence length. Phase coherent transport at the level of individual rings leads to a measurable Sagnac effect in the conductance of the chain. We use the signal to noise ratio (SNR) to determine the number of rings needed to measure a desired rotation rate.     

New Perspectives on the Relativistically Rotating Disk and Non-Time-Orthogonal Reference Frames

The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a spurious non-null effect on the order of 10^–13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.     

Neutron interference in the Earth’s gravitational field

This work relates to the famous experiments, performed in 1975 and 1979 by Werner et al., measuring neutron interference and neutron Sagnac effects in the earth’s gravitational field. Employing the method of Stodolsky in its weak field approximation, explicit expressions are derived for the two phase shifts, which turn out to be in agreement with the experiments and with the previously obtained expressions derived from semi-classical arguments: these expressions are simply modified by relativistic correction factors.     

一种基于微波谐振测量Sagnac效应的新方案

目前光学陀螺的主要工作原理是Sagnac效应, 如何提高Sagnac效应的测量精度是提高陀螺精度的一个重要研究课题. 传统的光学陀螺利用光短波长的特性来提高检测精度. 但考虑到微波的相位(频率)检测精度远高于光波的相位(频率)检测精度, 如果能够利用微波实现Sagnac效应的检测, 就能得到比光学陀螺更高的检测精度, 从而为实现高精度的微波陀螺提供了可能. 利用基于光电振荡器的光载微波结构实现了微波Sagnac效应的检测. 实验结果证明了微波检测Sagnac效应的可行性, 为将来实现高精度的微波谐振陀螺打下基础.     

Sagnac Effect of Gödel's Universe

We present exact expressions for the Sagnac effect of Gödel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Gödel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.     

Sagnac gyroscope using a two-dimensional array of coupled optical microresonators

Micron-scale-integrated optical gyroscopes based on the Sagnac effect have a broad array of potential applications in navigation and inertial motion sensing due to the benefit of on-chip integration and potential sensitivities exceeding micro-electromechanical gyroscopes. Here, we analyze the Sagnac effect in a two-dimensional array of evanescently coupled optical microring resonators. We show that the sensitivity to inertial rotations greatly exceeds that of a single resonator with equal enclosed area. Moreover, a comparison between two-dimensional arrays and Sagnac gyroscopes consisting of one-dimensional distributed microresonators arrays of equal footprint shows that the sensitivity to rotations of the two-dimensional array exceeds that of the one-dimensional structures by as much as several orders of magnitude for smaller arrays.     

基于全光纤萨格纳克干涉仪的温度不敏感磁场测量

研究了双折射磁光光纤萨格纳克 (Sagnac) 干涉仪透射谱的磁场和温度敏感性. 实验表明, 干涉仪透射谱会随着温度的增加向短波长移动 (温度系数为-0.435 nm/℃), 其波长依赖性则随着磁场的增加而降低. 据此, 通过调节干涉仪内偏振控制器状态实现了温度不敏感的磁场测量, 磁场系数为189 mW/T², 实验结果与理论分析一致. 关键词： 磁场测量 磁光效应 双折射 萨格纳克干涉仪     

Gravitational radiation antennas using the Sagnac effect

A new class of gravitational antennas that utilize the general relativistic Sagnac effect is proposed. These antennas may be more efficient than the Weber bar by a factor of (c/v_s)⁴ 10¹⁹, wherev _sis the velocity of sound in the bar. A specific case of such an antenna consisting of a superfluid helium Josephson interferometer is considered. A general relativistic theory of the interaction of the superfluid with the gravitational field is given. Using this theory, the phase shift due to a gravitational plane wave on one such antenna is obtained. More generally, the proposed interferometer involves the interplay of general relativity and quantum theory and may afford the possibility of testing general relativity in the laboratory at the quantum mechanical level. The possibility of detecting gravitons, assuming nearly unit coupling efficiency for the antenna, is explored.This essay received the second award from the Gravity Research Foundation for the year 1981-Ed.Research was supported by NSF grant No. PHY 79-13146.Research was supported by NSF grant No. ECS-8009834.     

Sagnac Effect in the Kerr-Newman and Reissner-Nordstrom Fields

By means of a formal analogy with the Aharonov-Bohm effect, the Sagnac time delay and the corresponding Sagnac phase shift in the Kerr-Newman and Reissner-Nordstrfm spacetimes are discussed. We find that the effect depends on the properties of the source of the gravitational field. The contributions made by the electric charge of the gravitational source can be employed to weaken it in the Kerr-Newman spacetime, even if a phase shift and a time delay still appear. This is due to the properties of the rotating source of the gravitational field.     

Performance of a wavelength-tunable erbium-doped fiber laser using a Sagnac interferometer

We experimentally demonstrate a wavelength-tunable erbium-doped fiber laser that is composed of a ring cavity and a single-mode fiber Sagnac interferometer in a new and simple arrangement. We find that the fiber laser output wavelength is tunable by adjusting the filter effect of the Sagnac fiber loop through a fiber polarization controller set there. The quasi-single-wavelength continuously tunable laser outputs could be achieved within some wavelength range. The multi-wavelength laser outputs could also be observed under some appropriate settings of the polarization controller. A theoretical demonstration of the wavelength tunability about the transmission-type Sagnac loop filter has also been achieved using the Jones calculus theory.     

High resolution polar Kerr effect measurements of Sr2RuO4: evidence for broken time-reversal symmetry in the superconducting state

The polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed nonzero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time-reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3He-A.     

Noninvariant one-way velocity of light

After discussing in the first five sections the meaning and the difficulties of the principle of relativity we present a new sel of spacetime transformations between inertial systems (inertial transformations), based on three assumptions: (1) The two-way velocity of light is c in all inertial systems and in all directions; (2) Time dilation effects take place with the usual relativistic factor; (3) Clocks are synchronized in the way chosen by nature itself, e.g., in the Sagnac effect. We show that our new transformation laws can explain the available experimental evidence in spite of the implied noninvariance of the one-way velocity of light.