Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: VII. Zero drift in a fiber ring interferometer with a circuit formed by a twisted optical fiber with weak natural linear birefringence

Zero drift and fading of the interference signal determined by polarization nonreciprocity at the exit from a fiber ring interferometer (FRI) of great length designed for recording a number of general relativity (GR) effects and made on the basis of a uniformly twisted single-mode optical fiber (SMF) with weak natural birefringence are considered. The calculations are carried out by numerical simulation using the model of random coupling between orthogonal polarization modes in an SMF, which was proposed in the first part of this work. The so-called minimum arrangement of an FRI with a nonmonochromatic radiation source, including a linear polarizer located between two beam splitters, is considered. Numerical estimates are made. It is shown that the FRI with a circuit on the basis of a twisted SMF has a significantly smaller zero drift and significantly smaller fading of the interference signal than the FRI with a circuit formed by an untwisted SMF. It is shown that the FRI produced on the basis of a twisted SMF provides the polarization sensitivity necessary for detecting the GR effects under study.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XII. Dependence of the zero drift in fiber ring interferometers in orthogonal polarization modes on the range of temperature variation in an optical fiber

Temperature dependences of the zero drift in a fiber ring interferometer (FRI) without a polarizer in the presence of random inhomogeneities in a single-mode optical fiber in the FRI loop are obtained by numerical simulation. The results are compared with known experimental data. It is shown that FRIs using a superluminescent diode as a source of nonmonochromatic radiation and a loop made of a single-mode optical fiber with weak linear birefringence can find application as low-accuracy fiber-optic gyroscopes and FRIs with a loop made of a single-mode optical fiber with strong linear birefringence can be used as medium-accuracy fiber-optic gyroscopes.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: X. Verification of the ergodic hypothesis for fiber ring interferometers

The problem of the validity of the ergodic hypothesis as applied to a fiber ring interferometer (FRI) is considered on the basis of a comparison between magnitudes of the zero drift of an FRI calculated upon changing temperature of the fiber and upon random realizations of inhomogeneities in a single-mode optical fiber (SMF). The physical nature and statistical characteristics of random inhomogeneities in an SMF, types of polarization nonreciprocity in an FRI, and thermo-optical parameters of an SMF are analyzed. An algorithm for calculation of the zero drift of an FRI on changing temperature is proposed. The conditions under which the ergodic hypothesis is satisfied in an FRI are formulated. In particular, it is shown that many random inhomogeneities have to be placed on the depolarization length of polychromatic radiation in the SMF loop of an FRI; otherwise, the zero drift of the FRI calculated by the method of averaging over an ensemble of independent realizations may significantly exceed its actual value. Numerical estimations are made. It is shown that thermostabilization of an FRI with a polychromatic radiation source may significantly reduce its zero drift.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XI. Dependence of the zero drift of fiber ring interferometers on the interval of temperature variation of the fiber

The dependence of the value of the zero drift of a fiber ring interferometer (FRI), which is caused by a change in polarization nonreciprocity as a consequence of a change in the random coupling of polarization modes at inhomogeneities of the FRI loop, on the value of the interval of possible temperature variation of the single-mode optical fiber (SMF) of the FRI loop is considered. It is shown that the value of the zero drift of an FRI with a nonmonochromatic radiation source—a superluminescent diode—in a rather broad interval of temperature variations (about 100 K) is proportional to the value of the interval itself and inversely proportional to the linewidth of the radiation source. Numerical estimations are made, and they show that, for practical values of the interval of temperature variation in a room, the value of the zero drift may be much smaller than the values calculated according to the method of averaging over independent realizations of random inhomogeneities in the SMF of an FRI loop. When temperature stabilization is used, the value of the zero drift of an FRI can be additionally reduced by one to two orders of magnitude.     

Zero shift in fiber ring interferometer with wideband radiation source

It is shown that the polarization zero shift of a fiber ring interferometer (FRI) is chiefly determined by the Stokes components of the radiation, which are circularly and linearly polarized at an angle of 45° to the axis of the polarizer. A birefringent element between the polarizer and coupler in conjunction with a wideband source results in disappearance of the FRI zero shift, regardless of the mutual orientations of the polarizer, coupler, and birefringent element.Moscow Physics and Technology Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 9, pp. 1001–1010, September, 1991.     

Sagnac quantum key distribution over telecom fiber networks

We present a new concept for compensation of single mode fiber (SMF) birefringence effects in a Sagnac quantum key distribution (QKD) setup, based on a polarization control system and a polarization insensitive phase modulator. Our experimental data show stable (in regards to birefringence drift) QKD over 1550 nm SMF telecom networks in Sagnac configuration, using the BB84-protocol [C.H. Bennett, G. Brassard, in: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Institute of Electrical and Electronic Engineers, New York, 1984, p. 175] with phase encoding. The achieved total Sagnac transmission loop distances were between 100 km and 150 km with quantum bit error rates (QBER) between 5.84% and 9.79% for the mean-photon-number μ = 0.1. The distances were much longer and rates much higher than in any other published Sagnac QKD experiments. We also show an example of our one-decoy state protocol implementations (for the 45 km distance between Alice and Bob, corresponding to the 130 km total Sagnac loop length), providing an unconditional QKD security. The measurement results have showed feasibility of QKD over telecom fiber networks in Sagnac configuration, using standard fiber telecom components.     

A new mixed birefringent filter

Birefringent filters can be used for tuning lasers, with some advantages over prisms, gratings and tilted etalons. In this paper the transmission characteristics of a new mixed birefringent filter are investigated. The term ‘mixed’ is used because both circular birefringence and linear birefringence have been utilized in the fabrication of this filter.It has a loss-less core, formed by a cascaded system of alternate rotators and retarders, and a linear polarizer at each end. The performance of this filter is better because of the more effective suppression of side peaks. Unlike previous birefringent filters, this one may be used inside a linear resonator.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XVI. Depolarization and repolarization of polychromatic radiation in single-mode optical fibers with random inhomogeneities

The dependences of the degree of polarization of polychromatic radiation on the length of a single-mode optical fiber (SMF) with random inhomogeneities have been obtained by mathematical modeling. The case is considered where radiation having both polarization modes excited with equal weights of linear polarization is first introduced into a depolarizer of polychromatic radiation (a SMF segment with high linear birefringence) and arrives at an SMF with low linear birefringence. It is shown that the degree of polarization of radiation after transmission through the first segment becomes significantly suppressed and remains almost constant upon propagation through the second segment, after which it begins to sharply increase at some length; i.e., repolarization of radiation occurs. It is shown that repolarization of radiation depends weakly on the angle made by the axes of unperturbed linear birefringence of the first and second segments. The conditions for the length of the first segment (depolarizer) under which the degree of polarization remains minimum throughout the second segment are determined.     

Measurement of the spectral dispersion curves of low birefringence polymer fibres

A method is suggested to overcome the difficulties of measuring the spectral dispersion of low birefringence fibres, that produce small optical path difference, δ<3λ, where δ is the optical path difference and λ is the wavelength of light used. This method depends on variable wavelength interferometry (VAWI). The suggested method is used to measure the spectral dispersion of birefringence of polypropylene fibre with a draw ratio 4 (low birefringence fibre). This method is also used to measure the spectral dispersion of birefringence of a polyester staple from ICI (high birefringence fibre). Also, the conventional VAWI method is used to measure the spectral dispersion of this fibre to confirm the results obtained by the suggested method. Microinterferograms are given for illustration.     

Effect of orthogonal-mode random coupling on polarization characteristics of single-mode fiber lightguides (SMFL) and SMFL-based ring interferometers. Part III. Zero drift in ring interferometers with nonmonochromatic-radiation depolarizers

A method is proposed for calculation of the zero drift and Fedding interference signal at the output of a fiber ring interferometer with a circuit made of a weakly anisotropic single-mode fiber lightguide (SMFL) and a depolarizer made of an anisotropic SMFL with a nonmonochromatic radiation source. The fiber is divided into sections equal to the depolarization length in the SMFL. Four FRI circuits all of whose parameters are the same with the exception of the location of the depolarizer are compared theoretically for the first time. Numerical estimates are made. It is shown that an FRI with a Lyot depolarizer located between the polarizer and the circuit is best from a practical point of view. The required precision of assembly of the elements of the Lyot depolarizer is considerably lower than that in the other FRI circuits.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1567–1575, December, 1994.     

Control of modulation and soliton polarization instabilities in photonic crystal fibers with birefringence management

Photonic crystal fibers with composite linear birefringence, that is induced by both microstructure geometry and stress applying parts, permit the management of the wavelength dependence of both group and phase birefringence. In this work we investigate the novel nonlinear propagation phenomena that are enabled by birefringence management. Vector modulation instability is enhanced near the zero phase birefringence wavelength. Soliton polarization instability is controlled by Raman self-frequency shifting across the zero phase birefringence wavelength.     

Coefficients of viscosity of a gaseous plasma

We present here an order of magnitude calculation for the coefficients of viscosity with the assumption that the drift velocity introduces asymmetry both in the single-particle distribution functionf ₁ and the correlation functionP(1, 2). These asymmetric parts have been estimated considering the self-relaxation of the system when the cause of drift velocity is suddenly removed. Using these, the kinetic part of the coefficient of electron viscosity has been calculated and the result fairly agrees with similar studies by others. The potential part of shear viscosity coefficient is found to be zero while both parts of the coefficient of bulk viscosity are non-zero.     

液晶磁控偏光特性的研究

利用偏光干涉理论,通过对BL-009型向列相液晶透射比的测试,分析了液晶透射比随磁场的变化情况,并对液晶的磁控双折射效应进行了研究.实验在室温20℃下用JG-3型连续可调磁场仪对液晶盒施加垂直于其表面的磁场,用CT5A型特斯拉计准确读出磁场强度数值,使液晶盒光轴方向与起偏镜和检偏镜偏振方向成45°,分别测出了起偏镜和检偏镜偏振方向平行和垂直时的透射光强度.通过数学函数拟合,得出了液晶的双折射率随磁场的变化规律,即：当磁场强度大于液晶的阈值磁场时,拟合函数能很好地描述液晶磁控双折射率的变化规律.     

一种用于高精度频率传输的光纤功率补偿技术

为了抑制偏振态漂移带来的功率变化给传输稳定度造成的影响,设计了一种能够快速补偿偏振变化的频率传输系统。该系统将锁模光作为光源,结合PID控制器反馈调节的原理,利用光功率放大器(EDFA)、起偏器、可变光功率衰减器(VOA)和单片机实现。实验结果表明:该系统能够有效抑制偏振态随着环境改变而发生的漂移,经过10 km传输之后的输出光功率稳定度达到110-5,与自由漂相比提高了200倍。将整个系统应用在光梳频率传输系统中,可以提高系统的鉴相精度,在5 GHz的传输频率上,可以有效消除偏振态变化引入的~50 fs的相位抖动。     

The Influence of Boundary Conditions on Solid-on-Solid Models

We investigate various 1D solid-on-solid (SOS) models using the transfer matrix method. The main results of the paper concern SOS interfaces near an attracting wall (line) when the end points of the interface are fixed away from the wall (line). We obtain typical interface shapes in the macroscopic scale. If attraction of the wall is strong enough, then a part of the interface is pinned to the wall (line) and the remaining parts of the interface form angles with the wall (line)—the contact angles. Explicit expressions for the contact angles are derived. We show also that for a certain range of parameters the models exhibit reentrant wetting and drying. As a result the free energy of the SOS model as a function of temperature can have up to three points of nonanalyticity. The fluctuations of the SOS interface are investigated in detail. Quite unusual fluctuations are observed at the contact points—the points where unpinned and pinned parts of the interface meet.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XIV. Spectral characteristics of nonreciprocal phase difference of counterpropagating waves at the output of a fiber ring interferometer at a change in the fiber temperature

Distributions of the spectral density of the dependence of the phase difference of counterpropagating waves in a fiber ring interferometer (FRI) on the temperature of the single-mode optical fiber (SMOF) in the FRI loop (temperature spectra of the FRI zero drift) due to polarization nonreciprocity have been obtained by Fourier analysis for different spectral linewidths of the FRI radiation source and different linear birefringences of the SMOF in the FRI loop. It is shown that a change in the temperature of the SMOF in the FRI loop changes mainly the SMOF linear birefringence. This effect leads to a change in the phases of the radiation that is transferred from one polarization mode to another at those points in the SMOF where the random twisting of the axes of unperturbed linear birefringence of the SMOF changes. The effect of the magnitude of the jump under consideration, its location with respect to the nearest FRI loop end, and the magnitude of the cross-correlation (visibility) function of the radiation transmitted along the slow and fast SMOF axes from the loop end to the point where a jump in twisting of the SMOF axes occurs on the character of the temperature spectra of the FRI zero drift is determined. It is shown that in the case where the depolarization length of nonmonochromatic radiation in an SMOF is smaller than the average length of the SMOF segment on which random twisting is constant, the qualitative and quantitative characteristics of the temperature spectra of the FRI zero drift depend strongly on the polarization state of the radiation at the input of the FRI loop. The reason for this difference is explained.     

Possibility of stationary and quasistationary modes of operation of an electroluminescence radiator

Using representations of the electrodiffusion mechanism of the degradation of electroluminescence radiators — semiconductor structures, operating in the prebreakdown mode, a model of the processes is constructed which regards electrodiffusion as the migration of charged impurities from one interstice to another. The solution of the system of differential equations obtained indicates the possibility of obtaining a quasistationary mode of operation of the radiator in which the volume part of the crystal is a supplier of a practically constant flow of impurities, which diffuse into the intense-field region and which then drift to the surface of the specimen. This mode of operation corresponds to a considerable slowing down in the aging process — the drop in the brightness of the prebreakdown electroluminescence structure, which may turn out to be useful from the practical point of view.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 8–12, January, 1995.     

Reflectometric measurements of polarization properties in optical-fiber links

Polarization sensitive reflectometric techniques can be effectively used to perform spatially resolved measurements of polarization properties of fiber optic link — such as birefringence, polarization mode dispersion and polarization dependent loss. In particular, this contribution is focused on polarization sensitive OTDR and provides a survey of its theory and main applications. Special emphasis is given to the characterization of fiber birefringence, that allows to inspect the fiber while cabled and, consequently, to test and improve the cabling process. In addition, the analysis of the birefringence also allows to define reliable mathematical models, which are essential for the design of low polarization mode dispersion fibers. Reflectometric measurements of polarization mode dispersion and polarization dependent loss are also discussed.     

A laboratory test of Mach's principle and strong-field relativistic gravity

A laboratory experiment that tests the validity of Mach's principle — the relativity and gravitational induction of inertia — and relativistic gravity in strong-field circumstances is described. It consists of looking for a stationary shift in the apparent weight of an object when a transient mass fluctuation is induced in one of its parts, that part then being subjected to a pulsed thrust. The transient mass fluctuation induced is of the order of a few tens of milligrams, and the stationary weight shift observed is several milligrams. Details of the apparatus used (capable of detecting an effect at the level of about a tenth of a milligram) are presented. Procedural protocols are laid out. The results obtained — signals some 10 to 15 times the standard error in magnitude — confirm to better than order of magnitude that the predicted effect is indeed present. The consequences of this confirmation of Mach's principle and relativistic gravity are briefly addressed. In particular, it is pointed out that in light of these results radical timelessness seems to be the correct way to understand reality and, from the practical point-of-view, it may prove possible to make traversable wormholes whenever we choose to devote sufficient resources to that end.