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.     

Effect of random coupling of orthogonal modes on polarization characteristics of single-mode fiber optical waveguides (SMF) and SMF-based ring interferometers. I. Change in the degree of polarization of nonmonochromatic radiation propagating through a single-mode fiber optical waveguide

We propose a method for calculating the degree of polarization of nonmonochromatic radiation as it propagates through a single-mode fiber optical waveguide (SMF), based on dividing the length of the fiber into segments equal to the depolarization length of the radiation in the SMF. We have obtained the dependences of the degree of polarization of the radiation on the length of the fiber for an SMF with strong and weak anisotropy. In the case of anisotropic SMF's characterized by weak coupling of orthogonal modes, the results match those obtained previously by other calculation methods. The results for weakly anisotropic SMF's characterized by strong coupling of orthogonal modes are obtained here for the first time.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, No. 10, pp. 1311–1320, October, 1994.     

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.     

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.     

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.     

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)     

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.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: VIII. Zero drift in a fiber ring interferometer with a white light source

Different schemes of fiber ring interferometers (FRIs) with a broadband nonmonochromatic radiation source manufactured on the basis of air-silica microstructured single-mode optical fibers (SMOFs) are considered. This source is close in spectral characteristics to a white light source, because the width of its emission spectrum is comparable to the mean wavelength. It is shown that an increase in the width of the spectrum of the radiation source can lead to either a substantial decrease or an increase in the zero drift, depending on the radiation polarization at the FRI entrance. The latter fact has defied explanation within simple phenomenological models of random coupling between polarization modes in SMOFs of an FRI circuit. The observed increase in the zero drift of the FRI can be explained in terms of the dependence of the parameter of polarization conservation (the parameter h) on the light wavelength for highly anisotropic SMOFs. This dependence is weak for nonmonochromatic radiation sources with a relatively small spectral width, for example, superluminescent diodes, which are traditionally used in FRIs. In contrast, for substantially more broadband radiation sources (including air-silica SMOFs), the above dependence is well pronounced and can lead to a number of undesirable effects in FRIs. Different variants of the FRI design are analyzed. It is demonstrated that the zero drift can be noticeably decreased with an increase in the width of the spectrum of the radiation source for an arbitrary radiation polarization at the entrance of an FRI with a depolarizer of nonmonochromatic radiation and a circuit fabricated from a weakly anisotropic SMOF, for which the parameter h does not depend on the light wavelength. The numerical estimates are obtained.     

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.     

Asymptotic Characteristics of the Evolution of Polarization of Nonmonochromatic Radiation in Single-Mode Optical Fibers with Random Twisting of Axes of Linear Birefringence. II. The Asymptotic Behavior of the Degree of Polarization at Large Fiber Lengths

In this paper, we determine the asymptotic behavior for the squared degree of polarization of nonmonochromatic radiation propagating in a large-length fiber with random irregularities. It is found that the average squared degree of polarization tends to zero with the fiber length as the inverse square root of the fiber length.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: Integrated statistical properties of polarization modes of single-mode optical fibers in the presence of random inhomogeneities

Using mathematical modeling, an explicit form is found for the Jones matrix of a segment of a single-mode optical fiber with random inhomogeneities, whose length is considerably greater than the correlation length of random inhomogeneities. It is shown that parameters of this matrix are of a statistical nature. A rational representation of the matrix is proposed. It is shown that, under certain conditions, one of the matrix parameters may be treated as constant, whereas the other parameter is assumed to be continuously distributed on the interval [0, 2π]. As the latter parameter is changed, which corresponds to a change from one random realization of inhomogeneities in a single-mode fiber to another, the ellipticity and the azimuth of the major axis of the polarization ellipse of natural polarization modes of a single-mode fiber simultaneously change.     

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: 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.     

Synchronization of optical polarization conversion and scattering in chiral fibers

We demonstrate that polarization transformation and scattering in adiabatically twisted single-mode birefringent optical fibers is synchronized so that light in one evolving elliptically polarized mode is freely transmitted while orthogonally polarized light is scattered out of the fiber. Thus, linearly polarized radiation initially oriented along the fast axis of the untwisted fiber is transformed to circularly polarized light with the same sense of rotation as the twisted fiber and is scattered out of the fiber. When the fiber twist is first accelerated and then decelerated, the fiber becomes a broadband, low-insertion-loss, linear polarizer.     

Evolution of polarization in an inhomogeneous isotropic medium

The depolarization and rotation of the polarization plane of radiation propagating in a two-dimensional graded-index medium is investigated on the basis of the quantum-mechanical method of coherent states. It is shown that the degree of polarization of both linearly and circularly polarized radiation decreases with increasing distance as a result of interaction between the polarization (spin) and the path (orbital angular momentum) of the beam. The wave nature of the depolarization is emphasized. The depolarization decreases as the radiation wavelength decreases. It is found that the degree of polarization exhibits oscillations of pure diffraction origin during the propagation of light in a single-mode optical fiber. It is shown that the rotation of the polarization plane is nonuniform in character and depends on the offset and the tilt angle of the incident-beam axis relative to the fiber axis. The Berry phase is found to undergo oscillations of a wave nature during the propagation of radiation in an inhomogeneous medium. It is shown that the spread in the angle of rotation of the polarization plane increases with distance and can be determined from measurements of the degree of polarization of the radiation. Zh. éksp. Teor. Fiz. 112, 1985–2000 (December 1997)     

The possibility for a significant decrease in the zero drift of fiber ring interferometers with a circuit formed by a highly anisotropic optical waveguide and a broadband radiation source

It is shown that the zero drift of interference of counterpropagating waves at the output from a fiber ring interferometer can be completely eliminated in the first order of magnitude and significantly decreased in the second order of magnitude if a sufficiently broadband source of nonmonochromatic radiation is used in a fiber ring interferometer with a circuit formed by a highly anisotropic optical waveguide when the depolarization length of nonmonochromatic radiation in a single-mode fiber-optical waveguide becomes significantly shorter than the correlation length of random inhomogeneities. Numerical estimates are made.     

Strong polarization in the optical transmission through elliptical nanohole arrays

Strong polarization dependence is observed in the optical transmission through nanohole arrays in metals. It is shown that the degree of polarization is determined by the ellipticity and orientation of the holes; the polarization axis lies perpendicular to the broad edge of the ellipse. Furthermore, the depolarization ratio shows a squared dependence on the aspect ratio of the holes, which is discussed in terms of coupling into and out of the surface plasmon modes. The observed results will be useful for tailoring the polarization behavior of metallic nanophotonic elements in many applications, including surface plasmon enhanced optical sensing and ultrafast optical switching.     

Linear Transformation of the Polarization Modes in Coiled Optical Spun-Fibers with Strong Unperturbed Linear Birefringence. I. Nonresonant Transformation

A linear transformation of orthogonal polarization modes in coiled optical spun-fibers with strong unperturbed linear birefringence, which causes the emergence of the dependences of the integrated elliptical birefringence and the ellipticity and azimuth of the major axis of the ellipse, as well as the polarization state of radiation (PSR), on the length of optical fiber has been considered. Optical spun-fibers are subjected to a strong mechanical twisting, which is frozen into the structure of the optical fiber upon cooling, in the process of being drawn out from the workpiece. Since the values of the local polarization parameters of coiled spunwaveguides vary according to a rather complex law, the calculations were carried out by numerical modeling of the parameters of the Jones matrices. Since the rotation speed of the axes of the birefringence is constant on a relatively short segment of a coiled optical spun-fiber in the accompanying torsion (helical) coordinate system, the so-called “Ginzburg helical polarization modes” (GHPMs)—two mutually orthogonal ellipses with the opposite directions of traversal, the axis of which rotate relative to the fixed coordinate system uniformly and unidirectionally—are approximately the local normal polarization modes of such optical fiber. It has been shown that, despite the fact that the unperturbed linear birefringence of the spun-fibers significantly exceeds the linear birefringence, which is caused by the winding on a coil, the integral birefringence of an extended segment of such a fiber coincides in order of magnitude with the linear birefringence, which is caused by the winding on the coil, and the integral polarization modes tend asymptotically to circular ones. It has been also shown that the values of the circular birefringence of twisted single-mode fibers, which were calculated in a nonrotating and torsion helical coordinate systems, differ significantly. It has been shown that the polarization phenomena occur in the process of linear transformation of local polarization modes, which lead to small quasi-harmonic oscillations of the birefringence integral parameters of the optical spun-fibers, which depend on their length, and the period of these oscillations is approximately equal to half of the effective period of polarization beating.     

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.     

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

A method is proposed for calculation of the zero drift and Fedding interference signal at the output of a fiber ring interferometer (FRI) based on a single-mode fiber lightguide (SMFL) with a nonmonochromatic radiation source. The fiber length is divided into sections that are equal to the depolarization length in the SMFL. It is shown that when the FRI is made of an anisotropic SMFL with weak orthogonal-mode coupling, the calculation results agree with those obtained earlier by other calculation methods. Results for an FRI made of a weakly anisotropic SMFL with strong orthogonal-mode coupling are obtained for the first time.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 11, pp. 1473–1480, November, 1994.