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.


INTRODUCTION
The spatial dimension of multi-mode fibers (MMF) is an unexploited resource for enhancing its information transmission capacity [1][2][3][4].Space-division multiplexing (SDM), whereby multiple data signals are multiplexed into different spatial channels, has attracted much research interest including the use of multiple cores sharing a common cladding or multiple modes with an enlarged core size and different mode field patterns in an SDM optical fiber.SDM fiber can thus be classified into multi-core fiber (MCF), few-mode fiber (FMF), and MMF [5].Nevertheless, utilizing the spatial dimension of optical fibers can be very challenging, particularly when it involves the higher-order modes in an FMF or MMF for mode-division multiplexing (MDM) systems.
Two major challenges are associated with MDM optical fiber systems, including the lack of cost-effective and scalable mode (de)multiplexers that can generate or decouple multiple orthogonal fiber modes, and the substantial energy consumption and large time latency incurred in descrambling high-speed optical signals using digital signal processing [6].
Mode (de)multiplexers for optical fibers in several pioneering works have been reported using optical phase plates [7,8], spatial light modulators (SLMs) [9], or multi-plane light conversion (MPLC) [10][11][12][13].While significant progress has been made in fiber-based photonic lanterns or laser-inscribed waveguides [5,14,15], a compact and cost-effective approach is still desired for costand footprint-sensitive short-reach optical communications inside data centers.Furthermore, when light passes through a circular-core MMF even without any disturbances, various speckle patterns can be formed due to the different dephasing conditions between the fiber eigenmodes [16][17][18][19].One-by-one mapping of the LP modes between the transmitter side and the receiver side therefore cannot be guaranteed.Intricate speckle patterns at the fiber end can cause significant scrambling of the information encoded on different fiber modes.Rectangular-core FMFs have thus been proposed to break rotational symmetry and prevent spatial degeneracy [18,19].In addition, inter-mode coupling may also arise from factors such as fiber non-uniformity or sharp bending.Essentially, the information is not lost, but separating the arbitrarily mixed signals in a circular-core FMF presents a significant challenge.Prior research has shown that this problem can be well solved using digital electronic multipleinput multiple-output (MIMO) processing [7,20].However, such approaches originally developed for wireless communications require high-speed digital circuits with high power consumption and large time latency when handling a data rate of over 100Gbaud, which severely hinders its potential use.
Integrated photonic processors present a promising alternative technology for manipulating the high-order fiber modes, especially on the silicon photonics platform, which offers low-cost, high-volume manufacturing with CMOS compatibility [21][22][23].The high refractive index contrast of the silicon photonics platform enables ultracompact confinement of the optical field for high-density and multichannel optical input/output (I/O) [17,[24][25][26][27].Meanwhile, integrated optical interferometers to implement arbitrary matrix transformations have been demonstrated for use in optical neural networks [28][29][30], reconfigurable signal processors [31][32][33][34], free-space and on-chip beam separation [35][36][37], and quantum networks [38,39].By integrating multimode optical I/O and optical matrix processing on the same chip, photonic processors have the potential to offer an enabling technology for MDM optical fiber systems.
In this work, we developed a reconfigurable integrated photonic processor that can selectively launch and separate orthogonal fiber modes.High-dimensional chip-tochip optical fiber communications can be directly realized by an FMF, involving the full set of six LP modes including LP 01-x , LP 01-y , LP 11a-x , LP 11a-y , LP 11b-x , and LP 11b-y .Selective mode excitation in the optical fiber is performed at the transmitter side by an efficient and multimode optical I/O.To solve the mode scrambling and polarization rotation after fiber transmission at the receiver side, a reconfigurable Mach Zehnder interferometer (MZI) based optical unitary mesh is utilized to apply optical matrix transformations and act as an all-optical MIMO descrambler.For the first time, a six-channel high-dimensional fiber optical communication relying on the integrated silicon photonic processor is experimentally demonstrated.

INTEGRATED PHOTONIC PROCESSOR
Figure 1 illustrates the high-dimensional optical fiber communication system enabled by the silicon photonic integrated circuits (PICs).The higher-order modes in an FMF can be described by eigenmodes with a rigorous vectorial treatment of the wave equation in cylindrical coordinates.LP mode is a description often used for the linearly polarized superposition of fiber eigenmodes.At the transmitter side, the chip-to-fiber coupling is realized by an efficient and multimode grating coupler as depicted by the bottom inset.By controlling the relative phase delay between the two counterpropagating quasitransverse-electric (TE) modes on chip, high-order fiber modes in the two orthogonal polarizations can be generated as elaborated in Supplementary Material S1.In our demonstration, all the six spatial-and polarization channels in a two-mode FMF can be selectively launched, including LP 01-x , LP 01-y , LP 11a-x , LP 11a-y , LP 11b-x , and LP 11b-y .It is worth noting that although selective decoupling is desired at the receiver side, this can only happen when the fiber LP modes are of high modal purity and polarizations are accurately aligned.In practice, LP mode scrambling and polarization rotation are inevitable in a circular-core FMF, which results in an unpredictable field pattern arriving at the coupling end between the fiber and the photonic chip [16][17][18].For example, when the LP 11a mode is launched into the FMF from the transmitter side, the resulting output pattern is typically a linear combination of all LP 11 spatial-and po-larization modes, which undergo continuous mixing along propagation in the optical fiber, as illustrated in Figure 1.This is due to the fact that LP modes are essentially formed by linear combinations of the fiber eigenmodes with varying interference conditions.Nevertheless, the proposed multimode grating coupler can efficiently support all the eigenmodes in a two-mode FMF, which allows non-selective decoupling of the multimode optical signals into the eight single-mode channels on chip.Efficient chip-to-fiber and fiber-to-chip coupling can be obtained with a small mode-dependent loss as shown by the simulation results in Figure S2.To undo the arbitrary intermodal signal mixing, reconfigurable optical mesh with eight output ports can be trained to apply the inverse transformation of the channel matrix and retrieve the six orthogonal channels in a two-mode FMF.
In this demonstration, a unitary optical mesh U( 8) is applied leveraging the low channel-dependent loss of the multimode optical I/O.More intricate optical meshes would be necessary to enhance the system performance with severe loss difference or differential mode group delay [40,41].A comprehensive explanation of the unitary matrix operations of the photonic processor is included in the Supplementary Material (refer to Section S2).
The experimental coupling loss spectra of LP 01 , LP 11a , and LP 11b in x-polarization for a two-mode FMF are measured and presented in Figure 2a, showing a peak experimental efficiency of -3.5 dB, -6.1 dB, and -4.3 dB at 1532nm, 1517nm, and 1515nm respectively.As the grating utilizes a symmetric structure for the orthogonal polarizations, similar coupling efficiencies for the ypolarized LP modes are guaranteed.To validate the selective launching of the LP 01 , LP 11a , and LP 11b modes when using the integrated photonic processor, diffracted mode field profiles of FMF are captured with a 10 × microscope objective and an infrared camera, as presented in Figure 2b.The FMF is twisted and bent by using the fiber loops until the captured image resembles the profile of a pure LP 11 mode.The schematic of the photonic processor at the receiver side is shown in Figure 2c.It comprises a multimode grating coupler, tapered asymmetric directional couplers (ADCs), MZI-based linear unitary matrix, and eight output single-mode grating couplers.An 8×8 triangular optical mesh consisting of 28 tunable MZIs is employed in our demonstration.Figure 2d shows the microscopic image of wire-bonded photonic processor at the receiver side.The total footprint of the photonic integrated circuits is 8.5 mm × 1.8 mm.

MODE DESCRAMBLING TRAINING
With various fiber modes selectively launched, the FMF is directly bridged with the photonic chip at the receiver side as indicated by Figure 3a.Because of the mode evolution and polarization rotation, the received speckle pattern at the fiber-to-chip end is uncertain, which results in a random received optical power distribution entering the optical mesh.A fiber array unit (FAU) and multichannel power meter are used to monitor the optical power from the eight output ports.Figure 3a shows the experimental setup for chip-to-chip MDM communications using a 5-meter FMF and the integrated photonic processor.The photograph of the photonic chip mounted on a printed circuit board at the received side under test is presented in Figure 3b.In the experiments, we have employed multichannel source measurement units (SMUs) and the particle-swarm optimization (PSO) algorithm to optimize the drive voltage of phase shifters within the optical mesh U (8).The figure-ofmerits has been defined as the minimum crosstalk suppression between the target output port and the other output ports.Once an acceptable solution is identified or the maximum number of iterations is reached, the optimization algorithm terminates and locks the unscrambling status by fine-tuning the driving voltage of each phase shifter.
Figure 3c presents the evolution of normalized optical power for eight output ports during the training process.It can be clearly observed that after a training epoch of around 120, selective decoupling can be effectively configured with a maximum crosstalk level suppression of ≥ 21.3 dB.Through the same experimental setup, six channels including the two orthogonal polarizations of the LP 01 , LP 11a , and LP 11b modes are selectively launched and decoupled with transmission matrices bar chart summarized in Figure 3d.The initial power randomization for all fiber modes can be configured to different output ports, with experimental power isolation ratios all above 15.2 dB.Different routing schemes of fiber modes are also implemented to validate the reconfigurability of our photonic processor, showing a similar performance as depicted in Figure 3e.A comprehensive optical loss breakdown of the entire optical system is in Supplementary Material S3.

INTER-CHIP MULTIMODE COMMUNICATION
To evaluate the high-speed communication performance of the reconfigurable photonic processor, 32Gbps non-return-to-zero (NRZ) signals are generated at a wavelength of 1530 nm.The pseudorandom binary sequence (PRBS) is obtained with a bit pattern generator (BPG) and a LiNbO 3 Mach-Zehnder modulator.The experimental setup is shown in Figure S4a, various orthogonal fiber modes including LP 01-x , LP 01-y , LP 11a-x , LP 11a-y , LP 11b-x , and LP 11b-y are selectively launched in the FMF at the transmitter side.After the training process at the receiver side, the photonic processor can route the modulated optical signals to any desired output port and undo the signal mixing process.Figure 4a presents clear and open eye diagrams for each of the fiber modes which primarily benefited from the low-loss multichannel optical I/O.The experimental results reveal that a high- dimensional optical fiber communication system can be realized by our reconfigurable integrated photonic processor.
To further evaluate the all-optical descrambling performance at the receiver side with additional concurrent channels injected, three spatially decoupled data channels are launched simultaneously from the transmitter side.It is worth mentioning that a mode-selective fiber photonic lantern [42] is used here, because the input grating couplers of our transmitter are not optimally positioned for an FAU in multichannel operation (as shown in Figure S4b), which can be addressed in the future design.The experimental setup with three concurrent channels injected is illustrated in Figure S4c.Due to the coherent interference between the three spectrally overlapped channels, the corresponding eye diagram is completely closed, as shown in Figure 4b.In contrast, when the optical mesh is carefully configured and trained, a clear and open eye diagram can be effectively reconfigured.As more concurrent data channels are activated, the eye diagram experiences very slight degradation due to a crosstalk suppression level of >21 dB.Bit error rate measurements are also performed as presented in Figure 4c, which shows a power penalty of about 0.5 dB at a BER threshold of 10 -8 when all three concurrent modes are switched on.

DISCUSSION
In summary, we have proposed and demonstrated a high-dimensional optical fiber communication system which is enabled by a reconfigurable integrated photonic processor.Selective mode launching and all-optical mode descrambling were realized by the integrated multimode optical I/O and MZI-based optical unitary mesh.The photonic processor is capable of unscrambling the random mode and polarization mixing that occurs during transmission through a circular-core FMF.Six spatialand polarization channels, including the full set modes in the LP 01 and LP 11 mode groups can be utilized for the MDM fiber communications with high transmission efficiency.High-quality eye diagrams can be retrieved even when additional concurrent modes are activated, showing a very small power penalty on the measured BERs.
To further reduce the residual crosstalk unscrambled by the integrated optical mesh, one approach is to optimize the center wavelength of the multimode optical I/O to decrease channel-dependent loss.Another universal solution is to implement more complex optical mesh architectures to execute non-unitary linear matrix transformations [40,41].This approach can descramble optical modes that have experienced substantial modedependent loss and differential mode group delay, at the expense of increased circuit complexity.Additionally, to prevent communication interruptions, progressive self-configuration with feedback can also be implemented for simple and precise control of the integrated optical mesh [35,36], and to handle the arbitrary mode evolution and polarization rotation during the long-distance optical fiber transmission.
The number of involved spatial channels can also be increased by optimizing the multimode optical I/O and the optical mesh.For instance, LP 21b mode can also be launched by feeding two counterpropagating TE1 modes with a relative phase shift of π, using the same multimode grating coupler at the transmitter side in this work.To undo the signal mixing, the receiver side would require a non-unitary optical mesh as not all of the degenerate modes in the LP 21 group can be efficiently coupled back to the photonic chip.This would also necessitate the scaling of the dimension size of the integrated optical mesh and optical I/O.Silicon photonic integrated processors are expected to be an enabling technology for future MDM applications in a variety of different fields, such as communications, imaging, sensing, and quantum networks.

Methods
Multimode optical I/O design.The multimode grating coupler is designed for operation around 1550 nm wavelength range with a perfect vertical coupling configuration.70-nm shallow etched holes are utilized as the low-index region for diffraction with a symmetrical pattern for the orthogonal polarizations.To reduce the coupling loss, chirped grating periods and hole diameter are optimized by genetic algorithm with effective medium theory and 2 dimensioanl (2D) finite-difference time-domain (FDTD) simulations.3D FDTD simulations are performed to validate the coupling performances of all the high-order fiber modes.Four asymmetrical directional couplers (ADCs) are used to (de)multiplex the TE 0 and TE 1 modes on chip.The relative phase shift is adjusted by a heater-based waveguide phase shifter with titanium-tungsten alloy (TiW) on the top.The two-mode FMF used in our experiment is fabricated by OFS.Photonic chip fabrication.The photonic chip is fabricated on a silicon-on-insulator (SOI) wafer with a 220 nm thick top silicon layer.The buried-oxide layer is 2 µm thick.Electro-beam lithography is used to define the device patterns, followed by dry reactive-ion etching process with a etch depth of 70 nm and a full etch.To protect the photonic circuits, a top cladding of silicon dioxide (SiO 2 ) with a thickness of 1.2 µm is used.Metallization is done using high-resistance titanium-tungsten alloy (TiW) for local heat generation and aluminum for electrical signal routing.A 300nm thick SiO 2 passivation layer is used and selectively etched later over the aluminum pads for probing.
MDM chip-to-chip data transmission.For high-speed interchip optical communications, the tunable laser (Santec TSL-570) is set at 1530 nm with an output power of 13dBm injected into a LiNbO 3 Mach-Zehnder modulator (AFR AM40).The optical modulator is driven by a BPG (Keysight 8045A) with an RF amplifier (SHF S807C).The modulator optical signals are spatially decoupled by SMFs with a transmission distance of 2 km and 5 km and sent to the mode-selective fiber photonic lantern with a two-mode FMF.The integrated photonic processor is controlled by a multichannel source measurement unit (Nicslab XDAC-120U-R4G8) and personal computer for the training process.An 8channel optical power meter (Santec MPM-210H and MPM-215) is employed to read the optical powers from the fiber array.For eye diagram characterization at the receiver side, the optical signal is boosted by an erbium-doped fiber amplifier (EDFA, Amonics AEDFA-PA-35-B-FA) and sent to a 50-GHz PIN photodiode (Coherent XPDV2320R).The eye-diagram and bit error rate are obtained from a sampling oscilloscope (Keysight N1000A) and BERT (Keysight 8040A).

Figure 1 .
Figure1.Schematic of the high-dimensional optical fiber communication system with reconfigurable integrated photonic processor.Top inset: mode field profile of the eigenmodes and linear polarized (LP) modes in a two-mode fewmode fiber (FMF).Bottom inset: ariel view of the integrated multimode grating coupler as optical I/O (not in scale).PICTX: photonic integrated circuits at the transmitter side; PICRX: photonic integrated circuits at the receiver side.Continuous mixing of optical signals occurs during propagation in a circular-core FMF due to rotation symmetry and spatial degeneracy.

Figure 2 .
Figure 2. (a) Experimental chip-to-fiber coupling loss spectra of the multimode grating coupler for various LP modes.(b) Field profile of the FMF captured by an infrared camera with a 10× microscope objective when different fiber mode is selectively launched by the PICTX.Schematic of the optical mesh based on Mach-Zehnder interferometers (MZIs) at the receiver side for mode unscrambling.(d) Microscopic image of the wired-bonded photonic integrated circuits used at the received side.

Figure 3 .
Figure 3. (a) Experimental setup used for inter-chip MDM fiber communication system.TL: tunable laser, BS: beam splitter, FMF: few-mode fiber, PD: photodiode.(b) Photograph of the wired-bonded photonic chip under test at the receiver side with FAU (fiber array unit) and FMF.(c) Evolution of the normalized transmission for eight output ports with the training process.(d) Bar chart of the initial random state, intermediate state, and final state for 6 space and polarization channels during the training process.(e) Bar chart of another routing configuration after training by the PSO algorithm.The mode 1-6 refer to LP01-x, LP01-y, LP11a-x, LP11a-y, LP 11b-x , LP 11b-y .

Figure 4 .
Figure 4. (a) 32Gbps eye diagrams of the six space and polarization channels retrieved by the integrated photonic processor.(b) Eye diagrams and (c) BERs retrieved and with a minor penalty when additional concurrent fiber modes are turned on.The eye diagram is completely closed without mode reconstruction due to the coherent beating of the three concurrent modes.

Acknowledgements:
This work was supported by Guangzhou -HKUST(GZ) Joint Funding Program (No. 2023A03J0159), Startup fund from the Hong Kong University of Science and Technology (Guangzhou), and Hong Kong Innovation and Technology Fund project ITS/226/21FP.The authors acknowledge the Novel IC Exploration (NICE) Facility of HKUST(GZ) for device measurement and Applied Nanotools Inc. for device fabrication.Conflicts: The authors declare no conflicts of interest.