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 polarization nonreciprocity in rotating fiber ring interferometers

The effect of polarization nonreciprocity in sensors of angular velocity of rotation—fiber ring interferometers (FRIs)—is considered for arbitrary polarization of eigenmodes of the single-mode optical fiber of an FRI loop and arbitrary polarization state of radiation at the FRI input. A new method for detecting the polarization nonreciprocity in an FRI is proposed. Numerical estimations are made.     

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.     

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.     

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.     

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.     

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.     

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.     

All-fiber optical gyroscopes on orthogonal polarizations

The expressions for the nonreciprocal phase at the output of a fiber ring interferometer (FRI) related to polarization phenomena are obtained in the general form. These expressions are used to analyze two systems of the FRIs on anisotropic elements without polarizer with one and two beam splitters with allowance for their phase anisotropy and losses. We formulate the requirements on the elements of circuits and their adjustment, which lead to minimization of the nonreciprocal polarization phase due to the single-loop realization of two independent orthogonal gyroscopic channels whose signals are added at the output. This allows us to use the above simple circuits for creating moderate-accuracy fiber gyroscopes. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 11, pp. 1448–1460, November, 1998.     

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.     

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.     

Mathematical simulation of random coupling of polarization modes in single-mode optical fibers: IX. Zero drift in a fiber ring interferometer with a loop made of an optical fiber with strong linear birefringence

Numerical simulation of random inhomogeneities in a strongly anisotropic single-mode optical fiber (SMOF) forming a loop in a fiber ring interferometer (FRI) designed according to the minimal scheme is used to obtain the dependences of an interference signal at the FRI output and the zero shift and drift of an interference pattern of counterpropagating waves on the angles of orientation of the axes of linear birefringence in an SMOF at both inputs of the FRI loop. It is shown that the use of a superluminescent diode as a radiation source makes it possible to increase the sensitivity of fiber-optic gyroscopes fabricated on the basis of FRIs by 1–2 orders of magnitude and to obtain the values of real sensitivity required for navigation purposes.     

Influence of anisotropy and losses in beam splitters on the output characteristics of fiber ring interferometers

We consider the influence of phase characteristics of a beam splitter on the output signal of fiber ring interferometer (FRI). The relation between energy losses in the beam splitter and its phase characteristics is established. Allowing for these characteristics, we obtain expressions for the spurious signal at the FRI output, which differ from the known formulas, and consider methods for decreasing its value and drift. Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 6, pp. 780–787, June, 1997.     

Methods for eliminating the influence of nonlinear Kerr effect on the zero drift of fiber ring interferometers

Nonlinear Kerr effect leads to the appearance of a periodic structure in the saturated refractive index of an optical fiber, which corresponds to a standing structure formed by counterpropagating waves in the circuit of a fiber ring interferometer (FRI). If the intensities of counterpropagating waves are slightly different, their reflection from this periodic structure leads to the appearance of a phase shift of interference of counterpropagating waves unrelated to rotation at the FRI output. If a nonmonochromatic radiation source is used in the FRI system, only radiation rereflected from the middle of the circuit makes a contribution to the phase shift. A method for eliminating the influence of the nonlinear Kerr effect on the zero shift of fiber ring interferometers is proposed. This consists in making the middle of the circuit discontinuous. Numerical estimates are made.     

半导体光放大光纤环形激光器的偏振混沌与相干性

研究了基于半导体光放大器(SOA)的光纤环形激光器的偏振混沌光的特性及其相干性。实验采集激光器的输出功率和偏振度,得到了基于半导体光放大器的光纤环形激光器的输出从自发辐射到受激辐射、再到偏振态混沌激光辐射的演化过程。利用马赫-曾德尔(M-Z)干涉仪验证了混沌激光的相干性,并发现混沌干涉只有零级。测量不同光程差时干涉仪的输出功率,计算相应的干涉条纹可见度,进一步算得混沌激光的相干时间约为40 ps。这一结果与根据光谱计算的该混沌激光的相干时间43 ps基本一致。实验还测得该混沌激光的相干性与半导体光放大器的电流无关。并指出了混沌激光相干应用于低相干光源探测领域的灵敏度和分辨力优势。     

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.     

White light interferometry test and analysis of LiNbO3 polarizer

White light interferometer can be used to measure the amplitude extinction ratio (ER) of polarizer and coupling distribution in fiber. A LiNbO₃ polarizer coupled with a polarization maintaining fiber and a silica planar waveguide at the two ends was measured using white light interferometer. According to the principles of optical coherence domain polarimeter (OCDP) technique, the test scheme is analyzed and presented to measure the ER of LiNbO₃ polarizer with its apparatus proposed correspondingly. By analyzing the interference intensity, both the ER of LiNbO₃ polarizer and its coupling crosstalk with optical fiber and waveguide are obtained. The results illustrate that the ER of a 5 mm-long LiNbO₃ polarizer is 71 dB and the crosstalk of the coupling points are around 40 dB. The results have good agreement with analysis.     

Multiwavelength erbium-doped fiber ring laser using a LiNbO<Subscript>3</Subscript> multifunction chip for fiber gyroscope

We present a novel configuration of multiwavelength erbium-doped fiber ring laser (MW-EDFL) using a LiNbO₃ multifunction chip for fiber gyros at room temperature. The polarizer incorporating a piece of high-birefringence fiber in the input port of the Y-type chip forms the Lyot periodic filter at intervals of 0.5 nm wavelength. One of two modulators inserted in the ring cavity has been used as frequency shifter by applying a sawtoothed signal, while the output port of the other is used as the output port of the laser. Simultaneous multiwavelength lasing is experimentally demonstrated by applying a sawtoothed signal with the order of 10 kHz to the phase modulator to prevent single-wavelength oscillation. The MW-EDFL output is linearly polarization light that meets the requirement of external modulation for wavelength-division-multiplexing applications.     

2.1 μm可调谐多波长掺钬光纤激光器

为了实现2.1 μm波段光纤激光器输出多波长激光，设计了一种基于光纤Sagnac干涉仪的可调谐多波长掺钬光纤激光器。采用1.9 μm波段掺铥光纤激光器泵浦一段长3 m的掺钬石英光纤，获得2.1 μm波段的光放大；环形腔中，由保偏光纤和偏振控制器构成的光纤Sagnac干涉仪，实现2.1 μm波段周期滤波，获得了2.1 μm波段多波长激光，输出功率1 mW~15 mW可调谐，最多可观测到6个波长的激光输出。通过调节环形腔内偏振控制器，能够实现2.1 μm波段1~6个波长的调谐。     

On possibility of using the lowest odd harmonics of the phase modulation frequency in the output signal of the fiber-optic ring interferometer for detection of the sagnac effect

The possibility of using the lowest harmonics of the phase modulation frequency in the output signal of the fiber-optic ring interferometer (FRI) for detection of the FRI rotation angular velocity is considered. It is shown that the use of the third harmonic of the phase modulation frequency is optimal, since, in this case, the effect of insignificant admixture of the second harmonic of the phase modulation frequency on the FRI baseline shift can be completely eliminated. When processing the signal using the first or the fifth harmonic of the phase modulation frequency, it is possible to compensate for the FRI baseline shift because of its weak dependence on the phase modulation amplitude. Upon processing of the FRI output signal using higher odd harmonics of the phase modulation frequency, the signal-to-noise ratio noticeably decreases.