Coupling between elliptic screw polarization modes in single-mode optical waveguides with linear birefringence and regular twist of anisotropy axes in the presence of random axis twist

An analysis is made of single-mode fiber optical waveguides with linear birefringence and regular twist of anisotropy axes in the presence of random twist, which shows that, in this case, the coupling of orthogonal polarization modes having elliptic polarization in the screw coordinate system comoving with twist cannot be characterized by one coupling parameter, as differentiated from the case where constant twist is absent. In this case, the coupling between polarization modes is characterized by three independent parameters, which are different in nature and have different effects on the coupling of polarization modes. An estimate is made of the domain of applicability of the classical formula for the h parameter in single-mode fiber optical waveguides without regular twist of anisotropy axes.     

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.     

偏振模色散矢量的研究

研究了无损光纤的密勒矩阵,进而得出了偏振模色散矢量的解析表达式、主偏振态对应的斯托克斯矢量的解析表达式,以及高阶偏振模色散矢量的解析表达式.这些解析表达式是由光纤参数决定的.讨论了局部偏振模色散矢量与整体偏振模色散矢量的关系,讨论了利用偏振模色散矢量进行偏振模色散补偿的原理.引入了偏振模色散补偿元件的偏振模色散补偿矢量C,具体计算了正规的非圆光波导类的补偿元件的C.从理论上证明了仅仅利用一个正规的非圆光波导类的补偿元件,例如一根保偏光纤或是一个双折射晶体,是不能实现偏振模色散补偿 关键词： 偏振模色散 密勒矩阵 色散补偿 主偏振态斯托克斯矢量     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: VI. Evolution in the degree of polarization of nonmonochromatic radiation traveling in a twisted optical waveguide

An analysis is made of the evolution of polarization of nonmonochromatic radiation travelling through single-mode optical fibers in the presence of random coupling between orthogonally polarized modes, which is caused by the random twist of axes of natural linear birefringence of an SMF, and in the presence of a regular axis twist. It is shown that the depolarization length of nonmonochromatic radiation in an SMF increases with increasing regular SMF twist, regardless of the presence of a random axis twist. Using the Monte Carlo method, the dependences of the mathematical expectation and the mean-square deviation of the degree of polarization of nonmonochromatic radiation on the fiber length for SMFs with different linear birefringences and regular axis twists are calculated. It is shown that the fiber length on which the degree of polarization of nonmonochromatic radiation reaches its limiting value increases and the limiting value itself decreases with an increasing regular twist. It is also shown that an induced SMF twist is able to improve parameters of a fiber interferometer, in particular, to decrease random phase changes and intensity fadings of the interference signal, which are caused by random coupling between polarization modes.     

Exact Solutions for the Local Parameters of Polarization Modes in Coiled Optical Spun Fibers with Strong Unperturbed Linear Birefringence. I. Nonresonant Linear Transformation

Optics and Spectroscopy - The propagation of monochromatic radiation in coiled spun optical fibers is considered. The local parameters of the elliptical polarization eigenmodes, elliptic...     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XV. Dependence of integral statistical parameters of polarization modes in single-mode optical fibers with random inhomogeneities on the wavelength of light

Spectral dependences of integral statistical elements of the Jones matrix of an extended segment of a single-mode optical fiber (SMOF) with random inhomogeneities, whose length considerably exceeds the correlation length of random inhomogeneities, are found by the method of mathematical modeling. The boundaries of the ranges of optical wavelengths are determined, within the limits of which the parameters under consideration remain quasi-constant. This allows the derivation of analytical expressions for the degree of polarization of nonmonochromatic radiation in an SMOF and for the zero drift in fiber ring interferometers with the help of the approximate method of small perturbations. It is shown that the small-perturbation method leads to adequate results for SMOFs with strong and intermediate linear birefringence.     

Propagation of optical vortices in coiled weakly guiding optical fibers

The structure of the l = 1 modes of regularly coiled weakly guiding optical fibers with round cross section is determined. The l = 1 modes are shown to be represented by two right-and left-hand polarized stable optical vortices, as well as by TE and TM modes. The polarization corrections to the scalar propagation constant are found. The stability of an optical vortex transmitted along a coiled fiber is estimated. The parameters for optimal coiling at which the transmission of vortices along the fibers is the most stable with respect to fiber perturbations are determined.     

Twisted optical fibers sustaining propagation of optical vortices

The mode structure (the orbital number l = 1) of a few-mode weakly guiding optical fiber with high linear birefringence and a regular twist of its anisotropy axes is investigated. It is shown that, for certain values of twist pitch, the modes with l = 1 are almost pure linearly polarized optical vortices in the local coordinate system associated with the anisotropy axes. The range of values of twist pitch in which twisted fibers sustain propagation of linearly polarized optical vortices is determined numerically.     

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.     

Determination of stress-induced intrinsic birefringence in a single-mode fiber by measurement of the two-dimensional stress profile

The two-dimensional (2-D) axial stress profile of a single-mode fiber is obtained with an optical tomographic measurement technique. All stress components of the fiber are calculated from a measured axial stress profile. We demonstrate that the differential group delay induced by intrinsic nonsymmetric stress as well as the induced linear birefringence between two orthogonal polarization modes can be determined with an analytic technique based on a vector perturbation method from a measured asymmetric 2-D stress distribution.     

Increase in the correlation length of nonmonochromatic radiation during propagation in a single-mode optical fiber containing random inhomogeneities and the influence of this increase on the operation of a fiber ring interferometer

An analysis is made of the conditions under which the coupling of orthogonal polarization modes at random inhomogeneities in single-mode optical fibers leads to an increase in the correlation length of a source of nonmonochromatic radiation. It is shown that when long-base fiber ring interferometers with a single-mode fiber ring system possessing weak linear birefringence are used, the correlation length of the nonmonochromatic radiation at the interferometer exit is increased, which means that the interference pattern can have satisfactory visibility even when there is an appreciable difference between the interferometer arms as a result of the Sagnac effect due to the Earth’s rotation. The calculations were made by mathematical modeling of random inhomogeneities in the fiber. Zh. Tekh. Fiz. 69, 140–143 (July 1999)     

高数值孔径双芯光纤的双折射研究

具体分析了具有高数值孔径的双芯光纤的双折射特性。首先利用超格子正交函数法和耦合模理论分析了双芯光纤的几何双折射,并将两种方法计算的几何双折射进行了比较分析。数值计算结果表明双芯光纤在两纤芯非常接近的情况下,几何双折射仍较小,只能到10-5量级。利用超格子正交函数法计算了双椭圆芯光纤的双折射,改变结构参量可使几何双折射达到10-4量级。高的数值孔径需要高的掺锗量,理论上分析了高数值孔径时双芯光纤功率集中区域的应力双折射,应力双折射接近10-4量级。设计制作出了具有良好保偏性能的双芯掺铒光纤,测试、分析了它的几何参量和折射率分布;双芯光纤双折射系数达到了8.4×10-5。双芯掺铒光纤可以作为保偏掺铒光纤,应用到制作具有稳定的单一偏振态输出的光纤激光器。     

椭圆芯非六角对称高双折射聚合物PCFs

采用全矢量平面波展开法,以聚合物PMMA为基材,研究了椭圆芯非六角对称聚合物光子晶体光纤（Photonic Crystal Fibers,PCFs）的传输模场和偏振特性,从理论上分析了其模式双折射和光纤结构参量的关系.研究结果表明,该PCFs基模的两个正交偏振态不再简并,模场呈现明显的椭圆并具有较强的线偏振特性；另外,该光纤的模式双折射强烈地依赖于光纤的结构参量,通过适当调节光纤的相对孔间距比,有望在给定波长范围内实现更高双折射单模运行.     

矩形点阵微结构聚合物光纤偏振特性研究

采用全矢量平面波方法,以聚合物为基材,研究了矩形点阵微结构聚合物光纤的传输模场和偏振性质.结果发现,矩形点阵微结构聚合物光纤基模两个正交偏振态不再简并,模场呈现类矩形且具有较强的线偏振特性;该光纤模式双折射产生于包层孔结构分布的不对称性,减小包层纵向孔间隔和横向孔间隔之比η值,双折射明显增强,适当调节η,可在更宽频带范围内实现高双折射单模运行.     

Influence of the irregularity of twisting of the birefringence axes of single-mode optical fibers on the polarization nonreciprocity of fiber ring interferometers

A particular example of the so-called minimum-configuration fiber ring interferometer whose loop comprises two different-length segments of a single-mode optical fiber with the same linear birefringence but different twisting is used to show that even in the case where the birefringence axes at the loop input coincide with the polarizer transmission direction, the phenomenon of polarization nonreciprocity of the fiber ring interferometer can emerge. It is shown that polarization nonreciprocity can be eliminated by the proper adjustment of the axes of a single-mode optical fiber, but the above adjustment should be changed if the waveguide temperature is changed. It is also shown that polarization nonreciprocity is a function of the light wavelength and the polarization nonreciprocity value in a fiber ring interferometer varies quasiperiodically in response to the temperature change in an optical fiber with random irregularities.     

Influence of the polarization mode dispersion on the propagation of ultrashort optical pulses in single-mode fiber lightguides with very weak linear birefringence and random inhomogeneities

We consider the influence of the polarization mode dispersion, which is stipulated by the presence of random inhomogeneities in single-mode fiber lightguides, on the propagation of ultrashort optical pulses in the fiber communication lines with very weak linear birefringence. Evolution of the envelope of ultrashort optical pulses and their spectra as functions of the length of a single-mode fiber lightguide with very weak linear birefringence and random inhomogeneities are obtained by the method of mathematical simulation. An increase in the pulse duration is shown to be proportional to the square root of the length of a single-mode fiber lightguide. The numerical-simulation results are compared with the results of experimental measurements of the polarization mode dispersion.     

Linear Transformation of Polarization Modes in Coiled Optical Spun Fibers. III. Approximate Analytic Presentation

Optics and Spectroscopy - We have obtained approximate analytical dependences of the integrated values of effective elliptic birefringence of eigenpolarization modes on the length of coiled spun...     

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.     

Nonholonomic relation between the electromagnetic field state and the torsion angle in a single-mode lightguide with linear birefringence

The relation between the electromagnetic field state and the torsion angle in a twisted single-mode fiber lightguide (SFL) with linear birefringence is considered for the case where the lightguide is stretched into a straight line. It is shown that this relation is nonholonomic, because of the noncommutativity of two infinitesimal but different changes in the length and torsion of the lightguide. This indicates that the relation between the radiation polarization and the torsion angle in a twisted lightguide is also nonholonomic, and so is the relation between the Pancharatnam geometric-optics phase increment due to the evolution of the light polarization state in an anisotropic optical medium and the SFL torsion angle. Institute of Applied Physics of the Russian Academy of Sciences, Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1125–1136, September, 1998.     

Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers

We report for the first time on the polarization analysis of higher-order modes in a few-mode optical fiber using a three-mirror ring resonator. Higher-order fiber modes were generated by carefully squeezing the fiber. The power fraction of the dominating modes was measured, and we determined the polarization state which is different for each mode due to transverse variations of birefringence in the fiber. PACS 42.81.Gs; 42.81.Cn