Crosstalk In Multi-core Fibers Research Articles

Unified Analytical Model Based on Lorentzian and Squared Lorentzian Power Spectrum Densities for Evaluating Crosstalk in Multicore Fibers

Unified Analytical Model Based on Lorentzian and Squared Lorentzian Power Spectrum Densities for Evaluating Crosstalk in Multicore Fibers

Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend: comment.

To estimate the intercore crosstalk in uncoupled multicore fibers with cores' propagation constants perturbed by bending, twist, and structure fluctuations, in the paper [Opt. Express21, 5401 (2013)10.1364/OE.21.005401] entitled "Physical interpretation of intercore crosstalk in multicore fiber: effects of macrobend, structure fluctuation, and microbend," Hayashi et al. derived an intuitively interpretable expression of the average power-coupling coefficient as the convolution of the arcsine and Lorentzian distributions, and calculated the derived expression numerically by performing the fast Fourier transform. In the present paper, we derive a closed-form solution of the convolution of the arcsine and Lorentzian distributions, and point out that the closed-form analytical expression derived here is exactly equivalent to the previously reported closed-form expression.

Analysis of Crosstalk in Multicore Fibers: Statistical Distributions and Analytical Expressions

We present a study of multicore fiber (MCF) crosstalk using the coupled mode theory. We derived a general closed-form simulation formula for the crosstalk of MCF under random perturbations, which includes both the average crosstalk and the crosstalk statistical distribution. From this general formula, we further derived simple analytical expressions for the average crosstalk under the assumption of exponential distribution of fiber segment lengths. We show that the analytical expressions approximate very well the results for other distributions, such as Dirac and Gaussian, and thus they can be used as a general analytical approach for estimating the average crosstalk. Results from numerical simulations of average crosstalk are shown to be in full correspondence with analytic results. We also performed numerical simulations of crosstalk statistical distributions generated from our general closed-form simulation formula and find that these agree well with the χ2-distribution function with four degrees of freedom. Finally, we conducted crosstalk measurements under different bending deployment conditions, and the measured crosstalk distributions and average crosstalk are found to be in agreement with the modeling results.

Behavior and measurement method of inter-core crosstalk in multicore fibers with core-dependent loss.

We quantitatively discussed the effect of core-dependent loss (CDL) on the crosstalk (XT) of multicore fibers (MCFs). In practical ranges of XT and CDL, CDL has no significant effect on power coupling coefficients and XT between cores. Therefore, taking into account the CDL-induced signal attenuation difference among cores is sufficient when considering the signal-to-XT ratio in an MCF with CDL. We also analytically investigated the effect of CDL on XT measurements, and found that the effects of the CDLs induced in an MCF as a measurement target and a measurement setup (including input/output devices) can be canceled in the geometric mean of linear values (or the arithmetic mean of decibel values) of the XT by switching the source core and destination core of the XT.

Investigation of crosstalk and BER in multicore fiber optic transmission link for Space Division Multiplexing

The explosive growth of optical communication (i.e., 6G or beyond 5G) will transform the way of communication. Advanced modulation schemes, guided media, high data rate, minimum dispersion, low transmission noise, and signal processing techniques are available to enrich optical networks. The multicore fiber (MCF) will play a significant role in spatial division multiplexing. The major bottleneck of the MCF is the crosstalk in different cores. This article analyzed the crosstalk in multicore fiber (i.e., 2, 3, 4, and five core) as a transmission length function and compared the Q factor, bit error rate, and output power by considering all nonlinearities of the fiber. Maximum BER obtained for 5, 4, 3, and 2 core MCF is 10-14, whereas minimum BER for 5, 4,3, and 2 core MCF are 10–248, 10–248, 10–281, and 10–242, respectively. Maximum crosstalk occurs for 5 core MCF i.e.3166.32 dBm and minimum for 2 core MCF i.e. −44.083dBm. The highest Q factor is obtained at 35.8 for 3 core 10 km, and the minimum Q factor is ∼ 7.351 for 5 core MCF.

Performance Enhancement in Multicore Fiber Using Trench Assisted Technique

Analysis of crosstalk in multi-core fiber is using the trench-assisted technique. To reduce the crosstalk between the cores in the fiber, coupled-mode theory and coupled power theory are adopted for crosstalk estimation and considering different design parameters such as core pitch, bending radius, and wavelength to optimize the crosstalk performance. The homogeneous fiber, which works under single-mode operation, has been considered. The study of performance by varying the trench width is also analyzed. Crosstalk variation in outer cores and center cores of the fiber is studied. The numerical simulation results of crosstalk behavior over bending radius and wavelength are obtained.

Protected Resource Allocation in Space Division Multiplexing-Elastic Optical Networks with Fluctuating Traffic

In this paper, we introduce a Protected Routing, Modulation, Spectrum, and Core Allocation (RMSCA) algorithms with fluctuating traffic in Space Division Multiplexing-Elastic Optical Networks (SDM-EONs). This RMSCA algorithm is called Traffic Awareness Cross-talk Interference Avoidance (TACIA-RMSCA). We investigate the efficiency of efficient allocation of spectrum resources to minimize the impact of crosstalk (XT), and blocking probability. We first assess the impact inter-core crosstalk in Multi-Core Fiber (MCF) with the peak load of the fluctuating traffic. This is usually caused by signal leaks generated by the adjacent cores. It can occur whenever the transmitted optical signals overlap their spectrum segments. We design the Triangular Iterative Core Assignment (TICA) strategy to overcome XT, and to minimize the blocking probability. We evaluate the performance of TACIA-RMSCA with the benchmark algorithm (GAK-RMSCA). Experimental results demonstrate that the proposed algorithm can achieve promising performance with the peak load of the fluctuating traffic.

Semi-analytical approach for calculation of intercore crosstalk in multicore fibers

In this paper, a semi-analytical method to calculate intercore crosstalk (ICXT) in bent and twisted multicore fibers (MCFs) is proposed. The modified refractive index of bent MCF is first computed using geometrically exact beam theory (GEBT) and conformal mapping technique. The computed refractive index profile is used to obtain mode field profiles of bent MCF by solving the wave equation using vectorial finite element method in COMSOL. To take twisting of MCF into account, outer cores of the MCF are approximated to be helically bent around the central core. Using the mode field profiles, mode coupling coefficient between the MCF cores is calculated for different bend radii which is then used to calculate ICXT by using closed form analytical expressions reported in the literature. The ICXT values obtained using our proposed approach are in very good agreement with the experimental values reported in the literature. The effect of change in core pitch and change in relative refractive index contrast of MCF on the mode coupling coefficient between the MCF cores is analysed. The influence of twisting rate of MCF on the ICXT values for different bend radii is studied and it is shown that, ICXT is constant with respect to twisting rate of MCF for bending radii greater than the critical bending radius of the MCF. The proposed approach is also extended to calculate ICXT between different modes of trench assisted few-mode MCF (FM-MCF). The ICXT values obtained for the trench assisted FM-MCF follow the expected trend.

Multicore Fiber Scenarios Supporting Power Over Fiber in Radio Over Fiber Systems

We propose the integration of power over fiber in the next generation 5G radio access network front-haul solutions based on spatial division multiplexing with multicore fibers. The different architectures in both shared- and dedicated- core scenarios for power over fiber delivery and data signals are described. The maximum power to be delivered depending on the efficiencies of the different components is addressed as well as the limits of the delivered energy to avoid fiber fuse and non-linear effects. It is shown how those limits depend on high power laser linewidth, fiber attenuation, link length and fiber core effective area. The impairments related to non-linear effects, multicore fiber crosstalk and temperature are also theoretically analyzed. Experiments show there is no degradation of signal quality for feeding powers of several hundreds of milliwatts for both scenarios in 4-core multicore fibers. This study helps in designing future power by light delivery solutions in Radio over Fiber systems with multicore fibers.

Characterization of the stochastic time evolution of short-term average intercore crosstalk in multicore fibers with multiple interfering cores.

A theoretical model for the stochastic time evolution of the intercore crosstalk (ICXT) in homogeneous weakly-coupled multicore fibers (MCF) with multiple interfering cores is proposed and validated experimentally. The model relies on the introduction of non-stationary time varying random phase shifts at every center point between the phase matching points of the MCF where the difference of the effective refractive indexes of the core of the originating signal and the core suffering from ICXT is zero. Closed form-expressions for the autocovariance of the short-term average ICXT (STAXT) with stationary and non-stationary phase shift models in MCFs with multiple excited cores are derived and validated by comparison with experimental results. These expressions enable estimating the decorrelation time of the STAXT generated by multiple interfering cores from the decorrelation times of the STAXT generated by each pair of cores. The proposed model and the ICXT measurements taken continuously over more than 150 hours show that the decorrelation time of the STAXT generated by multiple interfering cores exceeds the one obtained for the pair of cores with shorter decorrelation time. The proposed model is increasingly important to simulate and design MCF-based systems where the ICXT dynamics must be properly accounted for to develop efficient ICXT-tolerant techniques.

Stimulated Raman Scattering and Four-Wave Mixing Effects on Crosstalk of Multicore Fibers

The numerical analysis of inter-core crosstalk in multicore fibers (MCFs) based on a novel theoretical approach that includes stimulated Raman scattering (SRS) and four-wave mixing (FWM) nonlinearities in the presence of random perturbations is presented. The coupled propagation equations can be employed to numerically analyze wavelength-division multiplexed systems with homogenous and heterogeneous cores. Propagation of ten optical channels, 200-GHz spaced, along 10 km of a homogeneous two-core fiber shows that the wavelength dependence of the relative average inter-core crosstalk induced by SRS and FWM is comparable with the one produced by only considering the wavelength dependence of the linear coupling coefficient, thus allowing tuning of the overall effect. Our formalism represents a valuable tool in the design of future multi-channel MCF systems.

Dual Polarization Discrete Changes Model of Inter-Core Crosstalk in Multi-Core Fibers

The discrete changes model (DCM) of inter-core crosstalk (ICXT) in weakly-coupled homogeneous multi-core fibers (MCFs) is generalized to a dual polarization (DP) scheme. This model provides theoretical expressions for the two polarization fields of the ICXT at the MCF output. Therefore, it may be of particular interest in the design of direct-detection MCF systems, where the photodetected ICXT results mainly from the beating between the ICXT field at the MCF output and the carrier of the interfered core. The DP-DCM is validated by comparison of the mean ICXT power and ICXT field amplitude estimates with the ones obtained with a rigorous, yet much more computationally demanding, model based on the coupled local mode theory (CLMT). Good agreement between the mean ICXT power estimates obtained with the DP-DCM and CLMT is observed when the inter-core coupling coefficient variation along the MCF is small. Good agreement is also observed when comparing the probability density functions of the ICXT field amplitude.

Opto-mechanical inter-core cross-talk in multi-core fibers

Optical fibers containing multiple cores are widely regarded as the leading solution to the optical communications capacity crunch. The most prevalent paradigm for the design and employment of multi-core fibers relies on the suppression of direct coupling of optical power among cores. The cores, however, remain mechanically coupled. Inter-core, opto-mechanical cross-talk, among cores that are otherwise optically isolated from one another, is shown in this work for the first time, to the best of our knowledge. Light in one core stimulates guided acoustic modes of the entire fiber cladding. These modes, in turn, induce refractive index perturbations that extend across to other cores. Unlike corresponding processes in standard fiber, light waves in off-axis cores stimulate general torsional–radial guided acoustic modes of the cylindrical cross section. Hundreds of such modes give rise to inter-core cross-phase modulation, with broad spectra that are quasi-continuous up to 1 GHz frequency. Inter-core cross-talk in a commercial, seven-core fiber is studied in both analysis and experiment. Opto-mechanical cross-talk is quantified in terms of an equivalent nonlinear coefficient, per acoustic mode or per frequency. The nonlinear coefficient may reach 1.9[W×km]−1, a value that is comparable with that of the intra-core Kerr effect in the same fiber.

Crosstalk in rectangular cross-section heterogeneous multicore fiber

Using neighboring cores with different mode propagation constants (indexes) is a well-known way to reduce crosstalk in multicore fiber (MCF). However, in actual field-deployed fiber, random bends can cause a reduction in the difference between the mode indexes of neighboring cores, which consequently increases crosstalk. The level of crosstalk induced by bending in both rectangular cross-section and circular cross-section heterogeneous MCF with cores arranged in a line was investigated. The experimental results obtained indicate that in contrast to circular cross-section MCF, no bending-induced crosstalk occurs in rectangular cross-section MCF wound on the mandrel without special control of cross-section orientation. Thus, to eliminate undesirable bending-induced crosstalk in heterogeneous MCF a rectangular cross-section should be employed.

Experimental investigation of inter-core crosstalk tolerance of MIMO-OFDM/OQAM radio over multicore fiber system.

In this paper, the feasibility of space division multiplexing for optical wireless fronthaul systems is experimentally demonstrated by implementing high speed MIMO-OFDM/OQAM radio signals over 20km 7-core fiber and 0.4m wireless link. Moreover, the impact of optical inter-core crosstalk in multicore fibers on the proposed MIMO-OFDM/OQAM radio over fiber system is experimentally evaluated in both SISO and MIMO configurations for comparison. The experimental results show that the inter-core crosstalk tolerance of the proposed radio over fiber system can be relaxed to -10 dB by using the proposed MIMO-OFDM/OQAM processing. These results could guide high density multicore fiber design to support a large number of antenna modules and a higher density of radio-access points for potential applications in 5G cellular system.

Next-Generation Optical Fronthaul Systems Using Multicore Fiber Media

This paper proposes and investigates the use of multicore fiber (MCF) media performing space-division multiplexed transmission for next-generation optical fronthaul systems. We report the experimental demonstration of combined radio-over-fiber (RoF) transmission of full-standard LTE-Advanced (LTE-A) and WiMAX signals providing fronthaul connectivity in 150 m of 4-core fiber (4CF), transmitting simultaneously fully independent wireless services. Operating in linear and nonlinear optical power regimes, the experimental evaluation verifies that the error vector magnitude (EVM) is not degraded when intercore and intracore Kerr nonlinearities are excited in MCF with high input power levels. As a result, nonlinear regime is proposed as a key factor to reduce the temporal EVM fluctuation induced by the random nature of the intercore crosstalk in MCF. In addition, MCF fronthaul applied to converged fiber-wireless polarization multiplexed passive optical networks is demonstrated to transmit LTE-A and WiMAX signals over two orthogonal optical polarizations. The polarization-multiplexed signal is transmitted in RoF over 25.2 km of standard single-mode fiber and then demultiplexed and injected in different cores of the 4CF to provide fronthaul connectivity. Finally, the extension of multicore optical fronthaul capacity is proposed using MIMO LTE-A signals. The tolerance of the MIMO LTE-A RoF transmissions to in-band crosstalk is reported and compared to single-input single-output (SISO) configuration. The experimental results indicate that MIMO configuration is more tolerant than SISO to in-band crosstalk considering both internal and external interferences. MIMO and SISO configurations are compared when transmitted in RoF over a 4CF operating in linear and nonlinear regimes and core interleaving nonlinear stimulation is proposed to reduce the temporal and spectral EVM fluctuation when the same wireless standard is propagated in each core.

Unified Model of Linear and Nonlinear Crosstalk in Multi-Core Fiber

In this paper, the theoretical unification of linear and nonlinear inter-core crosstalk (IC-XT) in step-index single-mode multicore fiber (MCF) media is reported and validated experimentally. In order to estimate the IC-XT when operating in linear and nonlinear regimes, the coupled-mode theory (CMT) and the coupled-power theory (CPT) have been unified in both power regimes. The theoretical analysis of the CMT indicates that in coupled MCFs with reduced core-to-core distance (core pitch) the nonlinear self-coupling and cross-coupling effects should be considered when operating with high optical powers. However, considering a core pitch value higher than three times the core radius only the self-coupling effect should be taken into account for estimating the nonlinear IC-XT. Considering these results, the CPT is also extended to nonlinear regime including the dominant nonlinear coupling effect. Using both CMT and CPT, the statistical model of nonlinear IC-XT is completed with the closed-form expressions for estimating the cumulative distribution function, the probability density function and the crosstalk mean and variance as a function of the power level launched into a single-core of the MCF. The crosstalk model presented is additionally extended when multiple cores are simultaneously excited. Finally, the theoretical model is experimentally validated in a homogeneous four-core fiber considering different bending radius configurations.

CapEx advantages of multi-core fiber networks

We investigate capital expenditure (CapEx) advantages of multi-core fiber (MCF) networks by modeling and solving CapEx-minimized planning problem. Integer linear programming model is established, and numerical results are calculated and analyzed. We conduct the solving process under two kinds of traffic patterns of light traffic and heavy traffic. The influences of inter-core crosstalk on MCF and its multi-input multi-output (MIMO)-based crosstalk suppression are also evaluated. Numerical results show that when inter-core crosstalk in MCF is not considered, MCF networks have CapEx advantages under both given traffic patterns by using mixed MCF&SCF deployment strategy, despite the variation in MCF optical amplifier's price whose cost takes the largest share of the total network CapEx. However, when the inter-core crosstalk in MCF is taken into consideration, the costs of networks using MCF go higher than those of single-core fiber (SCF) networks. With the help of MIMO-based inter-core crosstalk suppression, the negative impact of inter-core crosstalk can be mitigated, and MCF can still show its CapEx advantages when the traffic load is heavy.

Experimental evaluation of nonlinear crosstalk in multi-core fiber.

In this paper we evaluate experimentally and model theoretically the nonlinear crosstalk random process in multi-core fiber. The experimental results indicate that mode coupling in multi-core fibers is reduced in presence of fiber Kerr nonlinearities. An analytical study of the inter-core crosstalk probability density function in nonlinear regime is performed, where the theoretical distribution, derived from the nonlinear coupled-mode equation, is experimentally validated in homogeneous four-core fiber. The herein presented analysis includes the evaluation of the inter-core crosstalk probability density function, mean and variance evolution considering the optical power launched into the fiber.

Experimental Investigation of Crosstalk Penalties in Multicore Fiber Transmission Systems

We experimentally study the impact of crosstalk in multicore fibers, using polarization-multiplexed quadrature phase-shift keying signals. Using a 7-core fiber, we perform single-span transmission experiments, where the level of crosstalk to the core under test can be varied. We find the penalty in the required optical signal-to-noise ratio (OSNR), compared to a system with no crosstalk, for different signal-to-crosstalk ratios and at different pre-forward-error-correction target bit-error rates (BERs). We show that, for a 1-dB penalty, a 15.7-dB signal-to-crosstalk ratio can be tolerated at BER = 1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . We also perform recirculating loop experiments with varying amount of crosstalk per span to find the impact on the achievable transmission distance.