Techniques and Formulations for Mode Coupling of Multimode Optical Fibers

We investigate the mode propagation and coupling in multimode fibers, based on modeling the wave propagation through the coupled power equation. Using this model, the power evolution of the various propagating modes in fibers can be visualized and the impact of mode-dependent loss and mode coupling can be quantitatively analyzed.

A step index multimode optical fiber with a perturbation on a micrometer scale, inducing a periodic deformation of the fiber section along its propagation axis, is theoretically investigated. The studied microperturbation is mechanically achieved using two microstructured jaws squeezing the straight fiber. As opposed to optical fiber microbend sensors, the optical axis of the proposed transducer is not bended; only the optical fiber section is deformed. Further, the strain applied on the fiber produces a periodical elliptical modification of the core and a modulation of the index of refraction. As a consequence of the micrometer scale perturbation period, the resulting mode coupling occurs directly between guided and radiated modes. To simulate the transmission induced by these kinds of perturbations, simplified models considering only total mode couplings are often used. In order to investigate the range of validity of this approximation, results are compared to the electromagnetic mode couplings rigorously computed for the first time, to our knowledge, with a large multimode fiber (more than 6000 linear polarized modes) using the Marcuse model. In addition, in order to have a more complete modeling of the proposed transducer, the anisotropic elasto-optic effects in the stressed multimode fiber are considered. In this way, the transmission of the microperturbed optical fiber transmission and, therefore, the behavior of the transducer are physically explained and its applications as a future stretching sensor are discussed.

Multimode and multicore optical fibers are pivotal for spatial division multiplexing, a key technology for future high-capacity optical communication systems. A critical transmission characteristic of these fibers is modal dispersion, which is made random by unpredictable perturbations and manufacturing imperfections. While the statistical properties of modal dispersion are well-explored, the underlying local phenomenon of mode coupling—its primary cause—has received comparatively less attention. Accurate modeling of mode coupling is essential for a deeper understanding of both the linear and nonlinear propagation dynamics in these fibers and for advancing their practical implementation. This paper provides a comprehensive review of mode coupling in multimode and multicore fibers, highlighting aspects of general validity and conducting an in-depth analysis of bending and twisting—the two most common perturbations affecting deployed fibers. The results reveal significant similarities between the mode coupling behaviors of multimode and multicore fibers, along with some remarkable differences.

For several decades silica-based optical fibres have been used for telecommunication and sensor purposes. The single-mode fibre is frequently employed in long-distance networks, whereas the multi-mode fibre is the preferred means of signal transport in campus and in-building networks. Because of the huge bandwidth of optical fibres in comparison to its electrical wireless and copper-based counterparts, the demand for optical fibres keeps increasing. In a competitive market, fibre manufacturers aim to produce ever better fibres that are as cheap and easy to employ as possible. As fibre research, development and manufacturing is a mature discipline, improvements in fibre design can only be achieved through the construction of robust, accurate and efficient numerical fibre models for the computation of those quantities that determine the behaviour of the fibre. We have developed a modular software code, based on Maxwell’s equations, to compute these quantities in a vectorial full-wave way for both single-mode and multi-mode optical fibres. Key is the refractive-index profile, or, more specifically, the dopant profile, as it defines the propagation, splicing and bending-loss characteristics of the fibre. For the single-mode fibre, the fibre quantities that we have concentrated on are dispersion, dispersion slope, mode-field diameter, effective area, bending loss, effective and theoretical cut-off wavelength and MAC-value. We highlight one fibre quantity in particular, viz. the computation of the bending loss in a single-mode fibre. Many approximate modelling techniques have been developed to estimate this loss in a fast way. Our numerical scheme, however, is the first rigorous one, as we have performed a vectorial full-wave analysis of the bent optical fibre. In this context, triple integrals involving products of Bessel functions with large, complex order and argument appear. Due to cancellations in the pertaining computation, a high relative accuracy is needed for the computation of each product. As a result, it takes weeks on a contemporary computer to compute the bending loss as a function of the radius of curvature. We have used the vectorial full-wave bending-loss results to determine the most appropriate approximate method. Subsequently, we have extended that approximate method to compute the bending losses of higher-order modes, since the required effective cut-off wavelength depends on the bending loss of the first higher-order mode. The selected approximate method has been used in the ensuing bending-loss calculations. Since the fibre properties are often conflicting, it is a challenging task to adapt the radial dopant profile to meet a set of predefined design goals. A design goal is a combination of desired values for (some of) the aforementioned fibre quantities, and can mathematically be translated into a cost function. The minimisation of this cost function provides us with the optimal dopant profile for that specific set. For the single-mode fibre, we have performed this minimisation for piecewise-linear profiles, by employing various global and gradient-based local optimisation strategies to speed up the design step considerably. Frequently,these optimisation strategies lead to counter-intuitive dopant profile designs that could not have been contrived otherwise. We have selected a deliberate mix of several optimisation routines and have compared their performances. Perhaps the most important conclusion is that there still appears to be room for improvement in the design of the radial dopant profile of commercially available fibres. For the multi-mode fibre, vectorial full-wave optimisation is not feasible yet because of the long computation times for the large number of propagating modes. Still, our numerical scheme allows for a manual fine-tuning of the popular power-law profile to minimise differential mode delay. Further, we have included mode coupling and differential mode attenuation in our model to obtain intensity patterns that match closely with measurements. We have also analysed the influence of profile variations, e.g. on-axis dips and kinks, on the intensity pattern. A selective excitation of different mode groups in a multi-mode fibre, offers the possibility to create several independent transmission channels, and thus a higher information capacity. Recently, the feasibility of this so-called mode group diversity multiplexing technique has been demonstrated. Simulations provide us with a means to better understand its operation and possibly increase its efficiency. The channel separation may be enhanced by employing a lens between the fibre and the detector, which is called mode-selective spatial filtering. Our numerical simulations of a mode group diversity multiplexing link, with and without mode-selective spatial filtering, are in agreement with the measurements. The above discussion makes clear that the developed software code has a wide range of applicability. Moreover, it is built in a modular way and thus extensions, like the inclusion of more fibre quantities or different profile dopants, are straightforward.

A comparison is made between the use of single and multimode optical fibers in a homodyne quasi-elastic light scattering experiment using simple optical hardware. The single-mode fiber is used without a spatial filter and gives a larger signal-to-noise ratio and counting rate than a multimode fiber with a spatial filter.

Influence of intermediate layer on transmission characteristics of W-type optical fibers

Growth dynamics of Bragg gratings in multimode optical fibre

Effect of Polarization Mode Coupling on Extrema Counting Fixed Analyzer PMD Measurement Method

Lateral viscosity variations introduce two problems in the study of glacial induced rotational deformation. One of them is mode coupling. The other arises because centrifugal deformations are dependent on the location of the rotational axis relative to the lateral heterogeneities in the earth. The effects of mode coupling and displacement of the rotational axis on centrifugal induced potential perturbations are studied on a layered earth with lateral viscosity variations inferred from seismic tomography. The modified coupled Laplace-finite-element method is used to calculate the centrifugal deformations. It is found that mode coupling is weak because the lateral viscosity variation in the deep mantle is relatively small. The effect of displacing the rotational axis is to shift the spectral amplitude from degree 2 and order 0 harmonic to other orders within degree 2 as is required for changing the orientation of the applied centrifugal potential, but again the leakage of spectral amplitude to other harmonics are small. This implies that rotational motion in an earth with lateral viscosity variations can be approximated by the calculation of the corresponding laterally homogeneous earth.

The main objectives of this paper is to improve knowledge of multimode fiber transmission over step-index plastic optical fiber SI POF with 1000 μm core. The thick SI POF fibers seem a very attractive alternative in local computer networks for the “classic” (thin) single- and multimode fibers because of their low price and easy installation. In the paper we show measurements of bandwidth and attenuation of various SI POF optical paths. In particular, there was investigated a cascade of passive components (couplers, patchcords) which can be part of transparent (passive) optical networks. Keywords : plastic optical fibre, passive optical network, multimode coupler. 1. INTRODUCTION Recently there has been publish a number of papers concerning optical data transfer over plastic optical fiber [1][2]. Both point-to-point and WDM passive network configurations are considered. The concept of passive network is well known as it comes to the access networks based on single mode fiber. Such networks were proposed in several standards (APON, BPON networks). Commercial solution have been developed and deployed since. We would like to extend benefits of this network type to home networks based on multimode optical fiber. We consider such networks as a viable solution of the optical home network architecture. Along with a multimode optical cable only multimode compatible elements (couples/splitters, connectors, etc.) may be used in the network. Once deployed the upgrade of such a network should be relatively easy. Unlike to the single mode PON where the bandwidth is not an issue, the multimode network maximum operational range is defined by the fiber bandwidth (related to the intermodal dispersion) rather than by the fiber attenuation [3]. The relation among the modal bandwidth of the fiber, the launching condition and mode coupling is fairly well known for silica GI optical fibers (

Chapter 13 - Fibre Channel Standard

Ultrashort pulses emerging from multimode optical fibers are spatiotemporally complex, because inside these fibers the modes have different spatial intensity patterns and experience different propagation velocities and dispersions. To determine the spatiotemporal field from multimode fibers, we applied a technique for the complete measurement of the output pulses called a spatially and temporally resolved intensity and phase evaluation device: full information from a single hologram. It yields the complete electric field over space and time from multiple digital holograms, simultaneously recorded at different frequencies on a single camera frame. Using femtosecond pulses from a Ti:sapphire laser, we measured the first few linearly polarized modes (LP01, LP11, LP02, and LP21) inside several few-mode fibers. We also generate movies displaying the measured spatial, temporal, and spectral field features.

For long haul coherent optical fiber communication systems, it is significant to precisely monitor the quality of transmission links and optical signals. The channel capacity beyond Shannon limit of Single-mode optical fiber (SMOF) is achieved with the help of Multi-mode optical fiber (MMOF), where the signal is multiplexed in different spatial modes. To increase single-mode transmission capacity and to avoid a foreseen “capacity crunch”, researchers have been motivated to employ MMOF as an alternative. Furthermore, different multiplexing techniques could be applied in MMOF to improve the communication system. One of these techniques is the Optical Code Division Multiple Access (Optical-CDMA), which simplifies and decentralizes network controls to improve spectral efficiency and information security increasing flexibility in bandwidth granularity. This technique also allows synchronous and simultaneous transmission medium to be shared by many users. However, during the propagation of the data over the MMOF based on Optical-CDMA, an inevitable encountered issue is pulse dispersion, nonlinearity and MAI due to mode coupling. Moreover, pulse dispersion, nonlinearity and MAI are significant aspects for the evaluation of the performance of high-speed MMOF communication systems based on Optical-CDMA. This work suggests a hybrid algorithm based on nonlinear algorithm (Dynamic evolving neural fuzzy inference (Dy-NFIS)) and linear algorithm (Recursive least squares (RLS)) equalization for ZCC code in Optical-CDMA over MMOF. Root mean squared error (RMSE), mean squared error (MSE) and Structural Similarity index (SSIM) are used to measure performance results.

We introduce a new drift model for slow environmental perturbation affecting modal coupling in optical multi-mode fibers. This model preserves the mode coupling strength asymmetries characteristic to mode pairs of different mode groups while decorrelating the fiber transmission matrix. Existing drift models were derived for the strong coupling regime, in which case the coupling matrix elements are identically distributed, and not suitable for the weak to intermediate coupling regime as shown here. The models' impact on the inherent crosstalk characteristic of a fiber were evaluated for all linear coupling regimes and for fibers with up to 42 spatial and polarization modes. Moreover, transmission performance of 32 GBd 16-QAM (per polarization mode) over the dynamic channel is studied considering singular value decomposition (SVD) pre-coding for the multiple-input multiple-output multi-mode fiber channel. The impact of slow drift on channel equalization performance is evaluated in terms of residual crosstalk. A large discrepancy is observed for fiber channels in the weak and intermediate coupling regimes, while converging in the strong coupling regime. Furthermore, we show that 2 × 1 multiple-input single-output equalizers can be sufficient to compensate for the residual crosstalk in the weak to intermediate linear coupling regime and achieve optimal performance.

In this work we demonstrate 3D imaging using two-photon excitation through a 20 cm long multimode optical fiber (MMF) of 350 µm diameter. The imaging principle is similar to single photon fluorescence through a MMF, except that a focused femtosecond pulse is delivered and scanned over the sample. In our approach, focusing and scanning through the fiber is accomplished by digital phase conjugation using mode selection by time gating with an ultra-fast reference pulse. The excited two-photon emission is collected through the same fiber. We demonstrate depth sectioning by scanning the focused pulse in a 3D volume over a sample consisting of fluorescent beads suspended in a polymer. The achieved resolution is 1 µm laterally and 15 µm axially. Scanning is performed over an 80x80 µm field of view. To our knowledge, this is the first demonstration of high-resolution three-dimensional imaging using two-photon fluorescence through a multimode fiber.