Multiple-input Multiple-output Digital Signal Processing Research Articles

Empowering high-dimensional optical fiber communications with integrated photonic processors

Mode-division multiplexing (MDM) in optical fibers enables multichannel capabilities for various applications, including data transmission, quantum networks, imaging, and sensing. However, high-dimensional optical fiber systems, usually necessity bulk-optics approaches for launching different orthogonal fiber modes into the optical fiber, and multiple-input multiple-output digital electronic signal processing at the receiver to undo the arbitrary mode scrambling introduced by coupling and transmission in a multi-mode fiber. Here we show that a high-dimensional optical fiber communication system can be implemented by a reconfigurable integrated photonic processor, featuring kernels of multichannel mode multiplexing transmitter and all-optical descrambling receiver. Effective mode management can be achieved through the configuration of the integrated optical mesh. Inter-chip MDM optical communications involving six spatial- and polarization modes was realized, despite the presence of unknown mode mixing and polarization rotation in the circular-core optical fiber. The proposed photonic integration approach holds promising prospects for future space-division multiplexing applications.

Design of Multilayered Ring-Core Fiber With Low-Level Inter-Group Crosstalk

We propose a novel ring-core fiber (RCF) with multilayered ring core and modulated refractive index profile (RIP). The simulated results indicate that such a special fiber design is able to support 5 orbital angular momentum (OAM) mode groups (18 OAM modes) with crosstalk between any two high-order adjacent mode groups (MGs) less than -28 dB/km over the whole C and L band. At the wavelength of 1550 nm, crosstalk between the two highest-order MGs is below -36 dB/km. Besides, with the limitation of the existing manufacturing restriction, the geometric size and doping concentration of the designed fiber are allowable and reasonable, which is promising for practical manufacturing. The designed RCF also shows good bending characteristics. Moreover, ultra-broadband performance is analyzed over the whole C + L band ranging from 1530 nm to 1625 nm. This kind of fiber design could be employed in small-scale multiple-input multiple-output digital signal processing (MIMO-DSP) assisted intra-group modes multiplexing transmission or MIMO-free inter-group modes multiplexing transmission combined with the mature wavelength-division multiplexing technique.

Weakly guiding graded-index ring-core fiber supporting 16-channel long distance mode division multiplexing systems based on OAM modes with low MIMO-DSP complexity.

We propose a weakly guiding graded-index ring-core fiber (RCF) with trench-assisted structure. The simulation analysis indicates that such a special fiber design is able to support 8 orbital angular momentum (OAM) mode groups (MGs) with low inter-group crosstalk (< -25 dB/km) and low intra-group differential mode delay (DMD) (< 125 ps/km) for higher order OAM MGs with topological charge |l| = 4, 5, 6, 7. The designed RCF also shows favorable tolerance characteristics to ellipticity and bending. Moreover, stable and distinguished broadband performance of proposed RCF is verified over the whole C band ranging from 1530 nm to 1565 nm. This kind of fiber design could be employed in small-scale multiple-input multiple-output digital signal processing (MIMO-DSP) intra-group modes multiplexing transmission combined with MIMO-free inter-group mode multiplexing transmission. The simulated results of the designed RCF show its great potential of the 16-channel long-distance mode division multiplexing (MDM) transmission with low MIMO-DSP complexity.

Demonstration of 10-channel mode- and polarization-division multiplexed free-space optical transmission with successive interference cancellation DSP.

We experimentally demonstrate 10-channel mode-division multiplexed free-space optical transmission with five spatial modes, each carrying 19.6925-Gbaud dual-polarization quadrature phase shift keying signals. Strong inter-mode cross talk is observed in our commercially available photonic lantern based system when using a complete orthogonal mode set as independent channels. A successive interference cancellation based multiple-input multiple-output digital signal processing (DSP) algorithm is first applied to mitigate the inter-mode cross talk in mode-division multiplexed systems. The DSP also supports unequal transmit and receive channel numbers to further improve the cross talk resiliency. Compared to the conventional minimum mean square error DSP, the required optical signal-to-noise ratio of the successive interference cancellation DSP is decreased by approximately 5 dB at the hard-decision forward error correction limit. As a result, this system demonstrates a record-high independent channel number of 10 and spectral efficiency of 13.7 b/s/Hz in mode-division multiplexed free-space optical systems.

Long-Haul Coupled 4-Core Fiber Transmission Over 7,200 Km With Real-Time MIMO DSP

In this work, we present an experimental demonstration of real-time transoceanic space-division multiplexed transmission with coupled-core multicore fibers. To compensate for modal coupling in the coupled-core multicore fibers, we implement real-time multiple-input multiple-output (MIMO) digital signal processing based on field programmable gate array circuits. Using optical receivers with a real-time MIMO, we demonstrate 16-channel wavelength-division multiplexed coupled four-core fiber transmission over 7200 km. The results show the feasibility of real-time coupled-core multicore fiber transmission.

Long-haul intermodal-MIMO-free MDM transmission based on a weakly coupled multiple-ring-core few-mode fiber.

Mode-division multiplexing (MDM) technique based on few-mode fibers (FMFs) can achieve multiplicative growth in single-fiber capacity by using different linearly polarized (LP) modes or mode groups as spatial channels. However, its deployment is seriously impeded because multiple-input multiple-output digital signal processing (MIMO-DSP) with huge computational load must be adopted to combat intermodal crosstalk for long-haul FMF transmission. In this paper, we present an intermodal-MIMO-free MDM transmission scheme based on weakly coupled multiple-ring-core FMF, which achieves ultralow distributed modal crosstalk (DMC) so that the signal in each LP mode can be independently received by single-LP-mode MIMO-DSP even after hundreds-of-kilometer transmission. Evaluation method for the required DMC levels is proposed and different transmission reaches are investigated by simulation. By adopting an improved method for quantitative DMC measurement, we show that the required DMC level for long-haul transmission is feasible. Finally, we experimentally demonstrate 1800-km LP01/LP02 multiplexed transmission and 525-km LP01/LP21/LP02 multiplexed transmission only adopting 2×2 or 4×4 MIMO-DSP. The proposed scheme may pave the way to practical applications of long-haul MDM techniques for the first time.

A novel microstructured polymer tube for THz vortex beams guidance

A novel microstructured polymer tube (MPT) incorporating a central hollow, ring core, porous outer cladding is proposed for terahertz (THz) orbital angular momentum (OAM) guidance, focusing on the enhancement of the quantity of modes and bandwidth. The proposed MPT can support 70 modes (66 THz OAM ones) with large mode effective refractive index separation (>2.197×10−3) over 0.6∼1.25 THz while maintaining single-mode condition radially, and the number of guiding modes can be further increased by properly equiproportional enhancing the size of the tube. Besides, the designed MPT has strong confinement property, high purity (>97.06%), and flat dispersion over the whole operating bandwidth. The result of this work reveals that this kind of MPT is promising to accelerate the development of the compact, light-weight THz communication system, and can be applied in OAM-based mode-division multiplexing combined with wavelength-division multiplexing technique without multiple-input multiple-output digital signal processing.

Design of steering wheel-type ring depressed-core 10-mode fiber with fully improved mode spacing.

We present a steering wheel-type ring depressed-core few-mode fiber (SWTR-DC-FMF) that features a central depressed step-index core and a novel SWTR structure consisted of two symmetrical high-index parts and low-index parts, respectively. The DC and SWTR make great contribution to separate the non-degenerated LP modes and spatial modes in the circular symmetry core, resulting in fully improved mode spacing. The designed fiber is able to support 10 spatial modes with the minimum effective index difference (Min Δneff) between adjacent spatial modes larger than 1.93 × 10-4 and the Min Δneff between adjacent LP modes above 1.51 × 10-3 at the same time, facilitating potential fiber spatial mode multiplexing transmission with less multiple-input multiple-output (MIMO-less) digital signal processing technique. The broadband performance including neff, Δneff, effective mode area (Aeff) and differential mode delay (DMD) is comprehensively investigated over the whole C and L band. Moreover, the birefringence and fabrication tolerance are discussed. The designed fiber targets emerging applications in short-reach weakly coupled space-division multiplexing (SDM) optical networking to increase transmission capacity and spectral efficiency and further reduce the system complexity effectively.

Weakly coupled 10-mode-division multiplexed transmission over 48-km few-mode fibers with real-time coherent MIMO receivers

For weakly coupled mode-division multiplexed (MDM) transmission systems, we design and implement optical coherent receiver prototypes with real-time multiple-input multiple-output (MIMO) digital signal processing to equalize two degenerate linearly polarized modes with dual polarization. Using field programmable gate array circuits, we implement real-value 8 × 2 MIMO adaptive equalization with externally separated phase compensators based on the least mean square algorithm, which enables not only training equalization but also fast carrier-phase tracking. With the optical coherent MIMO receiver prototype, we demonstrate real-time weakly coupled 10 × MDM wavelength-division multiplexed dual-polarization quadrature phase shift keying transmission over 48-km few-mode fibers. This report shows a record number of multiplexed spatial modes, namely, 10 modes with dual polarization, in real-time MDM transmission experiments.

Bend-Insensitive Grapefruit-Type Holey Ring-Core Fiber for Weakly-Coupled OAM Mode Division Multiplexing Transmission

We propose a bend-insensitive grapefruit-type holey ring-core fiber to support orbital angular momentum (OAM) modes. The large air domain in the cladding, results in a large refractive index contrast between the ring-core and the cladding, which makes this fiber bend-insensitive and makes the vector eigenmodes well separated. Therefore, the proposed fiber can be adopted for the OAM mode division multiplexing transmission without the use of any multiple-input multiple-output digital signal processing (MIMO-DSP). It is also proved that the thickness of the outer silica layer around the ring-core plays an important role in confining the light. If the OAM modes in the ring-core and the cladding modes in the outer silica layer are not phase-matched, the OAM modes in the ring-core will not be coupled into the outer layer of silica and can be well confined. We fabricate such fiber in two steps by using the “stack-and-draw” method. Two kinds of fibers with different thicknesses of the outer silica layer are fabricated under different pressures and temperatures. The testing results of the fabricated fiber demonstrate the mode purity and illustrate that the loss of the OAM $_{+1,1}$ and OAM $_{+2,1}$ modes are 0.095 dB/m and 0.25 dB/m, respectively.

402.7-Tb/s MDM-WDM Transmission Over Weakly Coupled 10-Mode Fiber Using Rate-Adaptive PS-16QAM Signals

The mode-division-multiplexing (MDM) transmission technique using a few-mode fiber (FMF) has been investigated to overcome the theoretical limitation of the transmission capacity of a single-mode fiber. In MDM transmission, multiple-input multiple-output (MIMO) digital signal processing (DSP) is generally required on the receiver side to compensate for the modal crosstalk (XT) between the spatial modes. However, the computational cost is high, especially for high-order MDM systems that use many spatial modes. To reduce the MIMO matrix size, MDM transmission with partial MIMO-based DSP has been proposed using weakly coupled FMFs. The modal XT in such fibers can be suppressed by a special fiber design; however, the modal XT still remains and strongly limits the signal-to-noise-ratio (SNR) and capacity. To further increase the capacity for a given SNR, an optimization of the modulation format is significant. Recently, probabilistic shaping (PS) has received attention since it can gradually change the entropy of a modulation format and maximize the capacity for a given SNR. In this article, we demonstrate weakly coupled 10-mode-multiplexed transmission with four 4 × 4 MIMOs and two 2 × 2 MIMOs using rate-adaptive PS-16QAM signals over 48-km FMF, achieving a record transmission capacity of 402.7 Tb/s in 125-μm cladding single-core fiber transmission experiments. Furthermore, we also show the possibility of a further capacity increase by adjusting the entropies of the PS-16QAM signals depending on the spatial mode.

OAM mode multiplexing in weakly guiding ring-core fiber with simplified MIMO-DSP.

We present a low-loss weakly guiding ring-core fiber for orbital angular momentum (OAM) mode group multiplexing (MGM) transmission. This special fiber design supports 50 radially fundamental modes divided into 13 mode groups with only 0.7% relative refractive index difference between the fiber ring core and cladding. Except the first two groups with 10-5 mode spacing, the other mode groups are separated with each other with effective refractive index difference (Δneff) larger than 10-4, indicating relatively low-level inter-group crosstalk. One can directly use different OAM mode groups for MGM communications without multiple-input multiple-output digital signal processing (MIMO-DSP) technique. Besides, one can employ different OAM modes among the same mode group to carry different data information assisted by small-scale MIMO technique. The target fiber exhibits small and flat dispersion within (14.3, 39.7) ps/nm/km which is comparable to that in the standard single-mode fiber (SMF), and extremely large mode area within (787.9, 841.2) µm2 over the whole C + L band. MIMO equalization complexities for modified small-scale MIMO-DSP assisted intra-group modes multiplexing combined with MIMO-free inter-group modes multiplexing method in both time and frequency domain are much simpler compared to traditional 50×50 MIMO equalization.

Propagation characteristics of orbital angular momentum modes at 810 nm in step-index few-mode fibers

In free-space or in optical fibers, orbital angular momentum (OAM) multiplexing for information transmission has been greatly developed. The light sources used were well coherent communication bands, and the fibers used were customized. Here, we use an 810 nm femtosecond laser to generate optical vortices carrying OAM and then feed them into two kinds of commercial step-index few-mode fibers to explore the transmission characteristics of OAM modes. We also propose a method without multiple-input multiple-output digital signal processing to identify the input OAMs. It is of great guiding significance for high-dimensional quantum information experiments via the OAMs as a degree of freedom, using the light generated by the spontaneous parametric down-conversion as the source and the commercial fibers for information transmission.

Panda type elliptical core few-mode fiber

Mode division multiplexing together with multiple-input multiple-output digital signal processing (MIMO-DSP) has the potential for fulfilling future ever-increasing transmission capacity demand. However, for the mitigation of severe mode coupling, the cost and computation complexity of MIMO-DSP become prohibitive with the growing numbers of guided modes arising in the traditional circular core few-mode fiber. We design, fabricate, and characterize panda type elliptical core few-mode fiber (PE-FMF) supporting six eigenmodes of LP01x, LP01y, LP11ax, LP11ay, LP11bx, and LP11by independent transmission. Such PE-FMF, with both low refractive index difference of 0.006 between the core and the cladding and low ellipticity of 1.449, can alleviate the trade-off between the eigenmode numbers and the desirable mode spacing occurring in traditional elliptical-core FMF design. The numerical results indicate that the minimal mode spacing among six eigenmodes is above 1.95 × 10−4 over the whole C + L band. The maintaining capability of both mode intensity profile and polarization is experimentally verified, when the PE-FMF is under a twisting rate range from 0 to 1.57 rad/m. During the fiber twisting, the mode intensity profile can be maintained and the polarization extinction ratio of individual eigenmode is above 20 dB over 50 m PE-FMF.

Design of PANDA-type elliptical-core multimode fiber supporting 24 fully lifted eigenmodes.

We present a novel PANDA-type elliptical-core multimode fiber featured by the combination of an elliptical core and two symmetrical circular stress-applying parts (SAPs). The characterization results indicate that such a special fiber design is able to support 24 fully separated eigenmodes with minimum effective index difference (min(Δneff)) between adjacent modes larger than 1.35×10-4 over the whole C band. Specifically, the fiber geometric dimensions and doping concentrations are deviation tolerant and reasonable within the existing fiber manufacture facility restriction, thus would be promising for practical fabrication. The fiber bending effects are also investigated based on conformal mapping. Moreover, ultra-broadband performance is analyzed over the whole C+L band ranging from 1530nm to 1625nm. The designed fiber is targeted at applications in direct fiber vector eigenmode-division multiplexing combined with the mature wavelength-division multiplexing technique while eliminating the complex multiple-input multiple-output digital signal processing.

Route, Modulation Format, MIMO, and Spectrum Assignment in Flex-Grid/MCF Transparent Optical Core Networks

In this paper, we target an optimal multiple-input multiple-output digital signal processing (MIMO-DSP) assignment to super-channels affected by intercore crosstalk (ICXT) in multicore fiber (MCF) enabled transparent optical core networks. MIMO-DSP undoes ICXT effects, but can be costly with high core density MCFs. Hence, its implementation in the network must be carefully decided. We address our objective as a joint route, modulation format, MIMO and spectrum assignment (RMMSA) problem, for which integer linear programming formulations are provided to optimally solve it in small network scenarios. Moreover, several heuristic approaches are also proposed to solve large-scale problem instances with good accuracy. Their goal is to minimize both network spectral requirements and the amount of MIMO equalized super-channels, taking a crosstalk-free space division multiplexing (SDM) solution as a reference, for example, based on parallel single mode fibers [i.e., a multifiber (MF) scenario]. For our evaluation, we consider several state-of-the-art MCF prototypes and different network topologies. The obtained results, with the considered MCFs, disclose that in national backbone networks, the desirable percentage of super-channels with MIMO equalization to match the performance of an equivalent crosstalk-free SDM solution ranges from 0% to 36, while in continental-wide networks this range raises from 0% to 56%. In addition, in the case of a nonideal MIMO (with a 3 dB/km of crosstalk compensation), such percentages range from 0% to 28% and from 0% to 45% in national and continental-wide backbone networks, respectively, experimenting a performance gap up to 12% with respect to the MF reference scenario.

Fully degeneracy-lifted bow-tie elliptical ring-core multi-mode fiber.

We present a bow-tie elliptical ring-core multi-mode fiber (BT-ERC-MMF) that features an elliptical ring-core structure and two symmetrical bow-tie stress-applying parts (SAPs). This special fiber design breaking geometry and stress symmetry fully separates the two- or four-fold degenerate modes in traditional circular symmetry fiber with strong mode coupling during mode-division multiplexing (MDM) transmission. The designed fiber is able to support 53 fully degeneracy-lifted eigenmodes with minimum effective index difference between adjacent modes larger than 1.59 × 10-4 at 1550 nm, facilitating potential fiber eigenmode multiplexing transmission without using multiple-input multiple-output digital signal processing (MIMO-DSP) technique. The effect of bending on the designed fiber is investigated based on conformal mapping. Broadband performance including effective modal index (neff), effective index difference (Δneff), effective mode area (Aeff), nonlinearity and chromatic dispersion (D) is also comprehensively studied over the whole C band ranging from 1530 to 1565 nm. The designed fiber targets emerging applications in low-crosstalk direct fiber eigenmode-division multiplexing combined with the mature wavelength-division multiplexing (WDM) technique to increase transmission capacity and spectral efficiency.

DD-OFDM transmission over few-mode fiber based on direct vector mode multiplexing.

The fiber vector eigenmode based mode division multiplexing (VMDM) transmission over few-mode fiber (FMF) with the 1st-order cylinder vector beams (CVBs) has been demonstrated. The performances of generated CVB using q-plate (QP) have been characterized before and after transmission over the FMF respectively based on the high-order Poincaré sphere model and polarization grating (PG). The measured minimum mode isolations between the two CVBs (TM01 and TE01 modes) of the used 4-mode FMF are about 16.8 dB after transmitting over 5 m and 12.5 dB over 100 m respectively. Then the dual-vector-mode-multiplexed transmissions over FMF of 96 Gb/s with length of 5m and 48 Gb/s of 100 m have been realized in combination with the modulation of direct-detection (DD) orthogonal-frequency-division-multiplexing (OFDM) without using multiple-input multiple-output (MIMO) digital signal processing (DSP). The experimental results indicate that the CVB-based technology could find the potential in large-capacity short-reach optical interconnects.

18 km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation.

The space domain is regarded as the only known physical dimension of lightwaves left to be exploited for optical communications. Very recently, much research effort has been devoted to using orbital angular momentum (OAM) spatial modes to increase the transmission capacity in fiber-optic communications. However, long-distance low-crosstalk high-order OAM multiplexing transmission in fiber is quite challenging. Here we design and fabricate a graded-index ring-core fiber to effectively suppress radially high-order modes and greatly separate high-order OAM mode groups. By exploiting high-order OAM mode group multiplexing, together with wavelength-division multiplexing (WDM), i.e., 12.5Gbaud 8-array quadrature amplitude modulation (8-QAM) signals over OAM+4 and OAM+5 modes on 112 WDM channels (224 individual channels), we experimentally demonstrate 8.4Tbit/s data transmission in an 18km OAM fiber with low crosstalk. Multiple-input multiple-output digital signal processing is not required in the experiment because of the large high-order mode group separation of the OAM fiber. The demonstrations may open a door to find more fiber-optic communication and interconnect applications exploiting high-order OAM modes.

Orbital angular momentum mode groups multiplexing transmission over 2.6-km conventional multi-mode fiber.

Twisted light carrying orbital angular momentum (OAM) is a special kind of structured light that has a helical phase front, a phase singularity, and a doughnut intensity profile. Beyond widespread developments in manipulation, microscopy, metrology, astronomy, nonlinear and quantum optics, OAM-carrying twisted light has seen emerging application of optical communications in free space and specially designed fibers. Instead of specialty fibers, here we show the direct use of a conventional graded-index multi-mode fiber (MMF) for OAM communications. By exploiting fiber-compatible mode exciting and filtering elements, we excite the first four OAM mode groups in an MMF. We demonstrate 2.6-km MMF transmission using four data-carrying OAM mode groups (OAM0,1, OAM+1,1/OAM-1,1, OAM+2,1, OAM+3,1). Moreover, we demonstrate two data-carrying OAM mode groups multiplexing transmission over the 2.6-km MMF with low-level crosstalk free of multiple-input multiple-output digital signal processing (MIMO-DSP). The demonstrations may open up new perspectives to fiber-based OAM communication/non-communication applications using already existing conventional fibers.