Page 1

High Spectral-Efficiency, Ultra-low

MIMO SDM Transmission over a Field-

Deployed Multi-Core OAM Fiber

Junyi Liu1, †, Zengquan Xu1, †, Shuqi Mo1, †, Yuming Huang1, Yining Huang1,

Zhenhua Li1, Yuying Guo1, Lei Shen2, Shuo Xu2, Ran Gao3, Cheng Du4, Qian

Feng4, Jie Luo2, Jie Liu1,5 *, and Siyuan Yu1

1State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information

Technology, Sun Yat-Sen University, Guangzhou 510006, China.

2Yangtze Optical Fibre and Cable Joint Stock Limited Company, State Key Laboratory of Optical Fibre and Cable

Manufacture Technology, No.9 Guanggu Avenue, Wuhan, Hubei, China.

3School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China.

4Fiberhome Telecommunication Technologies Co. Ltd, Wuhan, 430074, China.

5School of Electronics and Information Technology and Guangdong Provincial Key Laboratory of Optoelectronic

Information Processing Chips and Systems, Sun Yat-sen University, Guangzhou 510006, China

†These authors contributed equally.

*Corresponding author: liujie47@mail.sysu.edu.cn;

Abstract

Few-mode multi-core fiber (FM-MCF) based Space-Division Multiplexing (SDM) systems possess the

potential to maximize the number of multiplexed spatial channels per fiber by harnessing both the space

(fiber cores) and mode (optical mode per core) dimensions. However, to date, no SDM transmissions

over field-deployed FM-MCFs in realistic outdoor settings have been reported, which contrasts with

SDM schemes demonstrated using single-mode multi-core fibers (SM-MCFs) installed in practical fiber

cable ducts. In this paper, we present the successful demonstration of bidirectional SDM transmission

over a 5-km field-deployed seven ring-core fiber (7-RCF) with a cladding diameter of 178 μm, achieving

a Spectral Efficiency (SE) of 2×201.6 bit/s/Hz. This work establishes a new record for the highest SE

attained in SDM demonstrations utilizing field-deployed fiber cables, achieving an approximate 10x

increase compared to the SE of reported field-deployed optical fiber cable transmission systems. Notably,

these results are realized through the utilization of small-scale modular 4×4 multiple-input multiple-

output (MIMO) processing with a time-domain equalization (TDE) tap number not exceeding 15,

maintaining a complexity per unit capacity comparable to that of MIMO equalization in SDM

demonstrations employing weakly coupled SM-MCF cables. These results underscore the significant

potential for achieving heightened SE and expanding capacity per individual fiber using SDM techniques

in practical applications.

Introduction

Due to the rapid development of techniques such as wavelength division multiplexing (WDM), advanced

modulation formats and coherent detection with digital signal processing (DSP), per-fiber capacity

growth of the single-mode fiber (SMF) communication systems has closely tracked the exponential

growth of traffic demand over the past few decades[1]. However, this growth trend is becoming

unsustainable as the SMF capacity approaches its limits imposed by the fiber nonlinear effects[2],

necessitating the development of novel technologies to keep up with traffic demand. In this context,

space-division multiplexing (SDM) techniques[3–15], which explore degrees of freedom in the

transverse spatial domain of optical fibers to enhance the per-fiber capacity and spectral efficiency (SE)

of communication systems, have garnered significant interest in recent years.

Several approaches have been implemented to increase the spatial channel counts and thus the

capacity/SE per fiber in the SDM systems, including mode-division multiplexing (MDM) schemes

utilizing few-mode fibers (FMFs)[3–6], core-multiplexing schemes employing multi-core fibers

(MCFs)[7, 8] and the combination of these two approaches based on few-mode multi-core fibers (FM-

MCFs)[9-13,15]. Compared with the former two schemes, the FM-MCF-based SDM systems can

potentially provide the highest number of multiplexed spatial channels per fiber by simultaneously

utilizing both the optical fiber modes and fiber cores while only require small-scale and, therefore, low-

complexity Multiple-Input Multiple-Output (MIMO) processing to handle the intra-core modal coupling,

as the inter-core coupling can be disregarded when the core pitch is sufficiently large[6].

Laboratory SDM demonstrations utilizing FM-MCFs have shown significant progress in the past few

years, substantially increasing both the per-fiber capacity and SE by orders of magnitude compared with

SMF transmission systems[9, 11, 12, 16–20]. However, to the best of our knowledge, no SDM

transmissions over field-deployed FM-MCFs in a realistic outdoor environment have been reported. This

stands in contrast to SDM demonstrations utilizing single-mode multi-core fibers (SM-MCFs) installed

in practical fiber cable ducts, which have been presented in several publications[21–23].

Fig. 1. SE versus MIMO complexity per unit capacity of the SDM demonstrations utilizing lab-deployed

FM-MCF spools or field-deployed MCF cables (Data points are evaluated based on information reported

from the cited references).

Figure 1 summarizes the SE versus MIMO complexity per unit capacity of recent SDM

demonstrations utilizing lab-deployed FM-MCF spools or field-deployed SM-MCF cables. Here the

SDM demos using fiber

spools in the Lab

SDM demos using

field-deployed

fiber cables

[12]

[11]

[9]

[3]

[18]

[22]

[21]

[20]

[19]

MIMO complexity per unit capacity is expressed as the required number of complex multiplications

(RNCM) per bit [9] (calculation details can be found in Supplement S1). The data indicates that the SE

of SDM transmission over field-deployed SM-MCF cables is considerably lower than that demonstrated

using lab-deployed FM-MCF spools. This discrepancy primarily arises from the fact that FM-MCFs can

provide the highest number of multiplexed spatial channels per fiber by simultaneously utilizing both

multiple fiber cores and multiple fiber modes in each core. High-SE transmission over field-deployed

FM-MCFs demonstrated in a realistic outdoor environment would take SDM techniques to a new stage

towards practical implementations.

In addition to improving SE, several other critical factors must be taken into account for practical

applications of SDM transmission over field-deployed FM-MCF cables. Firstly, given the importance of

managing power consumption and cost for the transceivers, the complexity of MIMO processing, which

addresses inter-SDM-channel crosstalk, should be kept at a minimum level, ideally comparable to that

employed in transmission systems over single-mode fibers or weakly coupled SM-MCFs (e.g., MIMO

complexity per unit capacity calculated according to information in references [8] shown in Fig. 1).

Furthermore, the fiber cladding diameters must be constrained within a specific range to maintain good

mechanical stability and the lifetime of optical fibers and fiber cables. Specifically, under the condition

of a minimum bend radius of 60 mm and 100 turns, the maximum acceptable fiber cladding diameter to

achieve a 1% failure probability over 20 years is 230 μm [24].

In this paper, we present the successful demonstration of SDM transmission over a 5-km field-

deployed seven ring-core fiber (7-RCF) with a cladding diameter of 178 μm, achieving a remarkable SE

of 403.2 bit/s/Hz. To the best of our knowledge, this sets a record for the highest SE achieved in SDM

demonstrations utilizing field-deployed fiber cables. In our demonstration, 84 orbital angular momentum

(OAM) mode channels (7 cores × 6 modes × 2 polarizations) are multiplexed, each carrying 40

wavelengths. By implementing bidirectional transmission in the fiber, the number of channels per-fiber

can be effectively doubled. Utilizing 12-Gbaud 8-quadrature amplitude modulation (8QAM) per data

channel, a raw (net) SE of 2 × 241.92 (2 × 201.6) bit/s/Hz and a capacity of 241.92 (201.6) Tbit/s have

been realized. These results are accomplished solely through the application of modular 4×4 MIMO

processing with a time-domain equalization (TDE) tap number not exceeding 15, whose complexity per

unit capacity is quite comparable to that of the MIMO equalization employed in SDM demonstrations

using weakly coupled (SM-MCF) cables, as illustrated in Fig. 1. Furthermore, we also conduct

experimental analysis to evaluate the effect of Rayleigh Backscattering (RB) on the bidirectional

transmitting signals.

Our demonstration surpasses the SE milestone of 400 bit/s/Hz for SDM transmission systems using

field-deployed fiber cables, representing an approximately 10x increase compared to the SE of reported

field-deployed optical fiber cable transmission systems. It also simultaneously maintains a low MIMO

complexity per unit capacity comparable to that utilized in the SM-MCF based SDM demonstrations,

and features a 7-RCF cladding diameter of less than 200 μm. Therefore, these results underscore the

considerable potential for achieving higher SE and expanding capacity per single fiber through SDM

techniques in practical implementations.

Methods and Experiment

7-RCF cable fabrication and installation

A 5-km fiber optic cable is fabricated with a diameter of 10.7 mm. The cross-sectional views of the

fabricated cable are depicted in Fig. 2(a). Twelve optical fibers each with a diameter of 250 μm are

wrapped in a jelly-filled loose tube made of polyethylene terephthalate acetate plastic, forming a fiber

unit. This fiber unit and other four filling ropes with the same outer diameter are located around the

central metal reinforced core. Two layers of polyethylene are wrapped around the exterior, serving as the

inner liner and outer protective layer of the fiber cable. The twelve optical fibers in the fiber unit can be

categorized into six types, each identifiable by a unique color-coded plastic tape. The specific parameters

of the six types of optical fibers are listed in Table 1. Our primary focus in this study is on the 7-RCF

incorporated in the cable, employed as the transmission fiber in our experimental demonstration. The

cross-section of the 7-RCF is illustrated in Fig. 2(b).

Table 1. Parameters of the optical fibers within the cable

No.

Color

Diameter (𝜇𝑚)

Type

1

Blue/Orange

150

7-core SMF

2

Green/Brown

125

1-core SMF

3

Grey/Red

125

1-core RCF

4

Black/Yellow

125

1-core RCF

5

Purple/Pink

125

1-core RCF

6

Nude/ Black-stripes

178

7-core RCF

Fig. 2. (a) Cross-section diagram of the fabricated 7-RCF cable; (b) Cross-sectional photo of the fabricated

7-RCF;(c) Schematic diagram of the field-deployed fiber cable route;(d) The optical fibers in the fiber

unit; (e) field-deployed fiber cable in a fiber pipeline.

The fabricated fiber cable was deployed in an outdoor environment, and the route is illustrated in Fig.

2(c). The installation commenced at our laboratory, traversing ducts within the State Key Laboratory of

Optoelectronic Materials and Technologies (OEMT) building. Subsequently, the cable was laid in the

underground cable ducts on the Sun Yat-sen University (SYSU) campus. Following the path of the

underground ducts, depicted by the blue line in Fig. 2(c), the cable formed a loop back to the OEMT

building, ultimately reaching back to the laboratory. The total length of the installed fiber cable extended

approximately 5 km, with ~ 4.5 km within the campus underground pipeline and ~ 0.5 km within the

duct of the OEMT building. This configuration allows for experimental setups at both the transmitting

Filling rope

Metal

reinforced core

Outer sheath

Loose tube

10.7 mm

Start & End

Deployed cable

Forward data

Backward data

8-QAM

Data

50 𝜇𝑚

Marker

0

1

2

3

4

5

6

(b)

(a)

(c)

(d)

(e)

Our fiber cable

and receiving ends to be established within the same laboratory setting.

High spectral-efficiency SDM transmission

Fig. 3. Experimental setup. ECL: external cavity laser; AWG: arbitrary waveform generator; EA: electrical

amplifier; EDFA: erbium-doped fiber amplifier; LP: linear polarizer; SLM: spatial light modulator; MR:

mirror; HWP: half-wave plate; BS: beam splitter; QWP: quarter-wave plate; PBS: polarization beam splitter;

PBC: polarization beam combiner; Col.: collimator; VPP: vortex phase plate; ICR: integrated coherent

receiver. The intensity profiles of OAM MGs |l| = (a) 4, (b) 3, and (c) 2 and the phase masks of OAM MGs

|l| = (i) 4, (j) 3, and (k) 2.

The experimental setup of the bidirectional OAM-WDM-SDM data transmission is depicted in Fig. 3.

The setup comprises five main parts: a WDM signal transmitter with 8QAM modulation, an OAM spatial

and mode multiplexing (MUX) module, the 5-km field-deployed 7-RCF, an OAM mode demultiplexing

(DEMUX) module and coherent optical receivers followed by DSP including the offline 4 × 4 MIMO

equalization.

WDM-8QAM signal generation

At the transmitter, to circumvent laboratory resource limitations, sliding test channels with high optical

signal-to-noise ratio (OSNR) and dummy channels with low OSNR are multiplexed together to generate

40 WDM carriers. Five optical carriers with wavelengths in a 0.1nm/12.5 GHz grid from external cavity

lasers (ECLs) are employed as sliding test bands. The light source of the dummy wavelength band is

generated by a WDM carrier generator based on multiple seed light sources that undergo modulation

through a cascaded phase modulator and Mach-Zehnder modulator (MZM)[28]. Following this, the test

and dummy bands are combined by a wavelength division multiplexer. Subsequently, the WDM carriers

are modulated by a 12-Gbaud 8QAM electrical signal sourced from an arbitrary waveform generator

(AWG) via an in-phase/quadrature (I/Q) modulator. This modulation process generates a set of 40-

channel WDM signals spanning from 1548.16 nm to 1552.16 nm, maintaining a grid of 0.1 nm/12.5 GHz.

The sampling rate of the AWG is set to 120 GSa/s and the data sequence is the pseudo-random binary

`

`

7-core OAM MG |l| = 4

AWG

IQ modulator

ECL3

EA

W

DM 8Q

A

M TX

ECL1

ECL2

ECL5

ECL4

WDM

Col.

5-km

7-core cable

`

7-core OAM MG |l| = 2

7-core OAM MG |l| = 3

FI + 7-core SMF

Lens

LP

SLM

MR

HWP

+l

-l

BS

QWP

OAM Mode DEMUX and Cable

W

DM

8Q

A

M

RX

EDFA

BS

Free-space

SMF

RF cables

SMF coupler

Dummy SMF

BPF

Dense WDM

Carrier Generator

Dummy channel band

Sliding test band

EDFA

1:6

…

1:6

…

1:6

…

Dummy

Modes/

Cores

Core Under

Test

VPP

-l

+l

Polarization

Mux.

PBC

PBS

LO

ICR

O

fflin

e DSP

ICR

EDFA

EDFA

25%

75%

PC

OAM Spatial and Mode MUX

DS

O

5

-km

fie

ld

-de

plo

y

ed

7

-RCF

A

B

A

B

(i)

(j)

(k)

(a)

(b)

(c)

sequence with a pattern length of 218-1. The electrical signals are digitally pre-shaped by a Nyquist filter,

specifically a raised cosine filter, with a roll-off factor of 0.01 to align with the 12.5 GHz WDM grid. It

is noted that due to device resource constraints, all WDM channels are modulated by a single electrical

signal. This configuration may result in limited decorrelation among the WDM channels, potentially

leading to an overestimation of system performance due to inter-WDM-channel nonlinear effects[29].

However, the high nonlinear threshold of the 7-RCF would ensure that the inter-WDM-channel nonlinear

effect has little impact on the system performance[9]. Due to limited equipment resources, only 40

wavelength channels were used in this experiment. Nonetheless, we do not anticipate a significant drop

in performance beyond this spectral band. A total of 312 WDM channels spanning from 1538.19 nm to

1602.10 nm were evaluated in the high-capacity SDM systems using a 7-RCF with similar design in[9],

and remarkably consistent performance was sustained across all of the WDM channels.

OAM Spatial and Mode MUX Module

After being amplified by a high-power erbium-doped fiber amplifier (EDFA), the generated WDM

signals are divided into four branches using an optical power splitter. Three of these are amplified and

further divided into six branches to implement mode channels with high OSNR in the fiber core under

test, while the remaining branch is amplified by the high-power EDFAs and used to implement low

OSNR channels in the dummy cores. The generated test and dummy mode/spatial channels are directed

toward three different OAM spatial and modal MUX modules. Within each OAM spatial and mode MUX

module, two hexagonally packed 7-core SMFs spliced with a fan-in device are included to convert the

in-fiber fundamental modes to free-space Gaussian beams. Then two sets of 7-core Gaussian beams are

collimated, linear-polarization filtered and finally images onto spatial light modulators (SLMs). The

SLMs are configured with phase masks (brown dashed box in the Fig. 3 and detailed parameters can be

found in Supplement S5) to generate 7-core OAM beams with topological charge +l or –l. Subsequently,

the six groups of 7-core OAM beams generated from the three MUX modules are power-combined and

directed through a quarter-wave plate (QWP) to facilitate circular polarization conversion. After

propagating through the polarization multiplexing module, which comprises a polarization beam splitter

(PBS), an optical de-correlation path with a 4-f configuration and a polarization beam combiner (PBC),

four OAM modes <+l, R>, <+l, L>, <−l, R> and <−l, L> are generated within each MG, where L and

R refer to the left- and right-handed circular polarization, respectively. Subsequently, the 84 spatial/mode

channels (7 cores × 6 OAM modes × 2 orthogonal circular polarizations) each carrying 40 wavelengths

are split into two branches equally via a beam splitter (BS), and they are coupled into the field-deployed

7-RCF from both ends, enabling bidirectional transmission. Here both forward and backward

transmissions for each mode and wavelength channel share the same laser source, owing to the limited

device resources, so the signal transmitted in both directions is the same. This could introduce coherent

Rayleigh noise, manifested as the beating noise between the signal in one transmission direction and

Rayleigh backscattering noise in the other direction[30–33]. However, this noise can be substantially

mitigated through coherent optical detection (refer to Supplement S6).

OAM Mode DEMUX Module and Coherent Receiver

After going through the 5-km field-deployed 7-RCF bidirectional transmission, the intensity distribution

of received OAM beams is illustrated in the inset figure (blue dashed box) of Fig 6. Due to the coherent

superposition of the four degenerate OAM modes within an MG, a linearly polarized (LP) mode-like

intensity distribution[34] is observed in each fiber core. Subsequently, the OAM beams are collimated

and split into two branches. After going through a vortex phase plate (VPP) that matches the topological

charge of OAM mode being tested, each branch is converted into a Gaussian beam and coupled into an

SMF-pigtailed dual-polarization integrated coherent receiver (ICR). Due to limitations in equipment

resource at the receiver, only the four OAM beams within the same MG are simultaneously mode

converted and then detected by the ICRs in only one direction. Subsequently, the eight electrical signals,

generated by two ICRs, are sampled and stored using an eight-channel real-time oscilloscope operating

at a sampling rate of 80 GSa/s for offline DSP, which includes timing phase recovery, 4 × 4 MIMO

equalization based on the constant modulus algorithm, frequency offset estimation and carrier phase

estimation. The measurement is repeated until all the mode/spatial channels in both direction have been

measured.

Power Budget Evaluation of the bidirectional OAM-SDM-WDM system

The power budget of the bidirectional OAM-SDM-WDM experimental system has been

comprehensively evaluated, with the results presented in Table 2. The average power of the WDM signals

at the input port of the fan-in device is standardized to 18–19 dBm, equivalent to approximately 2 to 3

dBm per WDM channel. This power level is subject to variations that depend on the OAM MG orders,

primarily due to variations in insertion loss attributed to the 7-core OAM MUX module. The total

insertion loss within the OAM MUX module includes optical element losses, such as those from the 3

dB beam combiner and the SLM, as well as coupling losses into the field-deployed 7-RCF. The observed

coupling loss to the field-deployed 7-RCF for OAM MG |l| = 4 is approximately 4 dB, which is 1 dB

higher than that of OAM MG |l| = 2 and 3. This MG-order dependent loss can be attributed to the radial

mismatch between the generated free-space OAM beams and the OAM modes supported within the field-

deployed 7-RCF. Additionally, alignment errors in the optical elements used for fiber mode coupling may

have contributed to this discrepancy. Such challenges can be addressed through the implementation of

precise local phase modulation for OAM modes with varying topological charges (|l|) in each fiber core

and improved alignment of optical elements. Before being coupled into the field-deployed 7-RCF, the

OAM beam is evenly divided into two branches and coupled from both ends of the field-deployed 7-

RCF to achieve bidirectional transmission, which causes a power loss of 3dB. After passing through the

5-km field-deployed 7-RCF and the OAM DEMUX module, ~ −24 dBm of optical power is received at

the input port of the optical pre-amplifier located before the ICR, higher than the sensitivity (~ −37 dBm)

of the pre-amplifier.

Table 2. Optical power budget evaluation of the bidirectional OAM-SDM-WDM experiment system.

OAM mode group

|l| = 2

|l| = 3

|l| = 4

Average power at Fan-In input

18dBm

18dBm

19dBm

Average power per wavelength at Fan-In input

1.98dBm

1.98dBm

2.98dBm

Insertion Loss of the OAM Mux. Module (including coupling loss)

13dB

13dB

14dB

The loss of being divided into two branches for bidirectional transmission

3dB

3dB

3dB

Average fiber loss/core

1.57dB

1.58dB

1.72dB

Insertion loss of OAM Demux. Module (including coupling loss)

9dB

9dB

9dB

Average received power before Pre-amp. EDFA for each fiber core

-24.59dBm

-24.60dBm

-24.74dBm

Results and analysis

Characteristics of the 7-RCF in the installed cable

The 7-RCF within the fiber cable supports a total of 35 OAM mode groups (MGs), encompassing 7 cores

with 5 OAM MGs each. Notably, each MG comprises degenerate OAM modes with topological charge

values +l and –l (l = 1, 2, 3 and 4) alongside the OAM MG with a topological charge l = 0. Each of these

modes carries two orthogonal polarizations.

The attenuations of all the MGs at the wavelength of 1550 nm are measured by means of optical time-

domain reflectometry (OTDR) as detailed in Supplement S2. As depicted in Fig. 4, the attenuation for

the OAM MGs of the 7-RCF within the installed cable averages 0.32 dB/km (seeing red triangles in Fig.

4). This is approximately 0.02 dB/km higher than that of the 7-RCF spools (as indicated by the blue

circles in Fig. 4). This slight increase can be ascribed to the minor micro-bending and additional stress

incurred during the cabling process. Notably, there is a pronounced attenuation difference for the highest-

order OAM MG with a topological charge of |l| = 4 in fiber core #1, observed in both the fiber spools

and the installed cable. This discrepancy could stem from deformation in the structure of this particular

core during the drawing process.

Fig. 4. The measured mode-dependent attenuation of 7-RCF spools and installed cable at 1550 nm.

The inter-MG crosstalk (XT) within an individual fiber core, as well as the inter-core XT of the 7-

RCF, have been experimentally characterized for both the installed cable and fiber spools. The

measurement details are provided in Supplement S3. As illustrated in Fig. 5, the aggregated crosstalk

among OAM MGs with |l| = 2, |l| = 3, and |l| = 4 within the same 7-RCF fiber core of the installed cable

is below −12 dB at a wavelength of 1550 nm, while this value is around -20 dB among different fiber

cores. In this case, MGs |l| = 0 and |l| = 1 are not used as spatial channels in this work due to their strong

inter-MG crosstalk. Therefore, the ring-core design can be further refined to reduce crosstalk between

these two MGs, ensuring that all MGs exhibit low inter-MG crosstalk and can be utilized effectively[25].

This performance closely mirrors that of the 7-RCF spool with the length of 14 km or even 34 km. Such

consistency arises because the crosstalk is predominantly caused by the OAM mode conversion and core

coupling modules at both ends of the 7-RCF (as illustrated in Fig. S3 in Supplement S3), rather than by

the fiber itself. We previously consistently measured typical in-fibre XT in the order of -35 dB/km or less

in fiber spools[9, 26].

Fig. 5. The measured crosstalk of 7-RCF spools and installed cable at 1550 nm: (a) inter-MG crosstalk within

the one single fiber core; (b) inter-core crosstalk.

The differential group delay (DGD) of the OAM MGs are measured with a vector network analyzer

(VNA) using a time-domain impulse response method[27], detailed in Supplement S4. As depicted in

Fig. 6, large DGD with values of more than 5 ns/km between adjacent pairs of OAM MGs of topological

charge |𝑙| > 1 can be achieved in each fiber core. This observation indicates weak coupling among

high-order OAM MGs within each fiber core[27]. This performance also closely aligns with that of the

7-RCF spool, implying that the effect of cabling and installation on the DGD is negligible.

Fig. 6. The measured DGD at 1550nm of 7-RCF spools and installed cable. One averaged DGD value is given for OAM MGs |l| =

0 & 1 in the measured results, as their impulse response merged into one Gaussian-distribution peak due to strong coupling between

these two MGs after transmission.

BER Evaluation for Bidirectional SDM Transmission

(b)

(a)

Fig. 7. The measured BERs of all channels after 5-km field-deployed 7-RCF bidirectional transmission: (a)

forward transmission and (b) backward transmission; the absolute values of tap weights in 16 FIR filters of

4 × 4 MIMO equalizers to equalize the four modes belonging to OAM MGs |l| = 3 at 1540 nm in the (c)

forward transmission and (d) backward transmission.

The measured forward and reverse transmission bit-error rate (BER) values of all 6720 channels (2

direction × 7 cores × 6 OAM modes × 2 polarizations × 40 WDM channels) are shown in Fig. 7(a) and

Fig. 7(b). For convenience, the BER evaluation for two orthogonal polarizations is performed together,

resulting in the display of only two values within each MG. Notice that the BER performance of the

OAM MG with topological charge |l| = 3 is inferior compared to the other OAM MGs, which is primarily

attributed to the relatively higher crosstalk from the adjacent two OAM MGs (|l| = 2 and |l| = 4). However,

the BER values of all bidirectional channels are below the 20% soft-decision FEC threshold of 2.4×10−2,

only utilizing modular 4×4 MIMO equalization with a TDE tap number not exceeding 15, as shown in

Fig. 7 (c) and (d).

Effect of Rayleigh Backscattering Noise

The signal-to-noise ratio (SNR) of the forward transmission signals are experimentally evaluated at

varying levels of backward transmission signal power within the same fiber core, to assess the effect of

RB noise in the bidirectional transmission system with coherent optical detection. As illustrated in Fig.

8(a), the SNRs of forward transmission signals decrease as backward transmission signal power increases.

Fig. 8(b) provides a comparison by illustrating the theoretically calculated signal-to-RB-noise power

ratio after coherent detection at different levels of backward transmission power. It is noteworthy that the

received signal and RB noise, post-coherent detection, are proportional to the photocurrents generated

through the beating process between the optical signal or RB noise and the optical light from the local

oscillator (LO) at the coherent optical receiver. As a result, the power ratio between the detected signal

and RB noise are expressed as 〈IS-lo〉2/〈IRB-lo〉2

in Fig. 8(b). Further details regarding the theoretical RB

analysis in the ring-core fiber together with coherent optical detection can be found in Supplement S6.

Fig. 8. The measured SNRs under different backward transmission power with 8 dBm forward transmission

power after (a) 5-km installed cable transmission and (b) 5-km theoretical transmission. lF: topological

charge of the forward transmission OAM light beam; lB: topological charge of the backward transmission

OAM light beam; 〈IS-lo〉2/〈IRB-lo〉2 represents the power ratio between the detected signal and RB noise after

coherent detection (details can be found in Supplement S6).

An observation from Fig. 8(a) and (b) reveals that the experimentally evaluated signal SNR is higher

than the theoretically predicted power ratio between received signals and RB noise. This discrepancy is

primarily attributed to various factors beyond RB noise in the experimental system, such as Fresnel

reflection of backward injected optical power at the fiber end facet, amplified spontaneous emission

(ASE) noise of the EDFAs, inter-mode crosstalk, electrical amplifier noise, quantization noise from the

digital-to-analog converter (DAC) in the AWG, and analog-to-digital converter (ADC) within the real-

time oscilloscope.

Since the optical carriers of the forward and backward transmissions for each mode and wavelength

channel share the same laser source due to equipment resource limitation (seeing Section OAM Spatial

and Mode MUX Module), beating noise is anticipated to exist between RB noise from the backward

transmission and signals transmitted in the forward direction, with its power theoretically being much

higher than that of the RB noise itself[35]. However, coherent detection utilizing balanced detectors

integrated into the ICR significantly mitigates such signal-RB beating noise, as explained in Supplement

S6. In the experimental system, the impact of Fresnel reflections of the backward transmission signals at

the fiber end facet, typically characterized by a power considerably higher than that of the RB noise[36,

37], is more pronounced on forward transmission signals at their receiving end. However, noise related

to backward transmission, including both Fresnel reflection and RB noise, constitutes a small portion of

total noise. Consequently, the experimentally evaluated SNR variation ranges, as depicted in Fig. 8(a)

with changing backward transmission signal power, are smaller than those theoretically predicted in Fig.

8(b).

Fig. 8(b) also illustrates that the signal-to-RB-noise power ratio is higher when forward and backward

transmission channels share the same mode index (lF = lB, blue triangle line in Fig. 8) compared to cases

with different mode indexes (lF ≠ lB, orange square line in Fig. 8), given fixed forward and backward

transmission powers. This is because the mode recapture factor, which represents the proportion of the

total scattered power of the backward transmitting mode channel recaptured by the forward transmitting

mode channel, is theoretically higher in the former case[38]. Detailed analysis can be found in

Supplement S6. Similar trends are observed in the experimentally evaluated results shown in Fig. 8(a).

However, we attribute this phenomenon mainly to the further suppression of Fresnel reflection power by

the OAM mode DEMUX module when the backward transmission mode index is different from the

forward transmission one.

(a)

(b)

For mode-multiplexed transmission in both forward and backward directions, the theoretical analysis

indicates a deterioration in the signal-to-RB-noise power ratio compared to single-mode transmission

cases. This is due to the contribution of RB noise from two multiplexed backward transmission modes

[e.g., lB = 3 and 4 in Fig. 8(b)] to the target evaluated forward transmission mode [e.g., lF= 3 in Fig. 8(b)].

In the experimental evaluation, the degradation in SNR performance in mode-multiplexed transmission

results not only from increased backward-transmission-power-dependent noise but also from inter-mode

crosstalk.

Based on the above analysis, it is found that in short-distance bidirectional transmission systems, the

effect of Fresnel reflection at the fiber end facet surpasses that of RB noise. To enhance the SNR of the

received signal, one effective strategy involves mitigating Fresnel reflection, such as by applying an anti-

reflective film to the fiber end facet. Furthermore, in contrast to SMF based bidirectional transmission

systems, the received signal performance is affected not only by RB noise but also by inter-mode

crosstalk. In future investigations, we aim to conduct a comprehensive assessment of the collective

impact of these two noise sources on the performance of transmission systems at varying distances. This

evaluation will contribute to establishing the appropriate transmission distance range for bidirectional

SDM transmissions with weakly coupled mode channels.

Stability of Transmission System over Field-Deployed 7-RCF

The fiber cable was laid in standard conduits without specialized fastening methods. Portions of these

cables hang freely, as shown in Fig. 2(e). Environmental elements such as wind, vehicular traffic,

temperature shifts, and humidity variations are unavoidable.

These environmental factors induce random coupling among the degenerate modes within the same

mode group of a single fiber core, which leads to fluctuations in the received power over time when only

one intra-group mode is received. As a result, measuring the temporal variation of this power fluctuation,

whose details can be found in Supplement S7, allows us to gauge the influence of external environmental

factors on the intra-group mode coupling. According to the measured results (seeing Fig. S7 in

Supplement S7), the power fluctuation of the field-deployed fiber cable due to the random coupling

among intra-group modes changes more rapidly than what is seen in optical fiber spools used in

laboratory settings, even though the former exhibits relatively smaller magnitude of the power fluctuation

due to the protection of the outer sheath in the cable. However, our adaptive MIMO equalization

algorithm effectively tracks such variations. In addition, the modal differential delay (DMD) among the

intra-group modes remains relatively low, although their values change over time due to random strong

coupling. For a transmitting symbol rate of 12GBaud, 15 taps of the time-domain FIR filters for MIMO

equalization adequately cover such DMD variations.

In addition, as illustrated in Fig. 5, the measured data show no significant variation in either inter-

mode-group or inter-core crosstalk for the field-deployed fiber cable relative to the laboratory fiber spools.

This is primarily attributed to the MUX/DEMUX modules, which limit the inter-mode-group and inter-

core crosstalk of the entire transmission system. Consequently, variations in the minimal inter-mode-

group and inter-core crosstalk of the fiber cable have negligible impact on system performance.

Conclusions and discussions

A bidirectional SDM transmission based a 5-km field-deployed 7-RCF with a cladding diameter of 178

μm is experimentally demonstrated in this paper. Implemented over the 7-RCF supporting 84 OAM mode

channels each carrying 40 wavelengths, the SDM-WDM system achieves a raw (net) SE of 483.84 (403.2)

bit/s/Hz and a capacity of 241.92 (201.6) Tbit/s by utilizing a bidirectional transmission scheme solely

applying modular 4×4 MIMO equalization with a TDE tap number not exceeding 15.

Due to constraints in device resources, the demonstration did not extend to showcasing SDM

transmission over field-deployed fiber cables at longer distances using the recirculating loop scheme.

Nonetheless, the 7-RCF employed in our demonstration exhibits the potential to enable longer-distance

SDM transmission with high SE and capacity, whilst keeping low MIMO complexity, and consequently,

low cost and low power consumption. We have successfully demonstrated high SE / high capacity SDM

transmissions over 7-RCF spools covering distances of 14 km[16], 34 km[9], and 60 km[6], utilizing 4×4

MIMO equalization with low TDE tap numbers, thus ensuring low MIMO complexity. Additionally, we

showcased a 100-km transmission supported by a single-core RCF, employing 4×4 MIMO processing

with a low TDE tap number to address crosstalk among the degenerate intra-MGs[39].

The good performance of the SDM transmission for up-scaling of SE and capacity per optical fiber

while keeping low MIMO complexity within distances of tens of or even one hundred kilometers are

realized by exploiting the uniquely excellent characteristics of OAM modes in RCFs. The radial

confinement of the ring-shape core of the RCF makes the number of degenerate (or near degenerate)

modes in the OAM MGs fixed at four when their topological charge |l| ≥ 1 (OAM modes with

topological charge value +l and −l each carrying two orthogonal polarizations[40], whose differential

mode delays are very low due to their good degeneracy). The differential effective refractive index Δneff

between adjacent MGs increases with |l|[34], which leads to reduced inter-MG coupling therefore good

scalability to high-order mode space. Therefore, MIMO processing with a small 4×4 scale and a low

TDE tap number and thus low complexity[41–45] can be sustained in the OAM-RCF based systems

when more SDM channels are involved to realize high SE/capacity. In our 7-RCF OAM MUX module,

mode multiplexing currently relies on a straightforward power combining strategy, leading to insertion

losses that increase with the number of MGs utilized. While this method is sufficient for a small set of

modes, it becomes less efficient as the number of mode channels grows, with power combining losses

becoming more pronounced. Exploring advanced techniques such as multi-core spiral transformation[46]

or multi-plane light conversion[47] could offer better power efficiency. Additionally, there's a clear

advantage in developing MUX/DEMUX modules that are more integrated. However, such advancements

require tackling the significant challenge of converting densely packed input Gaussian beams into a

complex 2D input fiber array, a task that presents notable optical engineering challenges.

While the inter-MG crosstalk of the 5-km 7-RCF in field-deployed cable remains lower than that of

spatial and mode MUX/DEMUX modules, we anticipate a degree of performance degradation for field-

deployed fiber cables compared to lab-deployed optical fiber spools. For instance, fiber fusion errors

during the laying process may elevate the inter-MG crosstalk of the RCF[48]. However, judicious control

of the fiber fusion error range (e.g., no more than 0.4-μm radial misalignment for the RCF[49]) can

effectively manage the increase in inter-MG crosstalk, keeping it to a reasonably low level. By

overcoming additional challenges in field-deployed fiber cables for practical application in the future,

SDM schemes utilizing OAM modes in RCFs stand as a promising candidate for next-generation high

SE/capacity transmission over optical fibers with distances of tens of kilometers (e.g., metro areas, inter-

data center links, etc.), where weak coupling among the non-degenerate modes within each fiber core is

achievable, and in-line optical amplification towards FM-MCFs is unnecessary.

Acknowledgements

The work was supported by National Natural Science Foundation of China (62335019, 62101602) and

National Key R&D Program of China (2018YFB1801800).

Authors' contributions

Junyi Liu, Zengquan Xu and Jie Liu conceived the original idea and designed the experiment. Junyi Liu,

Zengquan Xu, Yuming Huang and Yining Huang conducted the experiment. Shuqi Mo analyzed the effect

of Rayleigh backscattering noise. Zhenhua Li and Yuying Guo experimentally realized the generation of

wideband WDM carriers. All authors analyzed their experimental results and contributed to writing and

proofreading the manuscript. Lei Shen and Shuo Xu contributed to the cable fabrication. Cheng Du, Qian

Feng and Jie Luo deployed the cable. Siyuan Yu and Jie Liu supervised the overall project.

Authors' information

Not applicable.

Conflict of Interest

The authors declare no conflict of interest.

Availability of data and materials

The experimental data that support the works of this study are available from the corresponding authors

on reasonable request.

Supplementary information is available for this paper

Declarations

Ethical Approval and Consent to participate

There is no ethics issue for this paper.

Consent for publication

All authors agreed to publish this paper.

competing interests

The authors declare no competing fnancial interests

Reference

[1]

Richardson DJ, Fini JM, Nelson LE. Space-division multiplexing in optical fibres. Nature Photon 2013; 7: 354–362.

[2]

Puttnam BJ, Rademacher G, Luís RS. Space-division multiplexing for optical fiber communications. Optica 2021; 8:

1186.

[3]

Rademacher G, Puttnam BJ, Luís RS, et al. Peta-bit-per-second optical communications system using a standard cladding

diameter 15-mode fiber. Nat Commun 2021; 12: 4238.

[4]

Lin Z, Liu J, Lin J, et al. 360-Channel WDM-MDM Transmission over 25-km Ring-Core Fiber with Low-Complexity

Modular 4×4 MIMO Equalization. In: Optical Fiber Communication Conference (OFC) 2021. Washington, DC: Optica

Publishing Group, p. W7D.5.

[5]

Wang F, Gao R, Li Z, et al. OAM mode-division multiplexing IM/DD transmission at 4.32 Tbit/s with a low-complexity

adaptive-network-based fuzzy inference system nonlinear equalizer. Optics Letters 2024; 49: 430–433.

[6]

Zhang J, Lin Z, Liu J, et al. SDM transmission of orbital angular momentum mode channels over a multi-ring-core fibre.

Nanophotonics 2022; 11: 873–884.

[7]

Kobayashi T, Nakamura M, Hamaoka F, et al. 1-Pb/s (32 SDM/46 WDM/768 Gb/s) C-band dense SDM transmission

over 205.6-km of single-mode heterogeneous multi-core fiber using 96-Gbaud PDM-16QAM channels. In: 2017 Optical

Fiber Communications Conference and Exhibition (OFC). 2017, pp. 1–3.

[8]

Puttnam BJ, Luís RS, Klaus W, et al. 2.15 Pb/s transmission using a 22 core homogeneous single-mode multi-core fiber

and wideband optical comb. In: 2015 European Conference on Optical Communication (ECOC). 2015, pp. 1–3.

[9]

Liu J, Zhang J, Liu J, et al. 1-Pbps orbital angular momentum fibre-optic transmission. Light Sci Appl 2022; 11: 202.

[10]

Soma D, Igarashi K, Wakayama Y, et al. 2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode

19-core fiber in full C band. In: 2015 European Conference on Optical Communication (ECOC). 2015, pp. 1–3.

[11]

Soma D, Wakayama Y, Beppu S, et al. 10.16-Peta-B/s Dense SDM/WDM Transmission Over 6-Mode 19-Core Fiber

Across the C+L Band. Journal of Lightwave Technology 2018; 36: 1362–1368.

[12]

Rademacher G, Puttnam BJ, Luís RS, et al. 10.66 Peta-Bit/s Transmission over a 38-Core-Three-Mode Fiber. In: 2020

Optical Fiber Communications Conference and Exhibition (OFC). 2020, pp. 1–3.

[13]

Qian D, Ip E, Huang M-F, et al. 105Pb/s Transmission with 109b/s/Hz Spectral Efficiency using Hybrid Single- and Few-

Mode Cores. In: Frontiers in Optics 2012/Laser Science XXVIII (2012), paper FW6C.3. Optica Publishing Group, p.

FW6C.3.

[14]

Arik SÖ, Askarov D, Kahn JM. Effect of Mode Coupling on Signal Processing Complexity in Mode-Division

Multiplexing. J Lightwave Technol 2013; 31: 423–431.

[15]

Kong D, Jørgensen AA, Henriksen MR, et al. Single Dark-Pulse Kerr Comb Supporting 1.84 Pbit/s Transmission over

37-Core Fiber. In: Conference on Lasers and Electro-Optics (2020), paper JTh4A.7. Optica Publishing Group, p. JTh4A.7.

[16]

Xu Z, Liu J, Liu J, et al. 241.92-Bit/s/Hz Spectral-Efficiency Transmission over 14-km 7-Core Ring Core Fiber with

Low-Complexity 4× 4 MIMO Equalization. In: 2023 Optical Fiber Communications Conference and Exhibition (OFC).

2023, pp. 1–3.

[17]

Liu J, Xu Z, Liu J, et al. 201.6-Bit/s/Hz Spectral-Efficiency Transmission Over a 180-μm Cladding-Diameter Seven Ring

Core Fiber Using Low-Complexity 4\times 4 MIMO Equalization. Journal of Lightwave Technology,

https://ieeexplore.ieee.org/abstract/document/10382488/ (2024, accessed 13 March 2024).

[18]

Luís RS, Rademacher G, Puttnam BJ, et al. 1.2 Pb/s Throughput Transmission Using a 160 μm Cladding, 4-Core, 3-Mode

Fiber. Journal of Lightwave Technology 2019; 37: 1798–1804.

[19]

Sakaguchi J, Klaus W, Delgado Mendinueta JM, et al. Large Spatial Channel (36-Core × 3 mode) Heterogeneous Few-

Mode Multicore Fiber. Journal of Lightwave Technology 2016; 34: 93–103.

[20]

van Uden RGH, Correa RA, Lopez EA, et al. Ultra-high-density spatial division multiplexing with a few-mode multicore

fibre. Nature Photon 2014; 8: 865–870.

[21]

Ryf R, Marotta A, Mazur M, et al. Transmission over Randomly-Coupled 4-Core Fiber in Field-Deployed Multi-Core

Fiber Cable. In: 2020 European Conference on Optical Communications (ECOC), pp. 1–4.

[22]

Hayashi T, Nakanishi T, Hirashima K, et al. 125-μm-Cladding Eight-Core Multi-Core Fiber Realizing Ultra-High-Density

Cable Suitable for O-Band Short-Reach Optical Interconnects. Journal of Lightwave Technology 2016; 34: 85–92.

[23]

Chen Y, Xiao Y, Chen S, et al. Field Trials of Communication and Sensing System in Space Division Multiplexing Optical

Fiber Cable. IEEE Communications Magazine 2023; 61: 182–188.

[24]

Matsuo S, Takenaga K, Sasaki Y, et al. High-Spatial-Multiplicity Multicore Fibers for Future Dense Space-Division-

Multiplexing Systems. Journal of Lightwave Technology 2016; 34: 1464–1475.

[25]

Mo S, Zhu H, Liu J, et al. Few-mode optical fiber with a simple double-layer core supporting the O + C + L band weakly

coupled mode- division multiplexing transmission. Opt Express 2023; 31: 2467.

[26]

Zhang J, Zhu J, Liu J, et al. Accurate Mode-Coupling Characterization of Low-Crosstalk Ring-Core Fibers Using Integral

Calculation Based Swept-Wavelength Interferometry Measurement. Journal of Lightwave Technology 2021; 39: 6479–

6486.

[27]

Maruyama R, Kuwaki N, Matsuo S, et al. Relationship Between Mode Coupling and Fiber Characteristics in Few-Mode

Fibers Analyzed Using Impulse Response Measurements Technique. J Lightwave Technol 2017; 35: 650–657.

[28]

Fujiwara M, Teshima M, Kani J, et al. Optical carrier supply module using flattened optical multicarrier generation based

on sinusoidal amplitude and phase hybrid modulation. Journal of Lightwave Technology 2003; 21: 2705–2714.

[29]

Dar R, Feder M, Mecozzi A, et al. Inter-Channel Nonlinear Interference Noise in WDM Systems: Modeling and

Mitigation. Journal of Lightwave Technology 2015; 33: 1044–1053.

[30]

Qian D, Huang M-F, Zhang S, et al. 30Tb/s C- and L-bands bidirectional transmission over 10,181km with 121km span

length. Opt Express 2013; 21: 14244–14250.

[31]

Kani J, Jinno M, Sakamoto T, et al. Bidirectional transmission to suppress interwavelength-band nonlinear interactions

in ultrawide-band WDM transmission systems. IEEE Photonics Technology Letters 1999; 11: 376–378.

[32]

Wood TH, Linke RA, Kasper BL, et al. Observation of coherent Rayleigh noise in single-source bidirectional optical

fiber systems. Journal of Lightwave Technology 1988; 6: 346–352.

[33]

Ko J, Kim S, Lee J, et al. Estimation of performance degradation of bidirectional WDM transmission systems due to

Rayleigh backscattering and ASE noises using numerical and analytical models. Journal of Lightwave Technology 2003;

21: 938–946.

[34]

Liu J, Zhu G, Zhang J, et al. Mode Division Multiplexing Based on Ring Core Optical Fibers. IEEE J Quantum Electron

2018; 54: 1–18.

[35]

Yan-Hong W, Guo-Qiang N, Pan G, et al. Theoretical Analysis on Coherent Noise by Rayleigh Backscattering in

Bidirectional Transmission System with Single Mode Fiber. In: 2009 International Forum on Information Technology

and Applications, pp. 209–212.

[36]

Shibita S, Hisano D, Mishina K, et al. Demonstration of Reflected Interference Cancellation in Single-Wavelength

Bidirectional PON System. International Conference on Intelligent Pervasive Computing, (2019, accessed 14 November

2023).

[37]

Danielson BL. Backscatter measurements on optical fibers.

[38]

Yu D, Fu S, Tang M, et al. Mode-dependent characteristics of Rayleigh backscattering in weakly-coupled few-mode fiber.

Optics Communications 2015; 346: 15–20.

[39]

Zhang J, Liu J, Shen L, et al. Mode-division multiplexed transmission of wavelength-division multiplexing signals over

a 100-km single-span orbital angular momentum fiber. pr 2020; 8: 07001236.

[40]

Lin Z, Hu J, Chen Y, et al. Single-shot Kramers–Kronig complex orbital angular momentum spectrum retrieval. Adv

Photon; 5. Epub ahead of print 12 June 2023. DOI: 10.1117/1.AP.5.3.036006.

[41]

Bozinovic N, Yue Y, Ren Y, et al. Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers.

Science 2013; 340: 1545–1548.

[42]

Zhu G, Zhu J, Wu X, et al. Scalable Orbital Angular Momentum Mode-Division-Multiplexed Transmission over 10-km

Graded-Index Ring-Core Fiber. In: 2017 European Conference on Optical Communication (ECOC), pp. 1–3.

[43]

Zhu L, Li J, Zhu G, et al. First Demonstration of Orbital Angular Momentum (OAM) Distributed Raman Amplifier over

18-km OAM Fiber with Data-Carrying OAM Multiplexing and Wavelength-Division Multiplexing. In: 2018 Optical

Fiber Communications Conference and Exposition (OFC), pp. 1–3.

[44]

Feng F, Jung Y, Zhou H, et al. High-Order Mode-Group Multiplexed Transmission over a 24km Ring-Core Fibre with

OOK Modulation and Direct Detection. In: 2017 European Conference on Optical Communication (ECOC), pp. 1–3.

[45]

Zhang J, Wen Y, Tan H, et al. 80-Channel WDM-MDM Transmission Over 50-km Ring-Core Fiber using a Compact

OAM DEMUX and Modular 4×4 MIMO Equalization. In: 2019 Optical Fiber Communications Conference and

Exhibition (OFC), pp. 1–3.

[46]

Feng X, Lin Z, Wen Y, et al. Arrayed Vortex Mode Demultiplexer Based on Spiral Transformation for Dense Space

Division Multiplexing. In: Asia Communications and Photonics Conference/International Conference on Information

Photonics and Optical Communications 2020 (ACP/IPOC). Beijing: Optica Publishing Group, p. M4A.175.

[47]

Lin Z, Wen Y, Chen Y, et al. Transmissive Multi-plane Light Conversion for Demultiplexing Orbital Angular Momentum

Modes. In: Conference on Lasers and Electro-Optics. Washington, DC: Optica Publishing Group, p. SF1J.5.

[48]

Hayashi T, Nagashima T, Nakanishi T, et al. Field-Deployed Multi-Core Fiber Testbed. In: 2019 24th OptoElectronics

and Communications Conference (OECC) and 2019 International Conference on Photonics in Switching and Computing

(PSC), pp. 1–3.

[49]

Huang C, Liu J, Liu J, et al. Splice Loss Characterization of High Order OAM Modes in Ring-Core Fibers. In: 2021 Asia

Communications and Photonics Conference (ACP), pp. 1–3.