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: 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: 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.     

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.     

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 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.     

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.     

Influence of radiation coherence on the effects of polarization nonreciprocity of fiber ring interferometers

In this paper, we consider the effects of polarization nonreciprocity taking into account coherence or partial coherence of radiation at the output of a fiber ring interferometer (FRI) and discuss the possibility of occurrence of additional effects of polarization nonreciprocity at the output of an FRI with a broadband radiation source due to the coherent component of radiation resulting from the coupling of orthogonal modes at the output segments of the fiber. Allowing for the coherence, we estimate the temperature instability of the interferometer signal related to the polarization nonreciprocity. The features of the polarization nonreciprocity effects for a fiber ring interferometer with polarizer or dichroism are considered. It is shown that if the conditions of conventional reciprocity theorem (no rotation) are satisfied for the interferometer, then the polarization nonreciprocity effects become hidden and cannot be detected in the interference signal without a priori information on the character of birefringence and on the orientation of anisotropic elements of the fiber loop of the interferometer and polarizer.     

Effect of higher harmonics of phase-modulation frequency on zero drift in a fiber ring interferometer

We show that the presence of the second harmonic of phase modulation frequency leads to the appearance of spurious modulation of radiation intensity at a fiber-ring interferometer (FRI) output at the first harmonic, which results in FRI zero drift. Numerical estimates are given. Several methods are proposed to eliminate the influence of this spurious effect on FRI zero drift.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 5, pp. 624–630, May, 1996.The author thanks V. N. Listvin for useful remarks.This work was partially supported by the Russian Foundation for Fundamental Research, grant 94-02-03916.     

Ultrahigh-repetition-rate bound-soliton fiber laser

Ultrahigh-repetition-rate (over 100 GHz) bound-soliton pulses were experimentally generated in a fiber laser. Through incorporating a Loyt-type filter made of a piece of high birefringent fiber and an intracavity polarizer in a fiber laser, we found that not only ultrahigh-repetition-rate single-pulse soliton but also bound-soliton trains could be generated. Numerical simulations confirm the experimental observations.     

Effect on zero drift of accuracy of reciprocal tuning of elements of fiber-optic interferometer

The effect of the accuracy of reciprocal tuning of the elements of a fiber-optic interferometer (FOI) — laser, polarizer, and eigenaxes of single-mode-fiber (SMF) birefringence — is examined. It is shown that zero drift in the FOI consists of two parts — a constant part and a temperature-related variable part. Both of these parts are functions of the polarization state of the radiation at the entrance to the polarizer, the extinction coefficient of the polarized, and the orientation of the SMF eigenaxes with respect to the polarizer. The variable part of the zero drift is also a function of the birefringence and h-parameter of the SMF and the width of the radiation-source spectrum. Numerical estimates of FOI zero drift are made.Institute of Applied Physics, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 817–824, July, 1991.     

Design and analysis of a vertical directional coupler between a three-dimensional plasmonic slot waveguide and a silicon waveguide

The design of a vertical directional coupler between a three-dimensional plasmonic slot waveguide and a silicon waveguide is theoretically investigated in detail. It consists of two steps: the design of isolated plasmonic slot waveguide and silicon waveguide and the determination of the gap between the two waveguides and the length of a coupling region. The designed structure transfers 70.8% of the power carried by the silicon waveguide mode to the plasmonic slot waveguide mode when the gap is 150 nm and the coupling length is 2.14 μm. The wavelength dependence of our vertical directional coupler is also studied. The analysis shows that the amount of the transferred power changes slightly over a very wide wavelength range between 1.40 μm and 1.61 μm. Moreover, if we employ the fabrication technology for silicon photonics, it is quite tolerant to the variation of the length of its coupling section. Finally, the vertical directional coupler is considered for a polarizer.     

Vector soliton switching in a fiber nonlinear directional coupler

This paper reports a detailed numerical study of soliton switching in a high as well as low birefringent nonlinear coupler. It is shown that by controlling the polarization angle one can have nearly 100% transmission with excellent switching characteristics. It is shown that soliton remains stable during its propagation inside the coupler. However it is observed that high birefringent coupler exhibits relatively better soliton stability. We show that the coupler could be used as a soliton switch even at an input peak power less than the critical power, the power at which 50-50 power sharing takes place between the two cores, just by a judicious choice of the polarization angle.     

Tunable and switchable all-fiber comb filter using a PBS-based two-stage cascaded Mach-Zehnder interferometer

We propose and demonstrate a novel tunable and switchable all-fiber comb filter by employing a polarization beam splitter (PBS)-based two-stage cascaded Mach-Zehnder (M-Z) interferometer. The proposed comb filter consists of a rotatable polarizer, a fiber PBS, a non-3-dB coupler and a 3-dB coupler. By simply adjusting the polarization state of the input light, the dual-function of channel spacing tunable and wavelength switchable (interleaving) operations can be efficiently obtained. The theoretical analysis is verified by the experimental results. A comb filter with both the channel spacing tunable from 0.18 nm to 0.36 nm and the wavelength switchable functions is experimentally demonstrated.     

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.     

Nonlinear repolarization in optical fibers: polarization attraction with copropagating beams

We propose a type of lossless nonlinear polarizer, novel to our knowledge, a device that transforms any input state of polarization (SOP) of a signal beam into one and the same well-defined SOP toward the output, and perform this without any polarization-dependent losses. At the polarizer output end, the signal SOP appears to be locked to the input pump SOP. The polarizer is based on the nonlinear Kerr interaction of copropagating signal and pump beams in a telecom or randomly birefringent optical fiber.     

Effect of random orthogonal-mode coupling on polarization characteristics of monomode fibers (MF) and MF-based ring interferometers part IV. Zero drift in simplified fiber ring interferometers with nonmonochromaticradiation depolarizers

We considered four fiber-ring-interferometer (FRI) schemes without polarizers made of weakly anisotropic monomode fibers which differ from one another in the location of depolarizer of nonmonochromatic Lyot radiation from a highly anisotropic MF. The results of calculations conducted by numerical simulation with allowance for the h-parameter of the circuit and depolarizer MF show that the FRI zero drift is practically the same for all the four FRI circuits and strongly depends on the accuracy of setting of the angle of mutual orientation of the Lyot depolarizer elements. If the Lyot depolarizer is located at the FRI input (before the first beam splitter or between the first and second beam splitters), the interference signal fadings at the FRI output are practically not eliminated. If, however, the Lyot depolarizer is inside the FRI circuit (at one of its ends or in the middle), the interference signal fadings are, in practice, entirely eliminated, which makes these FRI circuits preferable.Institute of Applied Physics and Institute of Microstructure Physics Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1293–1304, December, 1995.     

电控径向滤波器的横向超分辨与轴向焦移

提出一种光瞳滤波器来同时实现横向超分辨和轴向焦移效应的电控制.该光瞳滤波器由两偏光镜及包含有径向双折射元件的任意偏振态的电控旋光器组成.利用径向双折射元件对光偏振态的空间调制作用,结合旋光器对任意偏振态光的旋光作用,与两个偏光镜结合,实现了空间偏振态的重新分布.利用庞加莱球及琼斯理论进行了分析,结果表明,借助这种电致位相延迟来实现的偏振态调制效应,可同时实现横向超分辨与轴向焦移效应.对能够同时获得横向超分辨与轴向焦移的情况进行了分析,得到了系统各组成参量及电光调制范围.     

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.     

Full-range, complex spatial light modulator for real-time holography

We demonstrate a full-range complex and transmissive spatial light modulator (SLM) for simultaneous and independent amplitude and phase modulation of an input wave field. Arbitrary scalar complex optical fields are generated by stacking a pixelated liquid crystal display operating in phase-only (2π) modulation with passive polarization-sensitive components. The principle is based on optical combining the light fields of two neighboring phase-only modulating pixels, which were made orthogonally polarized by a structured half-wave plate, then passing through a birefringent plate to laterally shift one of the beams collinear to the other, and finally bringing to interference by a linear polarizer. Complex modulation by the proposed SLM is experimentally verified in monochrome green operation.