Propagation In Multimode Fibers Research Articles

Harnessing the power of complex light propagation in multimode fibers for spatially resolved sensing

The propagation of coherent light in multimode optical fibers results in a speckled output that is both complex and sensitive to environmental effects. These properties can be a powerful tool for sensing, as small perturbations lead to significant changes in the output of the fiber. However, the mechanism to encode spatially resolved sensing information into the speckle pattern and the ability to extract this information are thus far unclear. In this paper, we demonstrate that spatially dependent mode coupling is crucial to achieving spatially resolved measurements. We leverage machine learning to quantitatively extract the spatially resolved sensing information from three fiber types with dramatically different characteristics and demonstrate that the fiber with the highest degree of spatially dependent mode coupling provides the greatest accuracy.

Space-time wave packets with reduced divergence and tunable group velocity generated in free space after multi-mode fiber propagation.

Previously, space-time wave packets (STWPs) have been generated in free space with reduced diffraction and a tunable group velocity by combining multiple frequency comb lines each carrying a single Bessel mode with a unique wave number. It might be potentially desirable to propagate the STWP through fiber for reconfigurable positioning. However, fiber mode coupling might degrade the output STWP and distort its propagation characteristics. In this Letter, we experimentally demonstrate STWP generation and propagation over 1-m graded-index multi-mode fiber. Fiber mode coupling is mitigated by pre-distortion according to the inverse matrix of the fiber mode coupling matrix. Measurement of the STWP at the fiber output shows that its group velocity can vary from 1.0042c to 0.9967c by tuning the wave number of the Bessel mode on each frequency. The measured time-averaged intensity profiles show that the beam radius remains similar after 150-mm free-space propagation after exiting the fiber.

Controlling light propagation in multimode fibers for imaging, spectroscopy, and beyond

Light transport in a highly multimode fiber exhibits complex behavior in space, time, frequency, and polarization, especially in the presence of mode coupling. The newly developed techniques of spatial wavefront shaping turn out to be highly suitable to harness such enormous complexity: a spatial light modulator enables precise characterization of field propagation through a multimode fiber, and by adjusting the incident wavefront it can accurately tailor the transmitted spatial pattern, temporal profile, and polarization state. This unprecedented control leads to multimode fiber applications in imaging, endoscopy, optical trapping, and microfabrication. Furthermore, the output speckle pattern from a multimode fiber encodes spatial, temporal, spectral, and polarization properties of the input light, allowing such information to be retrieved from spatial measurements only. This article provides an overview of recent advances and breakthroughs in controlling light propagation in multimode fibers, and discusses newly emerging applications.

Multimode Graded Index Fiber with Random Array of Bragg Gratings and Its Raman Lasing Properties

Light propagation in multimode fibers is known to experience various nonlinear effects, which are being actively studied. One of the interesting effects is the brightness enhancement at the Raman conversion of the multimode beam in graded index (GRIN) fiber due to beam cleanup at Raman amplification and mode selective feedback in the Raman laser cavity based on fiber Bragg gratings (FBGs) with special transverse structure. It is also possible to explore random distributed feedback based on Rayleigh backscattering on natural refractive index fluctuations in GRIN fibers, but it is rather weak, requiring very high power multimode pumping for random lasing. Here, we report on the first realization of femtosecond pulse-inscribed arrays of weak randomly spaced FBGs in GRIN fibers and study Raman lasing at its direct pumping by highly multimode (M2~34) 940-nm laser diodes. The fabricated 1D–3D FBG arrays are used as a complex output mirror, together with the highly reflective input FBG in 1-km fiber. Above threshold pump power (~100 W), random lasing of the Stokes beam at 976 nm is obtained with output power exceeding 28 W at 174 W pumping. The beam quality parameter varies for different arrays, reaching M2~2 at the linewidth narrowing to 0.1–0.2 nm due to the interference effects, with the best characteristics for the 2D array.

Thermalization of light waves in multimode optical fibers: Negative temperatures equilibrium states and the role of disorder - INVITED

Nonlinear random waves exhibit a phenomenon of irreversible thermalization, in analogy with the thermalization of a classical gas system. This irreversible process of thermalization to the Rayleigh-Jeans equilibrium distribution has been recently observed experimentally in multimode optical fibers. Here we discuss a recent progress along two different directions. Firstly, we report the observation of thermalization to negative temperature equilibrium states, in which high-order fiber modes are more populated than low-order modes. Secondly, we analyze the impact of disorder inherent to light propagation in multimode fibers. We identify an unexpected regime in which strong random coupling among non-degenerate modes leads to a nonequilibrium process of Rayleigh-Jeans thermalization.

Holographic Manipulation of Nanostructured Fiber Optics Enables Spatially-Resolved, Reconfigurable Optical Control of Plasmonic Local Field Enhancement and SERS.

Integration of plasmonic structures on step-index optical fibers is attracting interest for both applications and fundamental studies. However, the possibility to dynamically control the coupling between the guided light fields and the plasmonic resonances is hindered by the turbidity of light propagation in multimode fibers (MMFs). This pivotal point strongly limits the range of studies that can benefit from nanostructured fiber optics. Fortunately, harnessing the interaction between plasmonic modes on the fiber tip and the full set of guided modes can bring this technology to a next generation progress. Here, the intrinsic wealth of information of guided modes is exploited to spatiotemporally control the plasmonic resonances of the coupled system. This concept is shown by employing dynamic phase modulation to structure both the response of plasmonic MMFs on the plasmonic facet and their response in the corresponding Fourier plane, achieving spatial selective field enhancement and direct control of the probe's work point in the dispersion diagram. Such a conceptual leap would transform the biomedical applications of holographic endoscopic imaging by integrating new sensing and manipulation capabilities.

Intermodal synchronization effects in multimode fibers with noninstantaneous nonlinearity

The synchronization of spatial modes in the formation of multimode solitons can be considered as the transverse analog of mode locking. In this process, the inherent Kerr nonlinearity in the fiber core binds different spatial fiber modes together. However, compared to their temporal counterparts, the binding mechanism in multimode solitons is rather weak and susceptible to perturbation. In order to mitigate this effect, the propagation in multimode fibers with noninstantaneous Kerr media (NKM) is theoretically investigated. Our study focuses on the dynamics of intermodal energy transfer for the two cases of weak and strong walk-off. Both the moment method and numerical simulations of a multimode expansion of the nonlinear Schr\"odinger equation are employed. Scenarios of pure, hybrid, and varying NKM are investigated. For pure NKM, it is found that for weak walk-off, higher order spatial modes are accelerated in the time domain when their energy is transferred to lower order modes, that is, an effect that has previously been discussed as self-cleaning. In the hybrid case, when an additional instantaneous Kerr effect is present, this results in an enhancement of intermodal nonlinear coupling, leading to prominent oscillating evolutions of the derivatives of energy and pulse center. For varying NKM, the nonlinear refractive index and the proportion of noninstantaneous Kerr nonlinearity may both vary with pulse width. In this case, energy transfer and temporal shift are essentially determined by the magnitude of nonlinear response time of NKM. Significant temporal self-splitting at the trailing edge is observed for the lowest order mode provided only that the response time is large enough and irrespective of strong or weak walk-off.

Deep Learning for Computational Mode Decomposition in Optical Fibers

Multimode fibers are regarded as the key technology for the steady increase in data rates in optical communication. However, light propagation in multimode fibers is complex and can lead to distortions in the transmission of information. Therefore, strategies to control the propagation of light should be developed. These strategies include the measurement of the amplitude and phase of the light field after propagation through the fiber. This is usually done with holographic approaches. In this paper, we discuss the use of a deep neural network to determine the amplitude and phase information from simple intensity-only camera images. A new type of training was developed, which is much more robust and precise than conventional training data designs. We show that the performance of the deep neural network is comparable to digital holography, but requires significantly smaller efforts. The fast characterization of multimode fibers is particularly suitable for high-performance applications like cyberphysical systems in the internet of things.

Simulation of nonlinear signal propagation in multimode fibers on multi-GPU systems

Mode-division multiplexing (MDM) is seen as a possible solution to satisfy the rising capacity demands of optical communication networks. To make MDM a success, fibers supporting the propagation of a huge number of modes, i.e. several tens, are of interest. Many of the system aspects occurring during the propagation can be evaluated by using appropriate models. However, fibers are a nonlinear medium and, therefore, numerical simulations are required. For a large number of modes, the simulation of the nonlinear signal propagation in particular for telecommunication leads to new challenges, for example regarding the required memory, which we address with an implementation incorporating multiple GPU-accelerators. In this paper, we evaluate two different approaches to realize the communication between the GPUs and analyze the performance for simulations involving up to 8 Tesla GPUs. To the best of our knowledge, we are the first who explore a multi-GPU approach to simulate the nonlinear signal propagation in multimode fibers. This allows us to show results for an MDM transmission system utilizing the extremely large number of 120 spatial modes in a fiber with a core diameter of 62.5 µm as an application example and to analyze the impact of the nonlinear effects on the transmitted signals.

Averaged nonlinear equations for multimode fibers valid in all regimes of random linear coupling

Abstract We develop averaged equations to model nonlinear propagation in multimode fibers that are valid in all regimes of random, linear, intermodal coupling. The propagation equations apply to the three existing regimes of linear coupling – the two previously studied all-mode (strong) and mode-group (weak) couplings and the new intermediate coupling regime. The equations are therefore general and can describe nonlinear propagation for all types of intermodal linear coupling that can exist between modes in a fiber supporting multiple spatial modes. Numerical simulations are performed to validate the new averaged propagation equations in the nonlinear regime.

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

Recent progress in wavefront shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibres comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibres and its applications are in their infancy, opening opportunities to take advantage of complex nonlinear modal dynamics. Here, we demonstrate a wavefront shaping approach for controlling nonlinear phenomena in multimode fibres. Using a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization, we control a highly nonlinear multimode stimulated Raman scattering cascade and its interplay with four-wave mixing via a flexible implicit control on the superposition of modes coupled into the fibre. We show versatile spectrum manipulations including shifts, suppression, and enhancement of Stokes and anti-Stokes peaks. These demonstrations illustrate the power of wavefront shaping to control and optimize nonlinear wave propagation. The combination of a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization controls the nonlinear stimulated Raman scattering cascade and its interplay with four-wave mixing in multimode fibres.

A GPU-Accelerated Fourth-Order Runge–Kutta in the Interaction Picture Method for the Simulation of Nonlinear Signal Propagation in Multimode Fibers

The nonlinear signal propagation in fibers can be described by the nonlinear Schrodinger equation and the Manakov equation. Most commonly, split-step Fourier methods (SSFM) are applied to solve these nonlinear equations. The numerical simulation of the nonlinear signal propagation is especially challenging for multimode fibers, particularly if the calculation of very small step sizes or a large number of steps is required. Instead of utilizing SSFM, the fourth-order Runge–Kutta in the Interaction Picture (RK4IP) method can be applied. This method has the potential to reduce the numerical error while simultaneously allowing an increased step size. These advantages come at the price of a higher numerical effort compared to the SSFM method for the same step size. Since the simulation of the signal propagation in multimode fibers is already quite challenging, parallelization becomes an even more interesting option. We demonstrate the adaptation of the RK4IP method to simulate the nonlinear signal propagation in multimode fibers, including its parallelization. Besides comparing the performance of a parallelized implementation for multicore CPUs and a GPU-accelerated version, we discuss efficient strategies to implement the RK4IP method on a GPU accelerator with CUDA. In addition, the RK4IP implementation is numerically compared with a conventional SSFM implementation.

Bend translation in multimode fiber imaging.

Light propagation in multimode fibers is typically assumed to be extremely sensitive to changes in geometry. We study here a particular configuration where an S-shaped bend is translated between two sections of fiber. In this sliding bend configuration, we show that nearly constant propagation characteristics can be obtained in certain fibers. Several fibers were tested using a bend with a peak radius of curvature of 25 mm. We found large differences in bending behavior between fibers of varying core diameters and numerical apertures. Fibers with a large numerical aperture are found to be more stable. In several fibers, the bend can be translated over a distance of 25 mm with a limited impact on imaging performance. The experimental results are confirmed using simulations. Our findings shed a new light on bending sensitivity in multimode fibers, and open up more possibilities for their use as imaging devices.

Group Delay Management and Multiinput Multioutput Signal Processing in Mode-Division Multiplexing Systems

Multi-input multi-output (MIMO) digital signal processing (DSP) for mode-division multiplexing (MDM) may have high complexity, owing to a plurality of modes and a potentially long group delay (GD) spread in multimode fiber (MMF). This paper addresses the management of GD in MMF and its implications for the complexity and performance of MIMO DSP. First, we review the generalized Jones and Stokes representations for modeling propagation in MMF, and describe key GD properties derived using the two representations. Then, we describe three approaches for GD management: 1) optimized fiber design, 2) mode coupling, and 3) GD compensation. For approach 1), we explain design principles for minimizing the GD spread. We review experimental results to date, showing that fabrication nonidealities significantly increase the GD spread, and this approach alone may not achieve sufficiently low GD spread. For approach 2), we describe mechanisms for inducing intragroup and intergroup coupling. We describe mode scrambler designs based on photonic lanterns or long-period fiber gratings, both of which can ensure strong intergroup coupling. For approach 3), we review GD-compensated system design principles and show that GD compensation is only partially effective in the presence of random intragroup or intergroup coupling. Finally, we provide an overview of adaptive MIMO frequency-domain equalization algorithms. Considering tradeoffs between complexity, performance, and adaptation time, we show that the GD spread is a key factor determining the feasibility of MIMO DSP, and its feasibility requires judicious GD management.

Controllable spatiotemporal nonlinear effects in multimode fibres

Highly nonlinear effects are observed in graded-index multimode optical fibres. Multimode fibres are of interest for next-generation telecommunications systems and the construction of high-energy fibre lasers. However, relatively little work has explored nonlinear pulse propagation in multimode fibres. Here, we consider highly nonlinear ultrashort pulse propagation in the anomalous-dispersion regime of a graded-index multimode fibre. Low modal dispersion and strong nonlinear coupling between the fibre's many spatial modes result in interesting behaviour. We observe spatiotemporal effects reminiscent of nonlinear optics in bulk media—self-focusing and multiple filamentation1,2—at a fraction of the usual power. By adjusting the spatial initial conditions, we generate on-demand, megawatt, ultrashort pulses tunable between 1,550 and 2,200 nm; dispersive waves over one octave; intense combs of visible light; and a multi-octave-spanning supercontinuum. Our results indicate that multimode fibres present unique opportunities for observing new spatiotemporal dynamics and phenomena. They also enable the realization of a new type of tunable, broadband fibre source that could be useful for many applications.

High-speed reconfigurable card-to-card optical interconnects based on hybrid free-space and multi-mode fiber propagations

In this paper, a high-speed reconfigurable card-to-card optical interconnect architecture based on hybrid free-space and multi-mode fiber (MMF) propagation is proposed. The use of free-space signal transmission provides flexibility and reconfigurability and the MMF extends the achievable interconnection range. A printed-circuit-board (PCB) based integrated optical interconnect module is designed and developed and proof-of-concept demonstration experiments are carried out. Results show that 3 × 10 Gb/s reconfigurable optical interconnect is realized with ~12 cm free-space propagation and a 10 m MMF length. In addition, since air turbulence due to high temperature of electronic components and heat dissipation fans always exists in typical interconnect environments and it normally results in system performance degradation, its impact on the proposed reconfigurable optical interconnect scheme is also experimentally investigated. Results indicate that even with comparatively strong air turbulence, 3 × 10 Gb/s optical interconnects with flexibility can still be achieved and the power penalty is <0.7 dB.

Robustness to mechanical perturbations of center-launching technique for transparent board-to-board and data server interconnects

Center-launching technique appears as a promising method to allow single-mode propagation in multi-mode fibers, guaranteeing full transparency to the transmitted optical signal also for applications in board-to-board and data server interconnects. In this paper we show that this technique is robust to mechanical perturbations up to about 1 kHz, demonstrating that the vibrations do not affect the transmission performances. Different experimental configurations are tested in order to exclude multimode propagation and to confirm the only fundamental mode propagation. Finally, a theoretical discussion comments the experimental results.

Coupled Manakov equations in multimode fibers with strongly coupled groups of modes

We derive the fundamental equations describing nonlinear propagation in multi-mode fibers in the presence of random mode coupling within quasi-degenerate groups of modes. Our result generalizes the Manakov equation describing mode coupling between polarizations in single-mode fibers. Nonlinear compensation of the modal dispersion is predicted and tested via computer simulations.

Numerical Investigation on Performance of In-Building Plastic Optical Fiber Transmission Systems and Role of Digital Television Broadcasting

This article reports a numerical investigation on the transmission performance of multilevel systems operating in building links encompassing step-index plastic optical fibers. For such an aim, a simplified model for the multimode fiber propagation is introduced. A sub-carrier multiplexing technique is also simulated to demonstrate the distribution of broadcasting television channels by adopting such fibers. The reported results show that a unique building network based on step-index plastic optical fibers is suitable to carry both Ethernet and broadcast TV signals in all rooms.

Nonlinear propagation in multi-mode fibers in the strong coupling regime

We show that light propagation in a group of degenerate modes of a multi-mode optical fiber in the presence of random mode coupling is described by a multi-component Manakov equation, thereby making multi-mode fibers the first reported physical system that admits true multi-component soliton solutions. The nonlinearity coefficient appearing in the equation is expressed rigorously in terms of the multi-mode fiber parameters.