Birefringent Optical Fiber Research Articles

Theory of polarization attraction in parametric amplifiers based on telecommunication fibers

We develop from first principles the coupled wave equations that describe polarization-sensitive parametric amplification based on four-wave mixing in standard (randomly birefringent) optical fibers. We show that in the small-signal case these equations can be solved analytically, and permit us to predict the gain experienced by the signal beam as well as its state of polarization (SOP) at the fiber output. We find that, independently of its initial value, the output SOP of a signal within the parametric gain bandwidth is solely determined by the pump SOP. We call this effect of pulling the polarization of the signal towards a reference SOP as polarization attraction, and such parametric amplifier as the FWM-polarizer. Our theory is valid beyond the zero polarization mode dispersion (PMD) limit, and it takes into account moderate deviations of the PMD from zero. In particular, our theory is capable of analytically predicting the rate of degradation of the efficiency of the parametric amplifier which is caused by the detrimental PMD effect.

Parametric gain control of a pulse in birefringent photonic crystal fibers

Propagation of a modulationally amplified Gaussian pulse is considered inside a birefringent optical fiber. We show analytically that, in addition to a reduction in the parametric gain and a change in the pulse's group velocity, the third-order dispersion allows the generation of a temporal Airy-shaped pulse. Furthermore, pulse spreading in the temporal domain and chirping in the spectral domain both can be controlled through an interplay between third-order dispersion and modulational instability.

Temperature-independent torsion sensor based on “figure-of-eight” fiber loop mirror

An interrogation sensor system combining the “figure-of-eight” fiber loop mirror using a single directional 3×3 fiber optic coupler was proposed. One fiber loop mirror was formed by inserting a length of high birefringent optical fiber at the input ports of the 3×3 coupler. Splicing the output ports of the 3×3 coupler between them created the other fiber loop mirror. The introduction of this second loop gave rise to two polarization states of light with the same frequency but different optical phase. The mechanical torsion sensing head was located at the second loop and was exhibited an average modulus torsion sensitivity of 7.9×10−4 degree/dB. The performance of the sensor was not affected by environmental temperature variations.

Modulation instabilities in birefringent two-core optical fibres

Previous studies of the modulation instability (MI) of continuous waves (CWs) in a two-core fibre (TCF) did not consider effects caused by co-propagation of the two polarized modes in a TCF that possesses birefringence, such as cross-phase modulation (XPM), polarization-mode dispersion (PMD) and polarization-dependent coupling (PDC) between the cores. This paper reports an analysis of these effects on the MI by considering a linear-birefringence TCF and a circular-birefringence TCF, which feature different XPM coefficients. The analysis focuses on the MI of the asymmetric CW states in the TCFs, which have no counterparts in single-core fibres. We find that the asymmetric CW state exists when its total power exceeds a threshold (minimum) value, which is sensitive to the value of the XPM coefficient. We consider, in particular, a class of asymmetric CW states that admit analytical solutions. In the anomalous dispersion regime, without taking the PMD and PDC into account, the MI gain spectra of the birefringent TCF, if scaled by the threshold power, are almost identical to those of the zero-birefringence TCF. However, in the normal dispersion regime, the power-scaled MI gain spectra of the birefringent TCFs are distinctly different from their zero-birefringence counterparts, and the difference is particularly significant for the circular-birefringence TCF, which takes a larger XPM coefficient. On the other hand, the PMD and PDC only exert weak effects on the MI gain spectra. We also simulate the nonlinear evolution of the MI of the CW inputs in the TCFs and obtain good agreement with the analytical solutions.

Polarization-resolved imaging of an ensemble of waveguide modes

We demonstrate polarization-sensitive measurement of the modal content of waveguides by generalizing the classic rotating wave-plate-based polarimeter to wide-field optical low-coherence interferometry. The spatial phases of the modes are retrieved with principal component analysis. By applying this polarization-sensitive cross-correlation (C2) imaging technique to the characterization of a few-mode fiber, we reveal that different modes experience distinct bend-induced birefringence in optical fibers. This polarization-resolved C2 imaging is well suited for analyzing the impact of polarization on wave propagation in high-power fiber lasers as well as in mode-division-multiplexed communications systems.

Vector–soliton bound states for the coupled mixed derivative nonlinear Schrödinger equations in optical fibers

In this paper, the vector–soliton bound states (VSBSs) are investigated for the coupled mixed derivative nonlinear Schrödinger equations, which can describe the pulse propagation in the femtosecond regime of birefringent optical fibers. Symmetric and asymmetric VSBSs with the periodic collisions are obtained and analyzed. The intensity profile and collision period of the bound state are related to the ratio of the real parts of two wavenumbers. The separation factors are introduced in the solutions to linearly adjust the soliton separations. Amplitude-changing collisions between the VSBS and vector bright solitons are also obtained. Via the split-step Fourier method, stability analysis shows that the VSBSs can resist the finite initial perturbations. In addition, the derivative cubic nonlinearity and cubic nonlinearity terms are found to both have no influence on the types of VSBSs, but leads to one-sided compression, center shifts and amplitude decrease of the VSBSs. Energy-exchanging phenomena during the amplitude-changing collisions are not affected, either.

Recording Bragg gratings in a birefringent optical fiber with a single 20-ns pulse of an excimer laser

This paper presents the results of recording Bragg gratings in a birefringent optical fiber having increased photosensitivity with a single 20-ns pulse from a KrF excimer laser. A description is given of a stand for recording fiber Bragg gratings by the phase-mask method and of experimentally produced Bragg gratings in a birefringent optical fiber with elliptical stress cladding, having an efficiency greater than 2% and a reflection spectrum about 0.1 nm wide at half-height.

Superstructured fiber-optic contact force sensor with minimal cosensitivity to temperature and axial strain

In this work a new superstructured, in-fiber Bragg grating (FBG)-based, contact force sensor is presented that is based on birefringent D-shape optical fiber. The sensor superstructure comprises a polyimide sheath, a stress-concentrating feature, and an alignment feature that repeatably orients the sensor with respect to contact forces. A combination of plane elasticity and strain-optic models is used to predict sensor performance in terms of sensitivity to contact force and axial strain. Model predictions are validated through experimental calibration and indicate contact force, axial strain, and temperature sensitivities of 169.6 pm/(N/mm), 0.01 pm/με, and -1.12 pm/°C in terms of spectral separation. The sensor addresses challenges associated with contact force sensors that are based on FBGs in birefringent fiber, FBGs in conventional optical fiber, and tilted FBGs. Relative to other birefringent fiber sensors, the sensor has contact force sensitivity comparable to the highest sensitivity of commercially available birefringent fibers and, unlike other birefringent fiber sensors, is self-aligning with respect to contact forces. Unlike sensors based on Bragg gratings in conventional fiber and tilted Bragg gratings, the sensor has minimal cosensitivity to both axial strain and changes in temperature.

Tunable photonic delay lines in optical fibers

AbstractA comprehensive overview is presented about optical fiber‐based tunable photonic delay lines, which have been steadily developed over the last decade for the realization of all‐optically controlled timing functions. The most widely used techniques, such as those based on slow & fast light and wavelength conversion associated to dispersion, are described and their physical limitations are discussed in terms of the maximal achievable delay, the associated signal distortion and signal bandwidth. Besides, an entirely different approach for all‐optical signal delaying is introduced. This technique is based on movable grating reflectors dynamically generated in highly birefringent optical fibers. This type of delay line has experimentally demonstrated large tunable delaying with a moderate signal distortion for high capacity optical data streams and even for wideband analog signals.

Artificially disordered birefringent optical fibers

We develop and experimentally verify a theory of evolution of polarization in artificially-disordered multi-mode optical fibers. Starting with a microscopic model of photo-induced index change, we obtain the first and second order statistics of the dielectric tensor in a Ge-doped fiber, where a volume disorder is intentionally inscribed via UV radiation transmitted through a diffuser. A hybrid coupled-power & coupled-mode theory is developed to describe the transient process of de-polarization of light launched into such a fiber. After certain characteristic distance, the power is predicted to be equally distributed over all co-propagating modes of the fiber regardless of their polarization. Polarization-resolved experiments, confirm the predicted evolution of the state of polarization. Complete mode mixing in a segment of fiber as short as ∼ 10cm after 3.6dB insertion loss is experimentally observed. Equal excitation of all modes in such a multi-mode fiber creates the conditions to maximize the information capacity of the system under e.g. multiple-input-multiple-output (MIMO) transmission setup.

Effect of High Pressure Carbon Dioxide Fluids on the Birefringence of Polymer Optical Fiber

In this paper we report a method for reduce the birefingence of polymer optical fiber by using high pressure carbon dioxide fluids. Polymer optical fiber, in the manufacturing and forming process, it is effected by the external drawing and cooling so that the optical fiber presents exhibit birefringence. The experimental result shows that after the treatments of carbon dioxide fluids, the birefringence of optical fiber drop from 2-2.1×10- 4to 4.1-4.6×10- 5.

Triple Wronskian solutions of the coupled derivative nonlinear Schrödinger equations in optical fibers

A type of the coupled derivative nonlinear Schrödinger (CDNLS) equations are studied by means of symbolic computation, which can describe the wave propagation in birefringent optical fibers. Soliton solutions in the triple Wronskian form of the CDNLS equations are obtained. Elastic and inelastic collisions are both presented under some parametric conditions. In addition, generalized triple Wronskian solutions of a set of the coupled general derivative nonlinear Schrödinger (CGDNLS) equations are derived. Triple Wronskian identities are given to prove such solutions, which may also be used for other coupled nonlinear equations. Rational solutions of the CGDNLS equations are also obtained.

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.

Influence of Angular Orientation of the Embedded Highly Birefringent Fiber on PMD Changes under Axial Stress

In the paper we present results of the research on polarization mode dispersion changes inside the polarimetric optical fiber sensors based on highly birefringent optical fibers embedded into composite materials with different angular orientations of the optical axes. Based on measurements made for different types of highly birefringent optical fiber sensors we have shown that strain sensitivities after lamination process are different in comparison to the data obtained before lamination. Our results indicate that polarization mode dispersion in side-hole highly birefringent fibers under axial stress strongly depends on fiber orientation in the composite material suggesting that orientation of the polarization axes of the highly birefringent fiber can be responsible for behavior of the fiber inside the composite material.

Tunable optical delay using parametric amplification in highly birefringent optical fibers

We theoretically study parametric amplification in highly birefringent optical fibers and show that large tunable optical delay or advancement can be achieved via slow and fast light propagation. We provide a clear derivation of the formula for the optical delay that originates from the imaginary part of the parametric gain. We also perform numerical simulations in both normal and anomalous dispersion regimes. In the latter case, results show that large nanosecond optical delay could, in principle, be obtained at 1550 nm in a 1-km-long polarization-maintaining fiber. We further demonstrate that the optical delay and advancement rely on a group-velocity locking between the two cross-polarized signal and idler pulses.

Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics

Abstract Under investigation in this paper are the coupled nonlinear Schrödinger equations (CNLSEs) and coupled Burgers-type equations (CBEs), which are, respectively, a model for certain birefringent optical fibers Raman-scattering, Kerr and gain/loss effects, and a generalized model in fluid dynamics. Special attention should be paid to the existing claim that the solitons for the CNLSEs do not exist. Through certain dependent-variable transformations, the CNLSEs are reduced to a Manakov system and the CBEs are linearized. In that way, some new solutions of the CNLSEs and CBEs are obtained via symbolic computation. Especially the one-dark-soliton-like solutions for the CNLSEs have been found, against the existing claim.

Loss effects in the spectra of polarization modulational instability in weakly birefringentoptical fibers

We analyze the effects induced by material absorption in the spectra of polarizationmodulational instability in weakly birefringent optical fibers. We show that a largeabsorption of the pump wave may cause significant decreases of the growth of sidebands inthe modulational instability process. This drop of gain is accompanied by a driftof the sideband frequencies. We demonstrate a technique for suppressing thesefrequency drifts, which is based on the use of fiber systems having a dispersion and abirefringence that decrease simultaneously and exponentially along the system.

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.

Soliton interaction in birefringent optical fibers: Effects of nonlinear gain devices

This paper presents the influences of polarization mode dispersion (PMD) on the performance of soliton transmission system in birefringent fibers. Dispersive waves generated in single mode fibers due to PMD degrade the soliton transmission system in two aspects. First, solitons continuously lose their energy, thus cause enhancement in pulse width. Second, the dispersive waves interact with neighboring pulses and cause distortion in a sequence of pulses. Both these effects reduce the effective bit-rate and degrade the performance of high-speed optical transmission systems. Optical fibers with large group velocity dispersion (GVD) have less dispersive waves and are relatively robust to pulse broadening, but it enhances the interaction between the adjacent pulses. In this paper, we analyzed these effects of PMD on soliton propagation in birefringent fibers and introduced nonlinear gain devices with perturbation terms proportional to second and fourth power of amplitudes to reduce these effects. We proposed Symmetric Split-Step Fourier Method to solve the coupled nonlinear Schrödinger equations (CNLSE); which yields better results over the existing Split-Step Fourier Method.

A diffusion approximation theorem for a nonlinear PDE with application to random birefringent optical fibers

In this article we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schr\"{o}dinger equations. This system arises in the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier and Marty [Wave Motion 43 (2006) 544-560], Marty [Probl\`{e}mes d'\'{e}volution en milieux al\'{e}atoires: Th\'{e}or\`{e}mes limites, sch\'{e}mas num\'{e}riques et applications en optique (2005) Univ. Paul Sabatier], where a linear electric field is considered, and we get an asymptotic dynamic for the nonlinear electric field.