Mode Crosstalk Research Articles

Statistics of mode couplings induced by concatenated multiple connections in weakly-coupled few-mode fibers

We numerically investigate the statistical characteristics of mode couplings induced by concatenated multiple few-mode fiber connections with lateral misalignments in weakly-coupled mode division multiplexed (MDM) systems. For the currently-feasible connectors, the probability of the crosstalk ratio being smaller than -20 dB is remarkably degraded as increasing the number of the connections. The currently-feasible connectors are not applicable to the weakly-coupled MDM systems. In order to suppress the mode crosstalk by smaller than -20 dB, the misalignment deviation is required to be smaller than 0.04, which corresponds to be 0.3% of the mode field diameter of the fundamental mode. In addition, we propose the simple model giving us intuitional understanding for mode couplings induced by few-mode fiber connections.

Ultra-Broadband Mode Splitter Based on Phase Controlling of Bridged Subwavelength Grating

An ultra-broadband mode splitter is proposed based on the phase controlling of the bridged subwavelength grating (BSWG) waveguides. An asymmetric directional coupler composed of two BSWG waveguides with an identical waveguide-width but two different bridge-widths is introduced to split the TM0 and TM1 modes based on the mode-sensitive phase-matching condition. The proposed mode splitter is optimized by utilizing the 3D full-vectorial finite difference time domain method. The results indicate that the proposed mode splitter can achieve a compact coupling length of 5.75 μm, the insertion losses of 0.41 dB and 0.53 dB, and the mode crosstalks of −19.6 dB and −27.8 dB for the TM0 and TM1 modes, respectively. The broad bandwidths of 430 nm and 372 nm can be achieved with the mode crosstalk of ≤−15 dB for the TM0 and TM1 modes, respectively. The fabrication tolerances are also studied in detail. The proposed mode splitter could be employed for signal selection and routing in the mode division multiplexing networks.

Fabrication-tolerant Fourier transform spectrometer on silicon with broad bandwidth and high resolution

We report an advanced Fourier transform spectrometer (FTS) on silicon with significant improvement compared with our previous demonstration in [Nat. Commun. 9, 665 (2018)2041-1723]. We retrieve a broadband spectrum (7 THz around 193 THz) with 0.11 THz or sub nm resolution, more than 3 times higher than previously demonstrated [Nat. Commun. 9, 665 (2018)2041-1723]. Moreover, it effectively solves the issue of fabrication variation in waveguide width, which is a common issue in silicon photonics. The structure is a balanced Mach–Zehnder interferometer with 10 cm long serpentine waveguides. Quasi-continuous optical path difference between the two arms is induced by changing the effective index of one arm using an integrated heater. The serpentine arms utilize wide multi-mode waveguides at the straight sections to reduce propagation loss and narrow single-mode waveguides at the bending sections to keep the footprint compact and avoid modal crosstalk. The reduction of propagation loss leads to higher spectral efficiency, larger dynamic range, and better signal-to-noise ratio. Also, for the first time to our knowledge, we perform a thorough systematic analysis on how the fabrication variation on the waveguide widths can affect its performance. Additionally, we demonstrate that using wide waveguides efficiently leads to a fabrication-tolerant device. This work could further pave the way towards a mature silicon-based FTS operating with both broad bandwidth (over 60 nm) and high resolution suitable for integration with various mobile platforms.

Design of Weakly-Coupled 16-Vector-Mode Coaxial Bragg FMF for Short-Haul Communication

Utilizing weakly-coupled few-mode-fibers (FMFs) for MIMO-DSP eliminating in short-haul mode division multiplexing(MDM) systems has attracted much attention recently, as an effective solution to suppress modal crosstalk. In this article, we propose a weakly-coupled 16-vector-mode coaxial Bragg FMF supporting 16 vector modes(HE11a, HE11b, TM01, HE21a, HE21b, TE01, HE31a, HE31b, EH11a, EH11b, HE12a, HE12b, EH21a, EH21b, HE41a, HE $_{\mathrm {41b}}$ ) which works across the C-band and explore the possibility for weakly-coupled Bragg FMFs. We optimize the geometric parameters and evaluate their effects on modal $n_{eff}$ , min $\Delta n_{eff}$ , and $A_{eff}$ . The DMD, modal confinement loss and bending loss are also investigated. The simulation results indicate that the proposed fiber can obtain large min $\Delta n_{eff}$ between adjacent vector modes ( $\sim 2\times 0.0001$ ), and can be a promising candidate for MIMO-DSP simplified short-haul MDM transmission systems.

Prototype system for real-time IM/DD MDM transmission based on multiple-ring-core FMF and degenerate-mode-selective reception.

Multiple-input-multiple-output digital signal processing (DSP) has become a severe bottleneck for mode division multiplexing (MDM) because of its huge computational complexity. In this paper, we propose a novel scheme for real-time DSP-free intensity-modulation/direct-detection (IM/DD) MDM transmission, in which the transmission few-mode fiber (FMF) is characterized by multiple-ring-core structure to suppress modal crosstalk among each LP mode, while each pair of non-circularly-symmetric degenerate modes is simultaneously demultiplexed by a degenerate-mode-selective fiber coupler for DSP-free reception. Based on a 10 km ultralow-modal-crosstalk double-ring-core FMF and a pair of all-fiber 4-LP-mode MUX/DEMUX, we demonstrate the first IM/DD MDM prototype system using commercial single-mode (SM) 10 Gbps SFP + modules and 4K video transceivers without any hardware modifications. The temperature and wavelength dependence are evaluated. The stable Q2-factor performance proves that it can be a smooth evolution scheme from conventional SM IM/DD systems. Moreover, the scheme can be further extended to support more modes with improved FMF design adopting more ring areas.

A compact silicon-based TM0-to-TM2 mode-order converter using shallowly-etched slots

Mode-order converter is a pivotal component in the on-chip multimode optical transmissions with different mode orders. In this work, we propose a compact and highly-efficient TM0-to-TM2 mode-order converter using shallowly-etched rectangular slots on the silicon-on-insulator platform. The proposed device consists of four same shallowly-etched slots in symmetrical arrangements (two by two) along the light propagation direction and a smaller one between them, which can change the refractive index distribution of the silicon waveguide and add accumulated phase difference through light propagation. With detailed optimizations, we realize the efficient mode conversion from input TM0 mode to output TM2 mode, which is different from some reported TE-polarized mode-order converters, and the insertion loss and conversion efficiency of the present device are 0.21 dB and 94.3%, respectively, in a total device length of only 8.97 μm. Meanwhile, the modal crosstalk is lower than −15 dB and the bandwidth can be extended to ∼100 nm. We believe this device could be applied in the on-chip multimode optical transmission systems with different mode orders to further improve the link capacity.

On-chip silicon dual-mode multiplexer via a subwavelength grating-based directional coupler and a mode blocker.

An on-chip silicon dual-mode multiplexer (MUX) is proposed via a subwavelength grating (SWG)-based directional coupler and a mode blocker. The proposed mode MUX is optimized by utilizing the three-dimensional full-vectorial finite-difference time-domain-based band structure and propagation calculations. The simulated results indicate that an ultralow mode cross talk of $ - {40}\,\,{\rm dB}$-40dB at the operating wavelength of 1550 nm can be achieved by introducing a ${{\rm TE}_0}$TE0 mode blocker. Benefiting from the triple SWG coupler, the mode-coupling strength can be significantly enhanced inside the proposed mode MUX, which can achieve a compact coupling length of 8.75 µm, a low insertion loss of 0.39 dB at 1550 nm, an ultrabroad bandwidth of 310 nm for the mode CT $ \lt - {15.0}\,\,{\rm dB}$<-15.0dB, and insensitivity to fabrication errors.

Adapting Mach–Zehnder Mesh Equalizers in Direct-Detection Mode-Division-Multiplexed Links

A Mach–Zehnder mesh (MZM), which is comprised of a network of tunable $2\times 2$ Mach–Zehnder interferometers and embedded photodetectors (PDs), can be used to perform arbitrary unitary matrix multiplications in the optical domain and compensate modal crosstalk in short-reach mode-division-multiplexed (MDM) links that use direct detection (DD). MZMs can be adapted using a self-configuration method, proposed by Miller, where multiple low-speed and low-power code sequences are superimposed on parallel high-speed information streams. We show that self-configuration in its original form is a sub-optimal equalization method for high-speed data transmission because adaptation based on detected code strengths is adversely impacted by low measurement signal-to-noise ratios and interference from the high-speed information streams. These impairments prevent the method from accurately tracking the millisecond-timescale modal dynamics of short-reach DD-MDM channels. We propose small modifications to the self-configuration method that can enable the MZM to track up to $10^8$ -fold faster channel dynamics. In particular, we show that replacing continuous equalization of low-power code sequences by periodic equalization of full-power training signals and using special optimization methods can yield faster MZM tuning. We also discuss the tradeoffs between MZM architectures that embed PDs inside the mesh and those that have PDs at the output ports only. Our results indicate that optimally designed MZMs and their associated control methods can increase the information capacity of short-reach multimode optical fiber links.

Mode- and wavelength-multiplexed transmission with crosstalk mitigation using a single amplified spontaneous emission source

We propose to use the low-coherence property of amplified spontaneous emission (ASE) noise to mitigate optical crosstalk, such as spatial, polarization, and modal crosstalk, which currently limits the density of photonic integration and fibers for dense space-division multiplexing. High optical crosstalk tolerance can be achieved by ASE-based low-coherence matched detection, which avoids dedicated optical lasers and uses spectrally filtered ASE noise as the signal carrier and as a matched local oscillator. We experimentally demonstrate spatial and modal crosstalk reduction in multimode fiber (MMF) and realize mode- and wavelength-multiplexed transmission over 1.5-km MMF supporting three spatial modes using a single ASE source. Performance degradation due to model dispersion over MMF is experimentally investigated.

Analysis of direction-decomposed and vector-based elastic reverse time migration using the Hilbert transform

Straightforward implementations of elastic reverse time migration (ERTM) often produce imaging artifacts associated with incorrectly imaged mode conversions, crosstalk, and back-scattered energies. To address these issues, we introduced three approaches: (1) vector-based normalized crosscorrelation imaging conditions (VBNICs), (2) directional separation of wavefields to remove low-wavenumber noise, and (3) postimaging filtering of the dip-angle gathers to eliminate the artifacts caused by nonphysical wave modes. These approaches are combined to create an effective ERTM workflow that can produce high-quality images. Numerical examples demonstrate that, first, VBNICs can produce correct polarities for PP/PS images and can compute migrated dip-angle gathers efficiently by using P/S decomposed Poynting vectors. Second, they achieve improved signal-to-noise and higher resolution when performing up/down decomposition before applying VBNICs, and left/right decomposition enhances steep dips imaging at the computational cost of adding the Hilbert transform to a spatial direction. Third, dip filtering using slope-consistency analysis attenuates the remaining artifacts effectively. An application of the SEG advanced modeling program (SEAM) model demonstrates that our ERTM workflow reduces noise and improves imaging ability for complex geologic areas.

Ultrabroadband and fabrication-tolerant mode (de)multiplexer using subwavelength structure

An ultrabroadband and fabrication-tolerant mode (de)multiplexer [(De)MUX] is proposed and optimized by inserting subwavelength gratings (SWGs) into a three-waveguide coupler (TWC). The coupling strength can be dramatically enhanced, benefitting from both the SWG and TWC structures. The proposed mode (De)MUX is optimized using a three-dimensional, full-vectorial finite difference time domain based band diagram and propagation analyses. The simulated results indicate that the optimal mode (De)MUX is with a compact coupling length of 14.75 µm, a low loss of 0.64 dB, and a low mode crosstalk of $ - 31.7\,\,{\text{dB}}$−31.7dB at the operating wavelength of 1.55 µm. With the mode crosstalk $ \lt - 15.0\,\,{\text{dB}}$&lt;−15.0dB, an ultrabroad bandwidth of 312 nm and a relaxed fabrication tolerance of $ - 42.7\,\,{\text{nm}}$−42.7nm to $ + 36.5\,\,{\text{nm}}$+36.5nm can be achieved. The 3 dB bandwidth is over 320 nm and the insertion loss is less than 1.6 dB for a $ \pm 50 \,\,{\text{nm}}$±50nm width change.

Design Analysis of OAM Fibers Using Particle Swarm Optimization Algorithm

We study the design of ring core fibers (RCFs) supporting orbital angular momentum (OAM) modes for mode division multiplexing (MDM) transmission systems. We develop target criteria to optimize fiber designs using a particle swarm optimization (PSO) algorithm under fabrication constraints. Effective index separation Δ neff and polarization purity of each OAM mode are known to determine modal crosstalk levels. To reduce the complexity of multiple-input multiple-output (MIMO) processing required to compensate for modal crosstalk, we define an objective function based on these quantities. Our design analysis focuses on four different concepts of step-index RCF leading to different modal and structural characteristics. The optimum design for each concept is derived using the PSO algorithm. We investigate the impact of hollow-core and/or higher-order radial modes on Δ neff and polarization purity. Design strategies for increasing Δ neff and polarization purity are discussed in light of robustness to fabrication errors. We finally discuss the scalability and potential limitations of this design.

A Design Guideline for Mode (DE) Multiplexer Based on Integrated Tapered Asymmetric Directional Coupler

A tapered asymmetric directional coupler is considered as a promising structure for high tolerance and efficient on-chip mode (de)multiplexers. However, the optimum geometry parameters selection still remains empirical without specific numerical guidance. Here, an in-depth analysis has been carried out based on coupling mode theory. A theoretical model is built aiming to combine the consideration of device efficiency, mode crosstalk and fabrication tolerance. According to that, mode (de)multiplexers (TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_0$</tex-math></inline-formula> -TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_1$</tex-math></inline-formula> , TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_0$</tex-math></inline-formula> -TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_2$</tex-math></inline-formula> , TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_0$</tex-math></inline-formula> -TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_1$</tex-math></inline-formula> , TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_0$</tex-math></inline-formula> -TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_2$</tex-math></inline-formula> ) with broad operation wavelength (C + L band) and low mode crosstalk (minimum −30 dB) are fabricated. The proposed theoretical model can serve as a guideline for the design and optimization of the tapered ADC based mode (de)multiplexers.

Modal crosstalk in Silicon photonic multimode interconnects.

We investigate modal crosstalk in silicon photonic MDM-based interconnects using tapered multiplexers. Crosstalk from coherent optical interference originates from variation in the physical structure and alters the transmission link performance. Through simulations and experimental work, optical crosstalk as a function of wavelength is analyzed to understand its impact in MDM and MDM-WDM dual-multiplexing applications. The detrimental effects are validated in the frequency and time domains through fabricated MDM interconnects of various lengths. Results indicate modal crosstalk must be < -22 dB to maintain a BER of 10-12. The experimental methodology assesses the optical modal crosstalk's impact on the data, towards a mitigation approach to improve the payload signal integrity and enable system-level optimization such as channel wavelength allocation.

Wavefront superposition method for accurate and efficient mode conversion

A wavefront superposition (WS) method is proposed for accurate and efficient mode conversion in mode-division multiplexing transmission. The WS method converts an input beam to the WS state, which is composed of the conversion target and radiation modes of a few-mode fiber. The appropriate weighting for the modal component of the WS state enables more efficient conversion than the conventional method in which the output beam consists only of the conversion target. Further, since the components of the radiation modes in the output are eliminated by the mode-filtering property of the few-mode fiber, no modal crosstalk occurs in the WS method. We examine the conversion performance of the WS method by a numerical simulation for the mode-multiplexing numbers 3, 6, 10, and 15. The WS method shows a 2.4dB higher efficiency than the conventional method, whilemaintaining an extremely low modal crosstalk (less than -80 dB), even when the number of multiplexed modes is 15.

Spiral spectrum of a Laguerre-Gaussian beam propagating in anisotropic non-Kolmogorov turbulent atmosphere along horizontal path.

Close to the ground, it is generally known that atmospheric turbulence exhibits strong anisotropy, which affects the performance of applications such as free-space optical (FSO) communication. In this paper, we establish a theoretical model for calculating the spiral spectrum, also called the orbital angular momentum (OAM) spectrum, of a Laguerre-Gaussian (LG) beam after propagation through anisotropic turbulence along a horizontal link. This model isolates the effects of anisotropy from other parameters of the turbulence. On the basis of this model, the effects of the anisotropy on the probability density of the OAM spectrum and its corresponding modal crosstalk are studied through numerical examples. Our simulation results show that the width of the OAM spectrum will increase or slightly decrease depending on the specific nature of the anisotropy. In addition, it is demonstrated that the inner scale is more likely to cause modal crosstalk than the outer scale. Some strategies to reduce modal crosstalk in anisotropic turbulence are also discussed. Our results may be useful in OAM-based FSO communication at ground level.

Mode-sorter design using continuous supersymmetric transformation.

We propose to use a continuous supersymmetric (SUSY) transformation of a dielectric permittivity profile in order to design a photonic mode sorter. The iso-spectrality of the SUSY transformation ensures that modes of the waveguide preserve their propagation constants while being spatially separated. This global matching of the propagation constants, in conjunction with the adiabatic modification of the refractive index landscape along the propagation direction, results in the negligible modal cross-talk and low scattering losses in the sorter. We show that a properly optimized SUSY mode sorter outperforms a standard asymmetric Y-splitter by reducing the cross-talk by at least two orders of magnitude. Moreover, the SUSY sorter is capable of sorting either transverse-electric or transverse-magnetic polarized modes and operates in a broad range of wavelengths. At the telecommunication wavelength, the 300-μm-long SUSY sorter provides the cross-talk of -35 dB and a broad operation bandwidth. The design proposed here paves the way toward efficient signal manipulation in integrated photonic devices.

Ultracompact and broadband asymmetric directional-coupler-based mode division (de)multiplexer

This paper presents an ultracompact, low-loss, and broadband two-mode division (de)multiplexer. The device structure is based on a two-waveguide asymmetric directional coupler. By maximizing the effective index difference of the even and odd supermodes through proper design of the geometrical parameters of the waveguides, the coupling length without taking the S-bend into account is obtained as 1.4 μm. This is the shortest coupling length, to the best of our knowledge, for transverse-electric modes in mode (de)multiplexers reported until now. In addition to reducing the footprint, this structure improves the mode conversion efficiency while maintaining low-loss and low-crosstalk behavior. The three-dimensional finite-difference-time-domain simulation results show that at the wavelength of 1.55 μm, the mode conversion efficiency, crosstalk, and insertion loss are 99.86%, −32.7 dB, and −0.49 dB, respectively. Simulation results also demonstrate that the proposed mode (de)multiplexer exhibits low crosstalk of less than −11 dB over a broad bandwidth of 100 nm around the central wavelength of 1.55 μm.

Compact six-mode (de)multiplexer based on cascaded asymmetric Y-junctions with mode rotators

A silicon waveguide mode (de)multiplexer is theoretically proposed for compact on-chip mode (de)multiplexing (MDM). The (de)multiplexing of E11y, E21y, E31y, E12y, E22y and E32y modes is realized by cascading asymmetric Y-junctions and the E21y∕E12y mode rotators. Beam propagation method is adopted in the design and optimization. For a 124 μm-long device, the mode crosstalk among all channels is less than -24 dB. The insertion loss can be lowered to 0.96 dB at optical wavelength of 1550 nm. This proposed design method can be extended to the construction of higher-order mode (de)MUX.

A 6-LP-mode ultralow-modal-crosstalk double-ring-core FMF for weakly-coupled MDM transmission

Weakly-coupled mode division multiplexing (MDM) technique based on few mode fiber (FMF) with low linear-polarized (LP) modal crosstalk is promising for capacity enhancement of short-reach transmission. In this paper, we propose a double-ring-core FMF for simultaneous 6-LP-mode weakly-coupled MDM transmission. FMF with ring-core structure is theoretically analyzed by deriving from a step-index circular-core FMF with perturbed ring areas. Then simplified method is proposed to define boundaries of ring areas in FMF and increase the minimum effective refractive index difference (min|Δneff|) among all the modes. Fabricated by commercial fabrication technique, the FMF achieves a min|Δneff| up to 1.49×10−3 while its maximum Δn between core and cladding is only 0.828%, which greatly reduces the difficulty of fiber fabrication. Thanks to the ultralow modal crosstalk of the FMF, we successfully demonstrate simultaneous 6-LP-mode (LP01, LP11, LP21, LP02, LP31 and LP12) 4-wavelength 71-km weakly-coupled MDM transmission using 10 Gb/s optical on-off-keying (OOK) intensity modulation and direct detection (IM/DD) without any digital signal processing (DSP). The design method can be extended to weakly-coupled FMFs with more ring areas.