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A general design rule of scrambling-type mode (de)multiplexers (mode scramblers) based on silica planar lightwave circuit (PLC) with small mode-dependent-loss (MDL) is presented for a mode-division multiplexing (MDM) system. First, we consider four- and eight-mode scramblers and demonstrate that if the number of modes is 2(N), it is possible to construct small-MDL mode scramblers by using Y-branch waveguides and mode rotators. Next, a 6-mode scrambler, which can be used for four linearly polarized (LP) mode transmission in MDM system, is considered, and the MDL is large if Y-branch waveguides are cascaded simply, originating from the radiation loss of unwanted modes at the Y-branch. We propose a 2 + 4-type mode scrambler by combining 2- and 4-mode scramblers and demonstrate that it is possible to design a small MDL 6-mode scrambler. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

We present a novel design of wholly fiber-based mode scrambler. The device consists of two multimode fibers with halfball microlens finish, being at some distance and connected via liquid of a certain refractive index. The prototype was made using standard components. The laser output profile was proved to be stable and almost entirely independent of input conditions, i.e. varying positions and angles of input laser beam. Moreover, the mode scrambler of the new design shows a very good power throughput, reaching as much as 90% of the light power compared to a single multimode fiber.

Modal dispersion in conventional multi-mode fiber (MMF) will cause serious signal degradation and an effective solution is to restrict the signal transmission in the fundamental mode of MMF. In this paper, unlike previous methods by filtering out higher-order modes, we propose to adopt low-modal-crosstalk mode converters to realize fundamental-mode MMF transmission. We design and fabricate all-fiber mode-selective couplers (MSC), which perform mode conversion between the fundamental mode in single-mode fiber (SMF) and fundamental mode in MMF. The proposed scheme is experimentally compared with center launching method under different MMF links and then its wavelength division multiplexing (WDM) transmission performance is investigated. Experimental results indicate that the proposed mode conversion scheme could achieve better transmission performance and works well for the whole C-band.

We theoretically model and numerically analyze the linear behavior of distributed mode crosstalk in a step-index weakly-coupled 7-mode fiber. This fiber is assumed to be used for one-polarization uncoupled mode-division multiplexing (MDM) systems with: (1) sparse MIMO equalizers which are performed over only degenerate LP modes, or (2) one single differential mode delay-independent MIMO equalizer which is performed over all non-degenerate LP modes. For the above two low-complexity MIMO configuration schemes, the impacts of distributed mode coupling on the multi-path interference-dependent achievable distance and system quality are empirically evaluated, through the numerical simulations for uncoupled MDM transmissions of a single-channel 28 GBaud QPSK signal over the fiber.

We propose and experimentally demonstrate LP11–LP01 mode conversion based on an angled-facet two-mode fiber (AFTMF). It is a simple device based on a standard two-mode fiber with an output facet angle of 43°. At a specific orientation, an incident LP11 beam on the angled-facet can be transformed into a transmitted beam with single-lobe mode profile. The single-lobe beam coupled into a target few-mode fiber (FMF) has successfully excited LP01 mode in the target FMF. The feasibility of the AFTMF to operate as a mode converter is demonstrated. The proposed device is a simple and low-cost mode conversion tool for the space division multiplexing system.

Environmental perturbations, such as wind, mechanical stress, temperature, and lightning, impose microsecond-time-scale changes to the transfer matrix of a multimode fiber (MMF), necessitating adaptive multiple-input multiple-output (MIMO) equalization to track the time-varying channel. It is of significant interest to accurately model channel dynamics so that adaptive MIMO equalization algorithms can be optimized and their impact on digital signal processing complexity and performance can be assessed. We propose a dynamic channel model using coupled-mode theory to describe time-varying polarization- and spatial-mode coupling in MMF caused by fast environmental perturbations. Our method assumes that the MMF has built-in refractive index and geometric defects that are responsible for random birefringence and mode coupling. Various time-varying perturbations modify the coupling coefficients in the coupled-mode equations to drive channel dynamics. We use our dynamic channel model to simulate an example aerial fiber link subject to a sudden gust of wind and show that increasing the strength of the perturbation, the number of modes, and the length of exposed fiber all lead to higher error at the output of an adaptive MIMO equalizer. We employ the model to study the convergence and tracking performance of the least-mean-squares adaptive equalization algorithm.

We present a theoretical study on the mode coupling between core modes and cladding modes of the tilted long period fiber grating (TLPFG) in dual-mode fiber. The TLPFG can be applied as mode filters at several specific wavelengths. Using the full vector complex coupled mode theory, numerical simulation shows the maximum coupling coefficients between core modes (LP01 and LP11) and cladding modes can be found near the tilted angle of 86°. The transmission peaks of modes coupling are sensitive to the titled angle. Furthermore, several peak amplitude between the LP11 mode and same azimuthal order modes increase with the growth of the titled angle. With the band-stop characteristic of specific mode, the TLPFG written in dual-mode fiber could be exploited as mode filters.

We experimentally demonstrate an all optical space-to-time mapping process using modal dispersion of large core high numerical aperture step-index multimode fiber in this paper. We use light beam with different input angle to excite various modes in a span of multimode fiber. The input optical pulses are stretched in time by modal dispersion and received by a large area, high speed photodiode. Through this process, the spatial information is directly mapped into device's temporal response. It has high speed, broad bandwidth and low system latency. Comparing with the widely used spectral imaging technology, this device is weak dependent of the input signal wavelength and optical carrier bandwidth.

Recently developed PLC-based mode multi/demultiplexers (MUX/DEMUXs) for mode division multiplexing (MDM) transmission are reviewed. We firstly show the operation principle and basic characteristics of PLC-based MUX/DEMUXs with an asymmetric directional coupler (ADC). We then demonstrate the 3-mode (2LP-mode) multiplexing of the LP01, LP11a, and LP11b modes by using fabricated PLC-based mode MUX/DEMUX on one chip. In order to excite LP11b mode in the same plane, a PLC-based LP11 mode rotator is introduced. Finally, we show the PLC-based 6-mode (4LP-mode) MUX/DEMUX with a uniform height by using ADCs, LP11 mode rotators, and tapered waveguides. It is shown that the LP21a mode can be excited from the LP11b mode by using ADC, and the two nearly degenerated LP21b and LP02 modes can be (de)multiplexed separately by using tapered mode converter from E13 (E31) mode to LP21b (LP02) mode.

We have successfully improved the transmission bandwidth of a step-index multimode fiber by applying torsional stress to the fiber using a variable mode scrambler device. At this time, the maximum radiation angle of the far-field pattern of the fiber did not change with the torsional stress.

We propose the mode dependent gain (MDG) reduction technique in few mode fiber amplifier using trench assisted GI fiber type long period grating. 1.8dB MDG reduction and wideband mode scrambling over 100nm are experimentally obtained.

We introduce a novel, low loss and compact mode scrambler, printed directly on fiber-tip. The device is optimized for high inter-mode-group mixing across all mode groups, achieving strong mixing in FMF links.

This paper presents an application of low-coherence interferometry for measurement of mode field diameters (MFDs) of a few-mode fiber and shows its performance compared with another method using a mode multiplexer.

A transverse mode converter based on a binary microrelief implemented directly on the end-face of a few-mode fiber was numerically investigated. The results of numerical simulation demonstrated the converter to form LP-11 and LP-21 modes with high efficiency, providing a more-than 92 % mode purity. Transformations of modes excited by a fiber microbending were also numerically investigated. The excited beams were shown to save their mode purity even in a strong bending as the arising parasitical modes were mostly unguided by the fiber. The resulting beam power and mode content were also demonstrated to depend on the beam and bending mutual orientation for beams with strong rotational symmetry.

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

This work presents fast and simple method for design and computing parameters of precision spatial positioning scheme for mode division multiplexing (MDM) system channels placement over optical fiber core end. Proposed solution is based on combination of well known mode field overlap integral method and earlier on developed modified Gaussian approximation. Computation results showed that fitting of MDM channel mode field radius and its corresponding offset launching position in relation to optical fiber core center provides transmission of the almost total channel injected mode power to only one particular excited fiber mode with the same azimuthal order. This work presents results of proposed method approbation for computation of spatial positioning scheme for modes of 5-channel MDM system placement over few-mode optical fiber 42/125 core end.

The effective mode field diameter (MFD) for the second-order (LP11) mode in two-mode fibers is determined to allow estimation of the coupling efficiencies at a splice with axial misalignment. Simulations are performed to verify its validity. In addition, we propose a novel technique for measuring the effective MFD distribution for the LP11 mode along two-mode fibers. The technique is based on optical time-domain reflectometry; it conducts measurements in the two-mode region of test fibers and individually observes the LP01 and LP11 modes of the backscattered light. Its feasibility is demonstrated experimentally.

We proposed a mode splitter based on directional coupler (DC), which is capable of splitting the TE0 & TE1 modes without changing the mode order. It is found that high coupling efficiency (>;1 dB), low mode crosstalk (

A quasi-optical (QO) mode converter for a 0.42-THz, TE26 mode, pulsed gyrotron is designed, fabricated, and tested. Based on the geometric optics principle, vector diffraction theory, and the iterative Stratton–Chu method, a computer code is developed to design and optimize the QO mode converter. The scalar Gaussian mode content is about 93.7%, which agrees well with that obtained by the electromagnetic simulation software. The preliminary experiment of the 0.42-THz, TE26 mode QO mode converter shows that a well-focused Gaussian-like beam with 90.4% scalar Gaussian mode content has been observed on the output window by using an infrared video camera. The experimental results agree well with the theoretical prediction.

We propose and demonstrate an effective method for mode analysis of a silicon-based two-mode waveguide using time-domain scanning low-coherence interferometry (LCI). An on-chip offset launch technique is implemented to motivate and couple out the two modes. From the low-coherence signal, it is convenient to simultaneously perform the mode identification and analyze the differential modal group delay in a silicon-based multimode waveguide. Our experimental results show good agreement with the simulation results. The low-coherence interferogram shows that only short samples of waveguide ( $ ) is sufficient for the LCI to do the mode analysis. This letter provides a feasible method for the mode identification and the transmission channel analysis in silicon-based multimode waveguide used for $2\times 2$ on-chip mode-division multiplexing.

An all-fiber broadband degenerate mode rotator for the rotation between arbitrary degenerate modes is proposed and investigated numerically. Furthermore, the rotator combined with a mode selective coupler (MSC) can be used to realize mode multiplexing. The mode multiplexing can be implemented in one physical dimension, which is considered easier than 3-D cascading MSCs. It is found that the rotator for any two degenerate modes rotation possesses a high rotating efficiency from 1450 to 1650 nm, and the insertion loss at the interconnection of a fiber-based rotator and a normal fiber is lower than 3 dB for any modes. Moreover, the rotators in performance are not sensitive to the four geometrical parameters of design. Finally, a six-mode multiplexer using the proposed rotator combined with MSC is modeled and analyzed. It is shown that multiplexing efficiencies of higher than 70% and mode extinction ratios of more than 20 dB for mode LP01, LP11a/LP11b, LP21a/LP21b, and LP02 are achieved in the $C$ -band.

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.

A high-order mode rotator based on a silicon-on-insulator strip waveguide with asymmetrical cross section is proposed and optimized to rotate the spatial distribution of the $E_{21}$ mode by 90° into that of the $E_{12}$ mode. The subscripts $i$ and $j$ of the mode $E_{ij}$ correspond to the number of lobes in the intensity distribution of the mode along the horizontal and vertical axes, respectively. The mode conversion efficiency and the corresponding length of the mode rotator device are presented as a function of design parameters for both the transverse magnetic (TM) and transverse electric (TE) polarizations. The fabrication tolerance of the structure is also analyzed. We further present simulation results of a two-mode multiplexing system based on $E_{21}$ and $E_{12}$ showing a mode extinction ratio exceeding 15 dB over a wide wavelength range of 100 nm.

An experimental coupling mechanism is presented that demonstrates efficient coupling between a high-power 980-nm laser diode and a lensed fiber by employing mode (spot size and wavefront) matching in the near-field regime. The results show that the beam spot pattern of the lensed fiber of a horizontally elliptical shape is spot-size matched to the laser. The wavefront of the lensed fiber with a minor radius of curvature ranging from −9 to $10~\mu \text{m}$ exhibits a curve wave that is also phase matched to the laser. This indicates that the similarity in the mode patterns of both the spot size and the wavefront between lensed fiber and laser is responsible for mode-matched beam coupling, leading to a coupling efficiency of more than 80%. In contrast to the lensed fiber, the spot-size of the cleaved fiber is round, and the wavefront is a plane wave. The different mode distributions between the laser and the cleaved fiber lead to a mode mismatch, resulting in a coupling efficiency of lower than 40%. This experimental coupling mechanism investigation in the near-field regime provides useful information for practical micro-optic design with better mode matching to achieve efficient coupling from active to passive components for interconnect applications.

We investigate experimentally the signal quality difference induced by differential modal loss and modal crosstalk (XT) in few-mode fiber during optical MIMO transmission. We measure the modal loss and modal XT properties of two LP mode fibers in the presence of tension and confirm that the coexistence of differential modal loss and modal XT leads to a signal quality imbalance even with MIMO digital processing. In addition, to compensate for the signal quality imbalance, we employ a novel equipartition multiplexing technique at the transmitter used in a mode-division-multiplexed transmission to equalize the mode-dependent impairment, and successfully achieve a two LP mode multiplexed transmission with a low signal quality difference.

We design and build a mode scrambler modes based on multiplane light conversion that completely inverts the first 10 spatial modes of of a graded index multimode fiber.

We report the optimization of a few-mode fiber, adapted to multiple-input multiple-output mode division multiplexing, that supports 9 LP modes (15 spatial modes). The fiber is fabricated using standard multimode processes, which allows for tight process tolerances, yielding low differential mode group delays (

A Single-mode flat fiber investigated by mode matching filtering technique is presented. This class of rectangular optical fiber employed a mode filtering technique to filter high order modes. Fresnel leakage loss induced the propagation modal loss favors fundamental mode, whereas significantly filtered higher-order mode due to modal loss. This resulting mode operation can be expanded via high-aspect-ratio. We numerically analyze the via full-vectorical numerical analysis. We also cover the dispersion analysis to be estimated around wavelength of 1268 nm.

Typical metallic waveguide mode converters convert electromagnetic waves from one mode to another mode for some frequency ranges. However, most electromagnetic waves outside of the specified frequency range are reflected. We report a design for a mode converter which passes the TE10 mode at a low frequency range and efficiently converts the TE10 mode to the TE20 mode at a high frequency range. To gradually shift the mode profile from TE10 to TE20, dielectric rods are placed in a sequence along the waveguide starting near the sidewall and moving to the center of the waveguide with decreasing radius of the rods. This design reduces reflection of electromagnetic waves. Experimental tests demonstrate the efficacy of the design.

We test Slemon and Wells's function and recently reported Hurand et al.'s (Appl. Opt., 50, 492–499, 2011) function for calculation of coupling characteristics in step-index optical fibers against experimental measurements and against calculations by a related method that is based on the power flow equation. Compared are the coupling length Lc (which is the fiber length where the equilibrium mode distribution is achieved) and length zs (where steady-state distribution is achieved) in three step index glass optical fibers as well as a liquid core optical fiber. The two functions, while simpler to apply being just algebraic formulas, are less accurate over a wide range of numerical apertures. It is also shown that fibers with same coupling coefficient can have much different coupling characteristics.

Efficient mode division multiplexing using the spatial aperture sampled concept from single-modefibers to a few-mode fiber is extended to circular step index fibers supporting up to ten spatial modes and to annular refractive index profile fibers supporting nine optical orbital angular momentum modes (mode counts double when considering polarization states for each case). Each sampling beam aperture is spatially shaped for lower average coupling losses and mode dependent losses or a balance thereof. The optimization demonstrates the scalability and consistent low losses for the aperture-sampled mode multiplexer for increasing mode counts, as opposed to the phase hologram-based mode conversion technique. The aperture-sampling approach is also found to be robust to small input fiber alignment errors and fiber geometrical distortions.

We investigate mode coupling in few-mode fibers induced by homogeneously and periodically applied mechanical stress. To view the power transfer between individual modes, a modal decomposition is performed at the end of the fiber using computer-generated holograms. Coupling between polarization and angular degenerated modes as well as between non-degenerated modes is confirmed experimentally and coupling parameters are inferred. The presented studies pave the way to detailed investigations of mode coupling in mode-multiplexed telecommunication systems and high-power high beam quality fiber lasers.

The ability of modal decomposition based on the analysis of the near-field intensity profile using the stochastic parallel gradient descent algorithm is experimentally characterized in detail for the first time. The results show that the decomposition method proposed in this letter turns to be highly accurate and rapid. Further, this method is applied to analyze the mode behavior in dependence on the pump power in a high-power fiber amplifier with different initial mode compositions.

In mode-division-multiplexing systems, multi-input multi-output (MIMO) equalization is used to compensate for linear impairments, including modal dispersion (MD) and modal crosstalk. The MIMO equalizer memory length depends on the group delay (GD) spread arising from MD. The GD spread arising from MD can be significantly reduced by introducing strong mode coupling via mode scramblers. We study the design of such mode scramblers implemented as long-period multimode fiber gratings for systems using $D = 12$ modes (six spatial modes). By optimizing the grating chirp function, we minimize the mode-dependent loss (MDL) of the grating while ensuring full intergroup mode coupling. We find a design yielding MDL and mode-averaged loss in the C band not exceeding 0.36 and 0.45 dB, respectively. We also verify the effect of such mode scramblers on the GD scaling of a long-haul system, demonstrating that the scramblers reduce the scaling of GD spread with length from a linear to a square-root dependence, as expected in the strong coupling regime.

A novel mode converter with broad bandwidth, high mode conversion efficiency, and large fabrication tolerance is proposed and fabricated on a silicon-on-insulator (SOI) platform. By using a modified 3 × 3 multimode interference coupler and an enlarged butterfly-shaped phase shifter, mode conversion from the fundamental mode (TE0) to second-order mode (TE2) is achieved numerically and experimentally. Performance analysis of the mode converter is carried out numerically, and the results show high performance of the mode converter with mode conversion efficiency larger than 91% (i.e., insertion loss less than 0.40 dB) in the whole C-band. In addition, the mode converter has large fabrication tolerance. For example, the width and the length deviations of the multimode interference coupler can be as large as 50 and 250 nm, respectively, whereas the width and the length deviations of the phase shifter can be up to 25 and 400 nm, respectively.

Based on the coupled wave theory, the TE01-HE11 mode conversion system has been designed and tested. The system is done in three steps. First, a smooth wall gradual TE01 mode bend with an arc radius 550-mm long is designed to satisfy the demands of the system. Second, a 595-mm-long waveguide converts TE01 mode to TM11 mode. Third, a 415.5-mm-long corrugated circular waveguide is designed to excite HE11 mode. The above designs are all verified by Commercial Microwave Studio CST Software. The calculation shows that the transmission efficiency of the whole system is over 95 % at the frequency of 35 GHz. The calculations, the simulations, and the test results are in well agreement.

We present the results on fabrication and the characterization of few-mode fiber Bragg gratings (FM-FBGs) inscribed in two mode and four mode step-index fibers. Under the conditions of selective input mode launching, coupling between specific modes of interest can be selectively excited and the self-coupling and cross-coupling properties at the associated resonant wavelengths can be clearly identified and verified by observing the reflected mode intensity profiles. Such FM-FBGs can potentially be used as reflective mode-converters for mode division multiplexed data transmission systems.

We fabricate mode converters by directly writing long-period gratings in a two-mode fiber with a CO2 laser. These mode converters allow the fundamental LP01 mode to be converted to any of the four higher order cylindrical vector modes or the LP11 modes. The transmission characteristics of these devices are insensitive to temperature variations and the mode conversion efficiency is insensitive to the polarization state of the input light. One of our typical gratings, which contains 15 grating periods, can provide a conversion efficiency >99% over a bandwidth of 34.0 nm in the C-band. These robust mode converters could find applications in mode-division-multiplexing systems and other applications that require cylindrical vector modes.

We demonstrate a mode scrambler using CO 2 -laser inscribed long-period gratings for mixing 3 spatial modes. The mode-dependent loss and modal transfer matrices versus wavelength are characterized using a swept-wavelength interferometer.

We use the power coupled-mode theory to study the interplay between multipath interference (MPI) and differential mode attenuation (DMA) in quasi-single mode (QSM) fibers. The analytical expressions derived assuming two mode propagation in QSM fibers show that MPI scales differently as a function of the span length for low and high DMA. Furthermore, we derive analytical expressions for the performance improvement of long-haul coherent optical communication systems using QSM fibers, taking into account the impact of excess loss and MPI on system performance. From these expressions, we calculate the maximum allowable coupling coefficient for different values of the DMA. We show, for example, that a QSM fiber with an effective area of 250 μm2, a coupling coefficient κ ≤ 6 × 10-4 km-1, and DMA equal to 4 dB/km offers a 1-dB performance advantage over a reference pure silica core single-mode fiber for spans of 100 km.

We proposed a short-fiber-length mode scrambler that reproduces the equilibrium mode distribution of an A3e fiber. The mode scrambler is compact, mode-controllable and has low attenuation. It is effective for not only hard plastic-clad fiber but also all step-index fibers, such as all-glass and plastic optical fibers.