Mode Delay Research Articles

A new method for extending rate equation based VCSEL model with multimode spectral characteristic

An accurate VCSEL model is important to evaluate the performance of VCSEL-based high speed short range optical interconnect system. Current VCSEL models show no evidence of the multimode spectral characteristic, which leads to an inaccurate performance estimation of VCSEL-based high speed optical interconnect system especially with large chromatic dispersion. To overcome this problem, we propose a new method to introduce multimode spectral characteristic into current VCSEL models, which extends the spatiotemporal multimode rate equations by calculating the wavelength shift of the VCSEL transverse modes. A VCSEL-multimode fiber (MMF) based short range optical interconnect simulation system is then built using our modified VCSEL model by VPItransmissionMaker. The symbol broadening and the BER performance of 15 Gb/s NRZ signal are tested in both left-tilted differential mode delay (DMD) profile MMF (L-MMF) and right-tilted DMD profile MMF (R-MMF). Simulation results validate our proposed method and indicate that the spectral characteristic is a key component for VCSEL models.

Investigation of Intermodal Four-Wave Mixing for Nonlinear Signal Processing in Few-Mode Fibers

We present a theoretical and experimental investigation of inter-modal four-wave mixing (FWM). After analyzing the phase-matching condition as the fundamental condition for efficient FWM, we show the impact of the individual mode’s propagation characteristics, such as differential mode delay and chromatic dispersion on the power of the generated idler. We verify the theoretical analysis with experimental measurements of intermodal FWM. We conclude that efficient broadband intermodal FWM can only be achieved for one specific FWM process and requires very close values of chromatic dispersion in all interacting fiber modes.

Sparse recovery of multiple dispersive guided-wave modes for defect localization using a Bayesian approach

Guided wave (GW) testing has become one of the most important nondestructive tools for evaluation of structural in-service degradation. Although GW testing was widely used to inspect and screen many engineering structures, there are still challenges associated with its applications, which mostly originate from the dispersive and multi-mode nature of GW signals as well as noise contamination. To deal with these challenges, an effective GW signal processing technique is introduced that enables one to accurately recover multiple modes from noisy dispersive GW signals for defect localization. To characterize the dispersion phenomenon, the chirp model is introduced first, which is derived from GW dispersion characteristics. Based on this model, an over-complete dictionary is designed by considering all possible defect locations (by discretization) and the propagation paths of GW modes caused by these defects. Then the prior knowledge that structural defects or damage typically occur in localized areas and correspondingly only a small number of modes are included in the GW signals is exploited by a robust sparse Bayesian learning (SBL) framework to reduce the ill-conditioning in the inverse problem. During the implementation of the robust SBL algorithm, irrelevant basis vectors in the dictionary are pruned out and the posterior probabilities of the small number nonzero basis coefficients corresponding to those “active” GW modes are established. After sparse representation of the GW signal, the information of propagation paths and group delays of GW modes are used to identify each GW mode and then localize defects. Illustrative results from numerical simulations and experiment studies on plate structures are presented to demonstrate the capability of the proposed method.

Transmission of wireless signals using space division multiplexing in few mode fibers

Evolution of next generation wireless networks brings challenges to efficiently transmit a large amount of data from a base station to a remote antenna unit. We investigate a space division multiplexing technique that employs few mode fibers (FMFs) to transmit 3 × 3 MIMO wireless signals, aiming to employ a common digital signal processing (DSP) unit to equalize both the fiber and wireless channel. We optimize system parameters and obtain above 28 dB and 23 dB signal-to-interference and noise ratio (SINR) for 3 meters wireless systems with 500 m and 2 km FMF, which correspond to the transmission capacity of 578 Mb/s and 468 Mb/s using a 20 MHz bandwidth, respectively. Moreover, we analyze that the nonlinear spectrum distortion due to the combined effect of nonlinearity in the directly modulated laser and the differential mode delay in multimode fibers and validate it by simulations.

Contactless Modal Phenomena Based Approach to Detecting, Identifying, and Diagnosing of Electrical Connections

This paper presents a unified description of a new approach for contactless detection, identification, and diagnostics of electrical connections and describes an idea and principles of using modal probing for these tasks. Simulation and experimental results on pulsed signal propagation through flat cables demonstrate the modal decomposition of a pulsed signal, which varies depending on the state of the probed wire. It is shown that the presented tasks can be solved by modal probing. The article also considers the analysis of modal distortions in frequency domain and gives the formula for its practical use. This formula can be useful when the pulse duration time is longer than the minimum of mode delay difference. In conclusion, we present further development ideas of the modal probing.

Multimode and single-mode fiber compatible graded-index multicore fiber for high density optical interconnect application

We designed and fabricated a graded-index (GI) multicore fiber (MCF) compatible with both standard multimode and single-mode fiber for high density optical interconnect application in large-scale data centers. The proposed fiber supports long-distance multimode transmission at 850 nm as well as quasi-single mode transmission at 1310 nm and 1550 nm. The parameters of the GI-MCF have been optimized to obtain both a small differential mode delay at 850 nm and a small mode field diameter mismatch of less than 0.5 μm with single-mode fiber at 1310 nm and 1550 nm with a negligible inter-core crosstalk. In experiment, we successfully realized the multimode operation over 1 km-long GI-MCF at 850 nm and the quasi-single mode operation over 12.4 km-long GI-MCF at 1310 nm and 1550 nm at a data rate of 7×10-Gb/s. The multi-wavelengths multicore transmission was demonstrated for the first time. The experiment results imply that the proposed GI-MCF satisfies various requirements in such as operating wavelength, accessible distance and interconnect density of large-scale data center, and can effectively reduce the fiber numbers and system complexity.

Six-Mode Seven-Core Fiber for Repeated Dense Space-Division Multiplexing Transmission

We propose the optimum design of high spatial density few-mode multicore fiber (MCF) for repeated space-division multiplexed (SDM) transmission. Numerical analyses reveal that a hexagonally arranged six-mode seven-core structure is potentially better than the other possibility, the six-mode multicore structure, in terms of realizing high spatial density and low mode-dependent loss (MDL) characteristics at the splice point; its benefits will enable us to construct long-haul dense SDM transmission links. We fabricate a 171 μ m cladding six-mode seven-core fiber and successfully demonstrate low loss, differential mode delay (DMD), crosstalk, and splice-induced MDL characteristics while maintaining the relative core multiplicity factor of more than 50. Finally, we demonstrate repeated optical 12 × 12 MIMO transmission of more than 100 km using our six-mode MCF and erbium doped fiber amplifier (EDFA).

Advanced MIMO Signal Processing Techniques Enabling Long-Haul Dense SDM Transmissions

Space division multiplexing (SDM) transmission technology is the prime candidate for next technological breakthrough in fiber-optic communication systems, as spatially structured multicore fibers and multimode fibers allow exploitation of the spatial degrees of freedom. Although the use of multi-input multi-output (MIMO) signal processing has significantly contributed to the development of MIMO-SDM transmission, differential mode delay (DMD) and mode dependent loss (MDL) remain as restricting factors of long-haul MIMO-SDM transmission. This paper starts by reviewing the recent progress demonstrated by SDM transmission experiments. Issues with MIMO-SDM transmission including DMD and MDL are then discussed with their methodologies based on optical and digital approaches. Next, brief descriptions of linear and nonlinear MIMO signal processing techniques that enable robust and reliable MIMO-SDM transmission are provided with complexity and performance comparisons, followed by a discussion of their adaptation in coherent MIMO-SDM transmission. We also elucidate the experimental evaluation of frequency selective channels in a multicore few-mode fiber with experimental evaluations, and discuss their impact on MIMO-SDM signal transmission from a signal processing perspective.

Improved results on sampled-data synchronization of Markovian coupled neural networks with mode delays

This paper studies the problem of synchronization for Markovian coupled neural networks (CNNs) with mode delays via sampled-data control. First, a new augmented time-dependent Lyapunov–Krasovskii functional (LKF) is constructed, which can fully capture the information of the sawtooth structure. Second, in order to strengthen the combinations of some resulting vectors, a new zero value equality is founded. Third, based on the augmented time-dependent LKF and zero value equality, synchronization criteria are derived. The desired mode-dependent sampled-data controllers can be obtained by solving a set of linear matrix inequalities (LMIs). In comparison with some existing results, our results are not only less conservative but also with reduced calculation complexity. Finally, two numerical examples are provided to show the effectiveness and advantages of the proposed results.

High-resolution measurement of differential mode delay of few-mode fiber using phase reference technique for swept-frequency interferometry

Abstract A method is described for the high-resolution measurement of the differential mode delay (DMD) of few-mode fiber based on the frequency-modulated continuous wave (FMCW) technique. With the conventional approach, a wider optical bandwidth is required for higher resolution, however, the effect of chromatic dispersion becomes critical and limits the actual resolution. This paper proposes and demonstrates a phase reference technique for FMCW signals that achieves high-resolution measurements without increasing the optical bandwidth. We can also further improve the resolution of our proposed method by reducing the phase fluctuation with signal averaging. The feasibility of the proposed method is confirmed experimentally with several kinds of FMFs including an offset-spliced fiber where mode couplings occur.

Transmission Over SSMF at 850 nm: Bimodal Propagation and Equalization

The combination of 850 nm vertical-cavity surface-emitting laser (VCSEL) with standard single-mode fiber (SSMF) presents an effective and low-cost interface to increase the reach provided by multi-mode fiber links. At 850 nm, SSMF propagates two modes, and in this study, it has been experimentally shown that the different commercially available SSMF's present dissimilar values of differential mode delay. To cope with this unequal behavior of modal dispersion, we propose a scheme based on bidirectional decision feedback equalization (BiDFE) to overcome limited performance of other solutions as mode filtering or classical equalizers. A single span SSMF cabling model, including a measurement-derived statistical characterization of optical connectors, is simulated to evaluate the reach provided by the equalizer attending to both the conditions of the fiber excitation and the characteristics of the VCSEL. A minimum 1.45 km link length at 10 Gb/s is achieved if a linear combining BiDFE (LC-BiDFE) equalizer is included in the receiver, whatever laser launching condition and employing a single-transverse mode VCSEL. If a multi-transverse mode VCSEL is used, the reach provided by LC-BiDFE is slightly reduced but assuring a minimum coverage of 1.15 km.

Trenched raised cosine FMF for differential mode delay management in next generation optical networks

Dispersion management in few mode fiber (FMF) technology is crucial to support the upcoming standard that reaches 400 Gbps and Terabit/s per wavelength. Recently in Chebaane et al. (2016), we defined two potential differential mode delay (DMD) management strategies, namely sawtooth and triangular. Moreover we proposed a novel parametric refractive index profile for FMF, referred as raised cosine (RC) profile. In this article, we improve and optimize the RC profile design by including additional shaping parameters, in order to obtain much more attractive dispersion characteristics. Our improved design enabled to obtain a zero DMD (z-DMD), strong positive DMD (p-DMD) and near-zero DMD (nz-DMD) for six-mode fiber, all appropriate for dispersion management in FMF system. In addition, we propose a positive DMD (p-DMD) fiber designs for both, four-mode fiber (4-FMF) and six-mode fiber (6-FMF), respectively, having particularly attractive dispersion characteristics.

Impulse Response Measurement of Few-Mode Fiber Systems by Coherence-Recovered Linear Optical Sampling

This paper presents impulse response measurements of few-mode optical fibers and transmission lines that were obtained by using coherence-recovered linear optical sampling or a two-comb interferometer. When performing a measurement, the probe pulse source and the sampling pulse source may be far from each other, particularly when the fibers are installed in the field, and the fiber length may exceed several tens kilometers. In this paper, by modifying a previously proposed referencing technique, the coherence between two pulse lasers is equivalently maintained by canceling out the phase noise caused both by the light sources and perturbations in the fiber. Hence, the amplitude averaging is used to enhance the signal-to-noise ratio. As a result, we can measure the impulse responses of multimode fibers with a dynamic range of 80 dB and a time resolution of a few picoseconds, over tens nanoseconds of differential mode delay.

Semi-Analytical Modelling of Linear Mode Coupling in Few-Mode Fibers

This paper reviews and extends a method for the semi-analytical solution of the coupled linear differential equations that describe the linear mode coupling arising in few-mode fibers due to waveguide imperfections. The semi-analytical solutions obtained proved to be accurate when compared to numerical solution methods. These solutions were integrated into a multisection model with split-steps for mode dispersion and mode coupling. Simulations using this model matched the analytical predictions for the statistics of group-delays in few-mode fiber links, considering different coupling regimes with and without mode delay management.

Complex imaging via coherent detection.

Complex imaging via coherent detection is proposed for acquiring two-dimensional (2-D) nearfield optical image that recovers amplitude and phase simultaneously. Based on the proposed complex imaging, we experimentally demonstrate the technique by detecting few-mode-fiber (FMF) modes with high extinction-ratio, and perform mode decomposition and differential mode delay (DMD) measurement.

Theoretical analysis of hollow ring-core optical fibre for transmitting orbital angular momentum modes

Ring-core optical fibre has been successfully demonstrated to have good performance for lifting mode degeneracy, and maintaining orbital angular momentum (OAM) modes in the first radial order, making it promising for applications of OAM mode multiplexing and generation of cylindrical vector beams. The degeneracy lift can be intensified using a hollow ring-core fibre, i.e. when the innermost layer of waveguide is air. The cut-off ring thickness for supporting the lowest OAM modes in radial order are obtained under various refractive index differences between the transport layer and the cladding. To optimize the design, our analysis addresses the dependence of modal properties on the fibre structure parameters, such as the effective area (Aeff) of respective OAM mode, and the differential mode delay.

Dual-Quality 4:2 Compressors for Utilizing in Dynamic Accuracy Configurable Multipliers

In this paper, we propose four 4:2 compressors, which have the flexibility of switching between the exact and approximate operating modes. In the approximate mode, these dual-quality compressors provide higher speeds and lower power consumptions at the cost of lower accuracy. Each of these compressors has its own level of accuracy in the approximate mode as well as different delays and power dissipations in the approximate and exact modes. Using these compressors in the structures of parallel multipliers provides configurable multipliers whose accuracies (as well as their powers and speeds) may change dynamically during the runtime. The efficiencies of these compressors in a 32-bit Dadda multiplier are evaluated in a 45-nm standard CMOS technology by comparing their parameters with those of the state-of-the-art approximate multipliers. The results of comparison indicate, on average, 46% and 68% lower delay and power consumption in the approximate mode. Also, the effectiveness of these compressors is assessed in some image processing applications.

Heterogeneous 12-Core 4-LP-Mode Fiber Based on Trench-Assisted Graded-Index Profile

We design a heterogeneous 12-core 4-LP-mode fiber having two different types of cores and trench-assisted graded-index profiles. For the optimum design of the index profiles of these two heterogeneous cores, we first investigate the impacts of various geometric parameters on the effective refractive index of each LP mode, maximum differential modal delay (DMD), and bending losses of the guiding and higher order modes. We then design a heterogeneous 12-core 4-LP mode fiber having a cladding diameter of 242 $\mu {\rm m}$ . The numerical analyses based on the coupled-mode equation show that the inter-core crosstalk levels of the proposed fiber are lower than $-$ 55 dB/km, regardless of modes, as long as the fiber is not bent tightly with a bending radius of $\times$ 10 $-$ 3 $\mu {\rm m}$ $-$ 2 and 42.2, respectively.

Evaluating Transit Priority Signal Phasing at Most Multimodal Intersection in Portland, Oregon

This research documents the operational benefits of additional phases, barrier bars, and a call-based transit priority signal-phasing strategy over a more traditional eight-phase, two-barrier preemption-based transit signal–phasing strategy. The call-based timing strategy, with a more flexible ring-and-barrier structure, takes advantage of additional phases to run less-impactful transit prioritization for light-rail trains. These two strategies have been field implemented in Portland, Oregon, at the signalized intersection of Southwest Porter Street and Southwest Moody Avenue, an intersection that has distinct signalized movements for the private-automobile, streetcar, light-rail train, bus, pedestrian, and bicycle modes. The operations of the two-intersection signal-phasing strategies were evaluated and tested by using hardware and software-in-the-loop microsimulation (in Vissim) to isolate the expected change in operational efficiency in modal delay. The two-barrier preemption-based transit signal-phasing strategy showed high variability in delay for certain movements, in particular, pedestrians. The call-based phasing strategy with flexible ring-and-barrier structure reduced total and average intersection delay. This research shows that the call-based phasing strategy with flexible ring-and-barrier structure can provide a less disruptive transit prioritization. Agencies should consider the call-phased transit priority strategy over the more traditional preemption-based strategy at a signalized intersection when ( a) delaying potential preemptive movements mode will not have large safety effects, ( b) pedestrian demand is high, ( c) preemption service will be frequent, or ( d) the intersection is operating at or over capacity.

Design of silica optical fibers with enlarged core diameter for a few-mode fiber optic links of onboard and industrial multi-Gigabit networks

This work presents alternative fast and simple method for design refractive index profile of silica multimode optical fibers (MMFs) providing effective mode bandwidth improvement under laser-based multi-Gigabit data transmission and few-mode regime operation in comparison with commercially available MMFs. Optimized profile equalizes delays of selected particular order guided modes being the main mode components of multi-Gigabit network transceiver laser excited optical signal transferred over proposed MMF in a few-mode regime. We present some results of refractive index profiles synthesis for MMFs with core diameters 50 and 100 μm under various combinations of the reference mode delay and the first iteration profile grade parameter as well as corresponding to these samples curves of differential mode delay spectral characteristics computed over “O”-band