Mode-dependent Loss Research Articles

Super- and Anti-Principal-Modes in Multimode Waveguides

We introduce a new type of states for light in multimode waveguides featuring strongly enhanced or reduced spectral correlations. Based on the experimentally measured multi-spectral transmission matrix of a multimode fiber, we generate a set of states that outperform the established "principal modes" in terms of the spectral stability of their output spatial field profiles. Inverting this concept also allows us to create states with a minimal spectral correlation width, whose output profiles are considerably more sensitive to a frequency change than typical input wavefronts. The resulting "super-" and "anti-principal" modes are made orthogonal to each other even in the presence of mode-dependent loss. By decomposing them in the principal mode basis, we show that the super-principal modes are formed via interference of principal modes with closeby delay times, whereas the anti-principal modes are a superposition of principal modes with the most different delay times available in the fiber. Such novel states are expected to have broad applications in fiber communication, imaging, and spectroscopy.

Low-Loss and Low-Mode-Dependent-Loss Fan-In/Fan-Out Device for 6-Mode 19-Core Fiber

This paper describes a low-loss fiber-bundle-type fan-in/fan-out (FI/FO) device for 6-mode 19-core fiber, which exhibits a low mode-dependent loss (MDL) with a physical-contact connection for all the cores. We reveal that reducing the offset at the connection of few-mode fibers (FMFs) at butt coupling does not necessarily result in a minimum MDL, and the FMFs should be aligned so as to minimize the MDL, by experimentally investigating the MDL as a function of the lateral offset at butt coupling. We develop a precise rotational alignment mechanism to accurately adjust the core position without any complex alignment equipment, and we introduce a hexagonal microhole into a ferrule to accurately arrange the fibers. With these technologies, we successfully suppress the mode-dependent loss of the FI/FO device. The device provides a low MDL variation of less than 2 dB for all the cores with good optical properties such as a low excess loss, low core-to-core crosstalk, and a high return loss. The fabricated FI/FO device also achieved the highest reported spatial multiplicity connection of more than 100 with a small footprint as well as a low connection loss. Other optical properties that we obtained such as the modal crosstalk are also described.

Comparing mode-crosstalk and mode-dependent loss of laterally displaced orbital angular momentum and Hermite-Gaussian modes for free-space optical communication.

There is interest in using orbital angular momentum (OAM) modes to increase the data speed of free-space optical communication. A prevalent challenge is the mitigation of mode-crosstalk and mode-dependent loss that is caused by the modes' lateral displacement at the data receiver. Here, the mode-crosstalk and mode-dependent loss of laterally displaced OAM modes (LG0,+1, LG0,-1) are experimentally compared to that of a Hermite-Gaussian (HG) mode subset (HG0,1, HG1,0). It is shown, for an aperture larger than the modes' waist sizes, some of the HG modes can experience less mode-crosstalk and mode-dependent loss when laterally displaced along a symmetry axis. It is also shown, over a normal distribution of lateral displacements whose standard deviation is 2× the modes' waist sizes, on average, the HG modes experience 66% less mode-crosstalk and 17% less mode-dependent loss.

Large-bandwidth, low-loss, efficient mode mixing using long-period mechanical gratings.

We propose a new architecture for using long-period fiber gratings (LPGs) to induce strong mode mixing with low loss for space-division multiplexing. In this architecture, LPGs are installed in step-index (SI) few-mode fibers that support more modes than the transmission fiber. Such a design could significantly reduce losses due to coupling from the highest-order mode group to cladding modes. In our experiment, efficient mixing of three spatial modes over a broad bandwidth was achieved by a mechanical long-period grating on a SI fiber that supports eight spatial modes. The insertion loss, including two splice losses, is less than 0.5dB, and the coupling matrix and mode-dependent loss (MDL) are characterized experimentally for the first time, to the best of our knowledge. Strong mixing between LP01 and LP11 for a whole C band is demonstrated, and MDL introduced to the system is negligible.

Few-mode fiber, splice and SDM component characterization by spatially-diverse optical vector network analysis.

This paper discusses spatially diverse optical vector network analysis for space division multiplexing (SDM) component and system characterization, which is becoming essential as SDM is widely considered to increase the capacity of optical communication systems. Characterization of a 108-channel photonic lantern spatial multiplexer, coupled to a 36-core 3-mode fiber, is experimentally demonstrated, extracting the full impulse response and complex transfer function matrices as well as insertion loss (IL) and mode-dependent loss (MDL) data. Moreover, the mode-mixing behavior of fiber splices in the few-mode multi-core fiber and their impact on system IL and MDL are analyzed, finding splices to cause significant mode-mixing and to be non-negligible in system capacity analysis.

Mode-dependent mechanical losses in disc resonators

Mechanical spectroscopy gives information on the structure of solids and their relaxation mechanisms through the measurements of the elastic constants and the mechanical loss angle of materials. One common way to estimate these quantities is the resonant method where the frequency and the characteristic decay time of oscillations are measured. Since many solid materials can be easily found in the shape of thin disc we have investigated the mechanical loss of these resonators and we have found experimentally that the loss angle dependence on the mode is not trivial but rather follow a distribution of modes into families. We give a model that is able to justify the existence of these families and to predict the level of losses in silicon, silica and brass discs. The model considers the thermoelastic effect and the excess damping caused by the condition of the disc edge. The results of this research are relevant to the research on thin films that are deposited on thin discs like the optical coatings used on the mirrors for the gravitational wave detectors.

Orthogonal STBC for MDL Mitigation in Mode Division Multiplexing System With MMSE Channel Estimation

Mode division multiplexing (MDM) has the potential of increasing the capacity of optical fiber transmission system. However, primary impaired factor mode-dependent loss (MDL) poses fundamental performance limitations. Recently MIMO space time coding technique has provided a potential solution to mitigate the MDL and hence started receiving considerable interests. In this paper, orthogonal space time block coding (OSTBC)-based MDM transmission system was investigated to test its efficiency in mitigating MDL. Considering the importance and necessity of channel estimation for coherent receivers and the paucity of literature on this subject, MMSE channel estimation process was introduced in the MDM system to test the robustness and efficiency of the OSTBC-MDM system in mitigating the MDL. Furthermore, an alternative linear decoding (LD) method was achieved by transferring the orthogonal characteristics of codes in OSTBC to the channel elements in MDM system. The LD method has the same performance as the optimal ML method, excepting that it only exhibits linear computational complexity, in terms of the number of modes and the size of constellations. Simulation results were provided to validate the efficiency and robustness of the proposed OSTBC-MDM system in mitigating the MDL in the presence of MMSE channel estimation.

Investigation of adaptive filtering and MDL mitigation based on space-time block-coding for spatial division multiplexed coherent receivers

Abstract In this paper, we explored the performance of space-time block-coding (STBC) assisted multiple-input multiple-output (MIMO) scheme for modal dispersion and mode-dependent loss (MDL) mitigation in spatial-division multiplexed optical communication systems, whereas the weight matrices of frequency-domain equalization (FDE) were updated heuristically using decision-directed recursive least squares (RLS) algorithm for convergence and channel estimation. The proposed STBC-RLS algorithm can achieve 43.6% enhancement on convergence rate over conventional least mean squares (LMS) for quadrature phase-shift keying (QPSK) signals with merely 16.2% increase in hardware complexity. The overall optical signal to noise ratio (OSNR) tolerance can be improved via STBC by approximately 3.1, 4.9, 7.8 dB for QPSK, 16-quadrature amplitude modulation (QAM) and 64-QAM with respective bit-error-rates (BER) and minimum-mean-square-error (MMSE).

Concatenation of Space-Time Coding and FEC for Few-Mode Fiber Systems

Space-division multiplexing (SDM) is becoming essential to increase the capacity of future optical communication systems. Propagating modes through multimode fibers are affected by a non-unitary crosstalk known as mode dependent loss (MDL), that requires either optical or digital signal processing solutions to be reduced. Space-time (ST) coding designed and used for wireless communications was proved to be efficient to reduce polarization-dependent loss in PolMux systems and MDL in SDM systems. In this letter, we study a complete transmission scheme, including forward error correction (FEC) and ST coding. FEC is used to protect the transmission from errors, but in the presence of MDL, system’s performance is reduced. We show by simulations and error probability derivation that coding gain summation is obtained, which makes both codes essential for the next generation of optical transmission systems.

All-fiber 6-mode multiplexers based on fiber mode selective couplers.

All-fiber 6-mode multiplexer composed of two consecutive LP11-mode selective couplers (MSC), two LP21-MSCs and an LP02-MSC is fully characterized by wavelength-swept interferometer technique. The MSCs are fabricated by polished-type fiber couplers coupling LP01 mode of a single mode fiber into a higher-order mode of a few mode fiber. A pair of the mode multiplexers has minimum mode dependent loss of 4 dB and high mode group selectivity of over 15 dB. Mode division multiplexed transmission enabled by the all-fiber mode multiplexers is demonstrated over fiber spans of 117 km employing an in-line multi-mode optical amplifier. 6 modes of 120 Gb/s dual polarization quadrature phase shift keying signals combined with 30 wavelength channels are successfully transmitted.

Mode-Based Reconstruction of Chemical Distributions in Optical Fibers

By using few-mode fibers (FMFs), it is possible to simultaneously determine the values of multiple parameters such as temperature and strain. In this work, we extend this capability to the case of mode-based reconstruction of the distribution of a continuous variable function. As a specific example, we theoretically demonstrate that by measuring the mode-dependent losses of multiple guided modes in an FMF, it is possible to determine the spatial distributions of chemicals diffused within the fiber.

Principal modes in multimode fibers: exploring the crossover from weak to strong mode coupling.

We present experimental and numerical studies on principal modes in a multimode fiber with mode coupling. By applying external stress to the fiber and gradually adjusting the stress, we have realized a transition from weak to strong mode coupling, which corresponds to the transition from single scattering to multiple scattering in mode space. Our experiments show that principal modes have distinct spatial and spectral characteristic in the weak and strong mode coupling regimes. We also investigate the bandwidth of the principal modes, in particular, the dependence of the bandwidth on the delay time, and the effects of the mode-dependent loss. By analyzing the path-length distributions, we discover two distinct mechanisms that are responsible for the bandwidth of principal modes in weak and strong mode coupling regimes. Their interplay leads to a non-monotonic transition of the average principal mode bandwidth from weak to strong mode coupling. Taking into account the mode-dependent loss in the fiber, our numerical results are in qualitative agreement with our experimental observations. Our study paves the way for exploring potential applications of principal modes in communication, imaging and spectroscopy.

Mode-selective coupling between few-mode fibers and buried channel waveguides.

With intensive computation, we analyze in detail butt-coupling between few-mode fibers and buried channel waveguides and discuss, in particular, the conditions to achieve mode-selective coupling for the first 6 spatial modes. In the case of coupling a buried rectangular-core waveguide to a step-index or a parabolic-index circular-core fiber, a modal crosstalk smaller than -20 dB for all the 6 spatial modes can be achieved, when the shape of the waveguide core is sufficiently close to a square (within ± 0.7% variation in its aspect ratio) and the waveguide and the fiber have close mode volumes. In the case of coupling a buried rectangular-core waveguide to a step-index elliptical-core fiber, it is possible to achieve a modal crosstalk smaller than -20 dB with many combinations of waveguide and fiber parameters. The aspect ratios of the elliptical core and the best matched rectangular core can be very different (e.g., 0.85 for the elliptical core and 1.05 for the rectangular core) and an elliptical core that has a moderate ellipticity and an area not close to the upper limit allowed for supporting 6 spatial modes is preferred. The use of a parabolic-index profile in the elliptical core can further improve the mode selectivity with greatly relaxed tolerances on both the aspect ratio and the area of the rectangular core required. In general, when the fiber and the waveguide core are matched for low-crosstalk performance, the butt-coupling losses for all the 6 spatial modes as well as the mode-dependent loss are also small (typically well below 1 dB). Our results are useful for the design of mode-selective waveguide devices, such as mode (de)multiplexers, mode converters, and mode switches, for fiber-based mode-division multiplexing applications.

Quantization and Feedback of Principal Modes for Dispersion Mitigation and Multiplexing in Multimode Fibers

The larger core diameter of multimode fibers (MMFs) allows several propagating modes, but differential group delays and modal cross talk cause modal dispersion, thus limiting the data rate. Recent results have shown the existence of a set of principal modes (PMs) that allow dispersion free communication to the first order. Moreover, the linear independence of the PMs also permits multiplexing in MMFs. To effectively utilize these PMs at the transmitter, it is essential to estimate them and feed them back to the transmitter. In this paper, we propose quantization schemes that enable efficient encapsulation of the PMs for feedback for MMFs with a small number of modes. For shorter links, we use vector quantization codebooks based on the Linde-Buzo–Gray (LBG) algorithm, while for long links with low mode dependent losses (MDL), we show analytically that the PMs are Haar distributed, and use Grassmannian line packing based codebooks. Simulations reveal that the quantization limits dispersion and the performance of the quantized PMs is within 2 dB of the ideal principal modes with only 6 bits quantization, both with and without MDL. In addition, the quantized PMs permit efficient multiplexing with low crosstalk in both the lossless and MDL cases.

Virtual Network Provisioning Over Space Division Multiplexed Optical Networks Using Few-Mode Fibers

In space division multiplexed optical networks (SDM-ONs) using few-mode fibers (FMFs), modedependent loss (MDL) is one of the major factors that influences network performance. While in softwaredefined optical networks (SDONs), virtual optical network (VON) provisioning requires considerations regarding their optical characteristics and constraints. In this paper, we present a new VON provisioning procedure that is specifically designed for SDM-ONs using FMFs. The impact of MDL on VON provisioning is investigated based on an analytical model of MDL. Furthermore, the impact of network topology on VON provisioning is also evaluated. Simulations show that MDL has a conspicuous impact on VON provisioning capacity.

Quantification of MDL-induced signal degradation in MIMO-OFDM mode-division multiplexing systems

Mode-division multiplexing (MDM) transmission over few-mode optical fiber has emerged as a promising technology to enhance transmission capacity, in which multiple-input-multiple-output (MIMO) digital signal processing (DSP) after coherent detection is used to demultiplex the signals. Compared with conventional single-mode systems, MIMO-MDM systems suffer non-recoverable signal degradation induced by mode-dependent loss (MDL). In this paper, the MDL-induced signal degradation in orthogonal-frequency-division-multiplexing (OFDM) MDM systems is theoretically quantified in terms of mode-average error vector magnitude (EVM) through frequency domain norm analysis. A novel scalar MDL metric is proposed considering the probability distribution of the practical MDM input signals, and a closed-form expression for EVM measured after zero-force (ZF) MIMO equalization is derived. Simulation results show that the EVM estimations utilizing the novel MDL metric remain unbiased for unrepeated links. For a 6 × 100 km 20-mode MDM transmission system, the estimation accuracy is improved by more than 90% compared with that utilizing traditional condition number (CN) based MDL metric. The proposed MDL metric can be used to predict the MDL-induced SNR penalty in a theoretical manner, which will be beneficial for the design of practical MIMO-MDM systems.

Surface Roughness Modeling of Substrate Integrated Waveguide in D-Band

In this paper, surface roughness models for a substrate integrated waveguide (SIW) are proposed. Frequency-dependent conductivity is introduced to model the conductor loss due to surface roughness. To be specific, two models, namely, the modified Huray model and the rigorous waveguide model, are developed. Both models take into account the mode-dependent loss. Formulations for enhancement factor are derived for both models to calculate the frequency-dependent conductivity. Key parameters of the analytical models are extracted from the surface profile measurement. A D-band (110–170 GHz) SIW structure is fabricated using a liquid crystal polymer substrate. The simulated results are correlated with measured data of the fabricated SIW, which shows the accuracy of the proposed methods.

Inverse Scattering Designs of Active Multimode Waveguides With Tailored Modal Gain

Darboux inverse scattering transforms are used to design active waveguides with individually tailored modal gain, introducing areas of distributed gain and loss inside the waveguide. Potential applications of such devices include multimode optical amplifiers for which mode-dependent loss and its associated deleterious effects on channel capacity have been compensated. We also show that the commonly used ring-doping approach to modal gain equalization in fibers is a subset of the design approach utilizing gain and loss that derives from the inverse scattering theory.

Dense Space Division Multiplexed Transmission Over Multicore and Multimode Fiber for Long-haul Transport Systems

In this paper, we review recent progress on space division multiplexed (SDM) transmission and our proposal of dense SDM (DSDM) with more than 30 spatial channels toward capacities beyond petabit/s. Furthermore, we discuss the requirements for realizing long-haul DSDM transport systems using multicore and/or multimode fiber, including power and space efficient amplification schemes, the use of fibers with large effective areas and transmission lines with low intercore crosstalk, low differential mode delay (DMD), and low mode dependent loss (MDL). Graded index heterogeneous 12-core × 3-mode fiber with low crosstalk, low DMD, and low MDL, parallel multiple-input and multiple-output signal processing, low mode dependent gain Erbium-doped fiber amplifiers, and MDL equalization technologies are significant as regards extending the reach of multicore and multimode transmission. We review our long-distance transmission experiment on polarization-division multiplexed 16-quadrature amplitude modulation signaling over 12-core × 3-mode fiber.

Mode-dependent loss measurement of a two-mode fiber using a conventional OTDR

Mode-dependent loss measurement of a two-mode fiber using a conventional OTDR