Towards universal multi-dimensional parallelization communications by direct diverse fiber/3D/2D chip hybrid integration

Domain: physics
Published: 2026-03-10
Editorial outcome: minor_revision

Abstract
Space-division multiplexing (SDM) is a promising technology for significantly increasing the capacity of
a single fiber or waveguide. Various SDM fibers, including few-mode fibers (FMFs), multi-core fibers
(MCFs), and orbital angular momentum fibers (OAMFs), demonstrate distinct advantages in fiber links,
driving a prevailing trend toward their parallel utilization. Photonic integrated circuits extend SDM from
long-distance fibers to chip-scale interconnects. However, mode-field mismatches between fibers and
chips pose compatibility challenges. Here, we develop diverse fiber-chip couplers via fiber/3D/2D chip
hybrid integration to achieve seamless “fiber-to-fiber” and “fiber-to-chip” mode-field conversions. Building
on this, we integrate large-scale, multifunctional 2D silicon chips to construct a fiber-chip-fiber system
compatible with FMF, MCF, OAMF, and single-mode fibers. This parallel communication successfully
demonstrates 288 channels (8 spatial modes and 36 wavelengths) and 30-Tbit/s capacity. This work
establishes a universal multi-dimensional parallelization communication architecture, paving the way for
next-generation multi-dimensional data transmission and management.

Introduction
Optical communication is a critical part of global communication infrastructure, meeting the growing data
demand1–5. While space-division multiplexing (SDM) technology utilizes orthogonal spatial/mode
channels to significantly enhance fiber communication capacity 6–13, there has been no trend showing
that a particular type of SDM fiber could dominate the field. Various types of fibers, such as few-mode
fibers (FMF)14–16, multi-core fibers (MCF)17, orbital angular momentum fibers (OAMF)18,19, and others,
each has its respective advantages in specific domains. With the development of integrated photonic
technologies20, SDM is progressively extending from long-distance fiber-optic communication to short-
distance waveguide transmission21–23. Multimode waveguide (MMW) can also multiply capacity by
transmitting multiple orthogonal on-chip modes24,25. Therefore, in both the present and for the
foreseeable future, compatible solution using multiple types of fibers and waveguides will remain the
status quo in optical communications. To meet these challenges, universal interfaces and parallel
communications supporting various fibers and waveguides have become more essential.

Integrated photonics can provide universal compact solutions. Despite the achievement of multi-
dimensional data transmission integrated communication systems, conventional schemes still struggle
to deliver the tailored interfaces and required data throughput while maintaining compact structure in
multi-fiber/chip data transmission and processing scenarios. The challenges arise from two key aspects.
Firstly, there are a significant shape/size mismatches in various fibers and waveguide, resulting in the
inability of direct, efficient, and low-crosstalk interconnection of various spatial channels. The most
convenient scheme to convert a spatially distributed field is to use the commercial spatial light modulators
26 and flexible fiber-optic devices 27, which, however, maintain their high performance with a large footprint.
It is worth noting that fs-laser-inscribed silica chip offers excellent capability for manipulating complex
two-dimensional optical field distributions within a compact footprint, owing to their intrinsic three-
dimensional fabrication flexibility. However, since 3D photonic chips are typically fabricated in transparent
dielectric substrates with waveguides embedded beneath the surface, integrating conductive electrodes
deep within the structure remains a significant challenge. Additionally, electrode routing can introduce
optical losses and degrade device performance, thereby limiting the realization of advanced signal
processing functions.

Another issue lies in the high-throughput data processing. Silicon photonics is considered to be an
attractive signal processing platform owing to its high refractive index difference and complementary
metal-oxide semiconductor compatibility. Recently, there have been notable advancements in the
performance of silicon photonic signal processors, particularly in terms of throughput, reconfigurability,
programmability, and multi-tasking. Some grating couplers and edge couplers have been proposed to
successfully achieve coupling between fiber and chip14,15,28–38, these couplers are only used to connect
single-mode fiber (SMF) or FMF to silicon waveguides. Silicon MCF and OAMF couplers have rarely
been reported. Therefore, different photonic chips possess complementary advantages and limitations.
Although interfacing these strengths of two distinct chips presents a straightforward and commendable
strategy for overcoming their respective shortcomings, until now, such a combination has typically relied
on multiple single-mode fibers and fiber-optic components for interconnection, thereby undermining the
anticipated merits of integrated photonics.

Here, we make a key step in combining these two essential integrated chips by the hybrid integration
technologies, which not only achieve the compatibility with various fibers and waveguides, but also take
advantage of 3D silica chip and 2D silicon chip in a compact form. Among them, the 3D silica chip
provides efficient, low-crosstalk interfaces for various types of fibers and waveguides (OAMF, MCF, FMF,
and MMW), therefore serving as a “bridge” between optical fibers and silicon chips. This bridging
capability enables fiber-to-fiber and fiber-to-chip multimode field conversion. On this basis, by combining
large-scale, multi-channel, multifunctional silicon chip, we construct a fiber-chip-fiber interconnection link
equipped with OAMF, MCF, FMF, and SMF, featuring 288 optical management channels and a system
capacity of 30 Tbit/s. This work provides an ideal compact platform to achieve mode manipulation and
parallelization communications, and will accelerate the proliferation of SDM fibers and integrated
photonics chips for the next generation of communication system.

Results
Design and fabrication

The proposed diverse parallel multi-dimensional communication is illustrated conceptually in Fig. 1.
The design enables parallel data transport and management through multi-fiber, multi-chip, and multi-
dimensional coordination. Multiple fibers including SMF, FMF, MCF, and OAMF, serve as the long-
distance data transmission medium, supporting multiple wavelengths. Each fiber can be directly coupled
through the low-loss interfaces based on the fs-laser inscribed 3D SiO chip. The 3D SiO chip not only
2 2
demultiplexes multiple spatial/mode channels of SDM fibers into arrayed single-mode channels with low
crosstalk, but also provides an interface for silicon chips with small spot sizes. Each-channel signals are
guided to the 2D silicon chip, where multiple on-chip channels can also be multiplexed in multimode
waveguides. Each channel can be manipulated individually to control the wavelength/amplitude of the
signals by reconfigurable optical add/drop multiplexer (ROADM) and Mach-Zehnder interferometer (MZI)
array. Building on the synergistic optimization enabled by hybrid integration technology, diverse optical
fibers, 3D SiO chip, and 2D Si chip can be directly edge-coupled to leverage their respective strengths
2
and compensate for their limitations. Based on this approach, the fiber-chip-fiber system facilitates
multiple functionalities. 1) Structured light tailoring: the system enables arbitrary mode-field conversion
not only between different fiber types but also from multiple SDM fibers to on-chip multimode waveguides.
2) Multi-dimensional signal management: a larger-scale 288-channel ROADM is employed to implement
dynamic interconnections in an 8-core fiber, with an MZI array used for channel equalization. 3) High-
capacity data transmission: a fiber-chip-fiber interconnection link incorporating OAMF, MCF, FMF and
SMF is constructed, supporting 288 optical signal channels and achieving a system capacity of 30 Tbit/s.

In this work, the implementation setup of this concept is depicted in Fig. 2b. It comprises input/output
fiber, add/drop fiber, 3D SiO chip, 2D Si chip, printed circuit board (PCB). The inset of Fig. 2a shows the
2
interface of input 8-core fiber in 3D SiO chip. By using the high-repetition-rate Ytterbium-based laser
2
that provides a fs-laser beam, these interfaces are fabricated in a footprint 20 × 30 mm2 glass-substrate
chip. Silicon chip is fabricated by the standard CMOS-compatible fabrication process with a 220 nm-thick
silicon core. More details about the two fabrication methods can be found in Supplementary Information
S1. Fig. 2c shows the photograph of silicon. The overall chip footprint is about 8 × 32 mm2. Fig. 2d and
Fig. 2e display the microring array, optical attenuation array, and crossing array. All of the tuning building
blocks are wire-bonded to a carrier PCB and controlled by a programmable control circuit for
reconfiguration. The scanning electron microscope images in Fig. 2f highlight the details of the edge
coupler, the multimode interferometer, and the microring, respectively. In order to conveniently test
individual add/drop channels, single-mode grating couplers are used to test each channel separately.

Structural light tailoring in fiber and chip

Due to the exceptional 3D fabrication capabilities of fs-lasers direct writing technology, the silica chip
offers advantages in insertion loss, size, and flexibility, while also being highly versatile. It can efficiently
tailor various optical fields in fiber with low loss and low crosstalk. Hence, arbitrary mode-field conversion
can be realized by introducing several high-performance components. First, we use the slit method for
beam shaping to improve the symmetry of the waveguide cross-section, thereby achieving ultra-low-loss
waveguides. As shown in Fig. 3a, by fixing a mechanical slit above the objective lens, the waveguide
shape can be transformed from a long and narrow form to an approximate circular shape. This
improvement arises because the femtosecond laser emitted from the laser source does not exhibit a
perfect Gaussian beam profile, which in turn affects the waveguide cross-section during fabrication. As
shown in the transmission spectrum in Fig. 3a, the transmission loss of the waveguide is reduced by an
order of magnitude, from 1 dB/cm to 0.1 dB/cm. Low-loss waveguides serve as the fundamental building
blocks for low-loss 3D photonic devices. Then, for multi-core fiber mode-field transformation, S-bend
waveguides are employed to distribute the spatial positions of the mode fields. An optimized bending
curve is utilized to reduce mode leakage, inter-core crosstalk, and transmission loss of 3D device. As
illustrated in Fig. 3b, the curvature of the bending curve is continuous, ensuring that the first and second
derivatives of the waveguide's curvature function are continuous, theoretically reducing the transition
loss to zero39,40. The detailed bending design process can be found in Supplementary Information S2.
Based on the optimized S-bend waveguides, we fabricated high-performance 8-core MCF fan-in/fan-out
(FIFO) devices. As depicted in the transmission spectrum in Fig. 3b, the device losses across the entire
C-band for all channels is <2.7 dB. The crosstalk is <-36 dB across the C-band, as shown in Fig. S8. The
transmission spectrum measurement setups for various devices can be found in Supplementary
Information S3. Next, we utilize a photonic lantern structure to (de) multiplex various modes in MDM
fibers. As shown in Fig. 3c, conventional photonic lanterns employ non-uniform waveguide designs due
to varying waveguide diameters41,42. However, 3D waveguides are fabricated with a minimum loss
diameter, and different waveguide diameters can degrade the performance of waveguide devices. Here,
uniform waveguides and 3D trajectories are used to achieve low-loss, low-crosstalk FMF (de)multiplexing,
by fully leveraging the 3D fabrication capabilities. Notably, we can achieve efficient, low-crosstalk OAM
mode multiplexing and demultiplexing by modifying the parameters of the 3D trajectory. The designs for
few-mode fiber and OAM fiber are detailed in Supplementary Information S4. Fig. 3c presents that the
insertion loss for all channels is less than 3 dB. Notably, the loss of the fundamental mode in the multi-
mode multiplexer is lower than the higher-order modes but noticeably higher than the loss for single-
mode interfaces. As shown in the Supplementary Information S5 the corresponding mode multiplexers
also exhibit crosstalk of <-15 dB, supporting high-speed optical communication. Finally, in addition to
providing interfaces for various optical fibers, our 3D silica chip can also provide interfaces for silicon
chips. As is well known, when single-mode coupling to the end face of a silicon chip, there is a significant
size mismatch. Typically, lens fibers or tapered fibers are used to achieve a small mode-field spot size,
reducing loss. Here, we utilize the fs laser to compress the spot size directly on the chip, as shown in
Fig. 3d. Usually, single-mode waveguides are fabricated by multiple direct writing steps with slight offsets.
In this case, we gradually focus the waveguide to a single point, thereby efficiently coupling it to the
silicon chip. The transmission spectra in Fig. 3d show that the simulation and measurement coupling
losses of the 2D/3D chip are lower than 1.6 dB and 2 dB in the C-band, respectively.

To demonstrate arbitrary structured light field conversion in optical fibers, we present in Fig. 3e a
structural diagram of mode-field transformations among an 8-core MCF, 3-mode FMF (LP , LP , LP ),
01 11a 11b
3-mode OAMF (OAM , OAM , OAM ), and 2 SMFs. Based on these fundamental building blocks, an
0 1 -1
integrated 3D silica photonic chip is fabricated incorporating an 8-core FIFO device, a 3-mode LP mode
(de)multiplexer, a 3-mode OAM (de)multiplexer, and two single-mode interfaces. All multimode ports are
located on one side of the chip, while the demultiplexed single-mode outputs are placed on the opposite
side. The single-mode output ports are spaced at 127 µm, enabling efficient coupling with commercially
available fiber arrays. Each single-mode port is equipped with a tapered waveguide to compress the
mode field diameter, facilitating low-loss coupling with silicon waveguides. Notably, silicon waveguides
can provide compact, low-loss 90° bending structures that are challenging to achieve in 3D glass-based
platforms. As in our previous work15, incorporating multi-channel non-blocking optical switches enables
reconfigurable mapping and conversion of structured light fields. Thus, each core channel of the 8-core
fiber can be dynamically mapped onto various higher-order or fundamental modes in other fibers.
Tailored 3D chips can be designed and fabricated to enable the desired spatial light field conversion. Fig.
3f shows measured cross-sectional intensity profiles of the input 8-core MCF and output FMF, OAMF,
and two SMFs. Interference patterns of the OAM modes are also included, confirming the device’s ability
to precisely manipulate and interconvert diverse structured optical fields among different fiber types. As
shown in Fig. S10 (Supplementary Information S6), the transmission spectra for various fiber conversion
exhibit an insertion loss less than 9 dB and crosstalk below –13 dB throughout the C-band.

Furthermore, as illustrated in Fig. 3g, our integrated devices allow for mode conversion not only
between fibers but also between fibers and silicon multimode waveguides. With on-chip mode
(de)multiplexers, multiple structured light fields can be directly coupled into and out of silicon photonic
circuits. The silicon multimode waveguide has a width of 1.2 μm and a height of 0.22 μm. Fig. 3h displays
the transmission spectra of the three LP modes, three OAM modes, and six directly converted modes
on-chip, showing insertion losses below 5.5 dB across the entire C-band. Fig. 3i and Fig. 3j report mode
crosstalk levels below –13 dB at both 1530 nm and 1550 nm. Fig. S10 shows that crosstalk remains
below –13 dB across other wavelengths, demonstrating broadband operational stability.

Large-scale multifunctional silicon chip

Silicon photonic signal managers, with their vast bandwidth, high refractive index contrast, compactness,
and robust information security, have ushered in a new era of information management. With the aid of
tunable components, programmable photonic signal managers can perform various signal management
tasks, thereby establishing a multifunctional hardware platform. Among these components, the MZI,
consisting of two 2×2 power splitters and a phase shifter, is one of the key tunable elements. It can be
used to construct multi-channel optical switches15, MIMO processors16, unitary matrices, quantum
gates43, and more, thereby driving the miniaturization of fields such as optical communication, optical
computing, and quantum computing. In this work, we employ the MZI as an optical attenuator array to
achieve optical power balancing. Fig. 4a shows the measurement results of the MZI device, which
demonstrate insertion loss of less than 1 dB and crosstalk below -22 dB. Based on this MZI array, we
can also selectively attenuate different spatial channels. As illustrated in Fig. 4b, we can independently
attenuate one channel, two channels, or four channels. In addition to managing spatial channels, the 2D
silicon chip can also perform wavelength management using micro-ring resonators (MRRs) based on its
own resonant characteristics. As shown in the inset of Fig. 4c, the wavelength-selective switch uses
elliptical micro-rings with adiabatically varying radii and core widths44. In the coupling region, a relatively
large bend radius and narrower waveguide width are designed to achieve sufficient coupling efficiency,
while a smaller bend radius and wider core width are used to reduce bending losses and cavity length.
The shortened cavity length helps achieve a free spectral range (FSR) of ~26 nm, supporting 36
wavelengths with channel spacing of ~0.4 nm (~50 Ghz). Unlike traditional MRR optimized for critical
coupling, this design slightly reduces the spacing between the coupling waveguides to enhance coupling
efficiency, thereby achieving an "under-coupled" state. In this under-coupled state, the 3-dB bandwidth
of the resonant peaks can be broadened with a slight sacrifice in insertion loss, facilitating higher-speed
signal processing. A detailed 3-dB bandwidth analysis of the MRR is provided in Supplementary
Information S7.

Fig. 4d displays the transmission spectra of 8 tuned micro-ring resonators within a 36 micro-ring array,
demonstrating their ability to effectively manage signals across 288 wavelengths. The inconsistency in
MRR insertion loss originates from two main factors. First, the cascaded structure inherently causes the
loss at the resonant wavelength to increase along the chain. Second, the MRR insertion loss is extracted
by subtracting the losses of other components from the total link loss, and the cumulative effect of
fabrication-induced variations across different channels contributes to a power fluctuation of
approximately 2 dB in the MRR response.

Diverse fiber-chip parallelization communications

Finally, we demonstrate an optical fiber-chip-fiber parallel communication system compatible with
various fiber types. Based on these devices, we further build a diversified system, achieving 288-channel,
30 Tbit/s multidimensional data transmission and management. Figs. 5a-c show the complete
experimental system for multidimensional data transmission and management, which consists of three
main parts: a wavelength-division multiplexing (WDM) signal transmitter with 16-level quadrature
amplitude modulation (QAM), the fiber/3D/2D hybrid integration system, and a coherent optical receiver
followed by digital signal processing. At the transmission end, 36 wavelength-tunable external cavity
lasers (ECLs) serve as the optical signal carriers, with wavelength spacing of 0.4 nm/50 GHz. To emulate
practical communication scenarios, the 36 ECLs are divided into odd and even groups, and a four-
channel arbitrary waveform generator (AWG: Keysight M8199A) is used to drive two in-phase/quadrature
(I/Q) modulators to independently modulate 28-GBaud 16-QAM signals. To prevent the underestimation
of bit-error rate (BER) in the WDM system, an optical delay line is employed to decorrelate the odd and
even optical signals. Alternatively, a 100G optical frequency comb can be used between the two channels
to reduce the size of the transmitter. The modulated odd and even signals are combined through a 50:50
optical coupler (OC) and amplified by a C-band EDFA. Subsequently, the 36-channel WDM signals
(wavelength range from 1530.2 nm to 1544.2 nm) are transmitted to the FMF-chip data transmission and
signal management system, as shown in Fig. 5d. The observed non-uniform channel spacing, resulting
from laser tuning inaccuracies, directly contributes to performance fluctuations in inter-wavelength
crosstalk and BER. The amplified WDM signal is divided into eight parts and further decorrelated via
different optical delay lines. Eight EDFAs are used to compensate for the losses in the fiber-chip-fiber
system. The maximum loss for the dropping function system is 25 dB, consisting of the following
components: a silica fan-in chip (< 3 dB), an 8-core fiber segment (< 1 dB), a hybrid integrated coupler
(< 4.5 dB), a silicon MZI (< 1 dB), an MRR array (< 9 dB), a grating (< 4.5 dB), and multiple bends and
crossings (< 2 dB). For the adding function system, the maximum loss is 27.5 dB. Compared to the
dropping system, the adding system exhibits an extra 2.5-dB loss due to the 1.2-cm-long waveguide loop
integrated in the silicon chip. These eight channels are multiplexed into eight different cores of an 8-core
fiber using silica photonic FIFO devices. After transmission through the 8-core fiber, the high-capacity
signal is coupled into the silicon chip using customized edge couplers. Next, an MZI switch array is used
to balance channel losses. Therefore, the 288-channel signals can be flexibly extracted from the 2D
photonic integrated circuits and sent to the integrated coherent optical receiver and local oscillator (LO).
A real-time oscilloscope (Keysight UXR0594) is used to sample and store electrical signals from the
coherent optical receiver for offline DSP and BER evaluation. The offline DSP includes signal resampling,
IQ non-orthogonal compensation using the Gram-Schmidt orthogonalization process, linear equalization,
frequency offset estimation and carrier phase recovery. In addition to signal dropping, external signals
can also be added to the communication system through micro-ring resonators. Similarly, the MZI array,
acting as an equalizer, can manage signals in individual spatial channels. Finally, the signals from these
eight spatial channels can not only be coupled into the eight-core fiber through the 8-core-fiber FIFO
devices but also be coupled into different fibers through the fiber/3D/2D hybrid integration coupler (3 LP
modes, 3 OAM modes, 2 base modes). Notably, only two fixtures are used to secure two fibers (one
input, one output), but in practice, more fiber arrays can be provided to customize multi-fiber input-output
systems.

To demonstrate the data throughput, we asynchronously demultiplexed, received, and tested each
spatial/wavelength channel in the multi-fiber/3D/2D hybrid integration fiber-chip system. Fig. 5e shows
the BER test results for all 288 channels in the 8-core fiber data transmission and management scenario.
The results show that the BER for each channel is below the 7% forward error correction (FEC) threshold
of 3.8 × 10⁻³. Fig. 5f shows the relationship between the BER and the received optical signal-to-noise
ratio (OSNR) for the eight different wavelength spatial channels extracted from the silicon ROADM
system. To simplify and ensure comprehensiveness, we select six mode channels: #8 (channel 1), #7
(channel 6), #6 (channel 11), #5 (channel 16), #4 (channel 21), #3 (channel 26), #2 (channel 31), and #1
(channel 36). It is clear that the BER curves for these six selected channels consistently stay below the
7% FEC threshold, even in the presence of mode-to-mode and wavelength-to-wavelength crosstalk.
When the OSNR exceeds 21 dB, the performance remains stable. Compared to the backhaul
transmission performance of each channel, the OSNR penalty for the six selected channels in the FMF-
chip system is less than 5 dB under the 7% FEC threshold. For the adding functionality, we choose a
multi-fiber scenario to demonstrate the observed OSNR penalty, with results showing that the penalty for
all eight spatial channels remains below 7 dB, as shown in Fig. 5g. Notably, the OSNR penalty for the
base mode channels is slightly lower than that for the higher-order mode channels due to increased
mode crosstalk in the latter. Fig. 5h presents the BER test results for all 288 channels in the multi-fiber
data transmission and management scenario, showing that all BER values remain below the 7% FEC
threshold. The inset shows the typical constellation diagram for the 16-QAM signal, highlighting the
excellent performance. Therefore, the proposed multi-fiber data transmission and signal management
system successfully achieve total transmission rate of 30.15 Tbit/s (28 Gbaud × 4 bits per symbol × 8
spatial modes × 36 wavelengths / (1 + 7%) ≈ 30.15 Tbit/s).

Methods
Femtosecond-laser fabrication. The 3D silica chip is processed using femtosecond laser fabrication
technology, employing a high-repetition-rate Ytterbium-based laser (wavelength: 1030 nm, repetition rate:
200 kHz, pulse duration: 234 fs). The femtosecond-laser, with linear polarization, is focused vertically
approximately 50 μm below the top surface of the silica photonic chip using a 50× 0.42 objective lens. A
linear slit is used to modify the laser beam profile, enabling the inscription of low-loss circular waveguides
in the glass. Additionally, waveguides with multiple scanning passes are introduced to enhance the
refractive index contrast and improve the waveguide's smoothness. The femtosecond-laser inscription
speed is maintained at a constant rate of 0.2 mm/s. The refractive index contrast of the resulting
waveguides is approximately 0.3%.

Silicon chip Fabrication. The 2D silicon photonic chip is fabricated using a CMOS-compatible process
on a silicon-on-insulator (SOI) substrate, which features a 220-nm-thick top silicon layer and a 2-μm-
thick buried oxide layer. Device patterns are defined using electron-beam lithography (EBL), followed by
dry reactive-ion etching to achieve etch depths of 70 nm and 220 nm. A 1.2-μm-thick SiO cladding layer
2
is then deposited to protect the photonic circuits. For metallization, a titanium (Ti) layer is used for local
heat generation, while aluminum is employed for electrical signal routing. To protect the electrode pads,
an additional SiO layer is deposited, and a final set of deep ultraviolet (DUV) lithography and reactive
2
ion etching (RIE) processes are applied to remove the dielectric material from the pads.

Measurements. For multimode silicon devices on the chip, a set of mode multiplexers and
demultiplexers are used to prepare and demodulate higher-order waveguide modes. These mode
multiplexers/demultiplexers are similar to other single-mode devices and are interconnected with single-
mode fibers through either end-face coupling or grating couplers. For 3D SiO₂ chips, devices with
multimode ports require two identical devices and shorter fibers to form an interconnection system for
testing. For devices containing only single-mode channels, measurements are taken via single-mode
end-face coupling. In all chip tests, a tunable laser (Santec TSL-710) is used as the light source, covering
the C-band, and its polarization state is adjusted using a polarization controller. Finally, the optical signal
is monitored using an optical power meter (PMSII-A). The detailed setup information can be found in
Supplementary Information S3.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this study, the authors present a universal architecture that overcomes the critical challenge of mode mismatch in space-division multiplexing systems. By innovatively combining fiber-chip hybrid integration with femtosecond-laser processing, they demonstrate highly efficient couplers compatible with various fiber types. Most remarkably, the authors achieve a 288-channel parallel communication system with 30 Tbit/s total capacity, establishing a versatile platform for next-generation multi-dimensional data transmission and paving the way for future high-capacity communication systems. The manuscript is well-structured and validated by comprehensive experimental results. It holds significant interest for audiences in optics, photonics, and communications. Overall, I recommend its publication in Nature communications after addressing the following minor comments:\n1. The authors have presented a highly impressive and innovative work. The heterogeneous integration approach between the fiber and chip is pivotal to the success of this architecture and deserves to be more clearly elaborated for the reader.\n2. The hybrid integration technology presented in this work is highly significant and represents a valuable approach that could benefit the research community. To fully enable readers to appreciate and learn from this key methodological advancement, it would be greatly beneficial if the authors could provide a more detailed description of the integration process, either within the main manuscript or as supplementary information.\n3. The use of a single AWG for 36 transmitters implies that odd/even wavelengths carry identical signals. The role of this division is unclear, especially since no decorrelation is applied.\n4. In fig.4d, the wavelength spacing does not appear to be strictly aligned. Please explain why this is the case.\n5. The statement \"... capability of 20 Tbit/s\" in discussion seems somewhat inaccurate in terms of numbers.\nIn conclusion, I believe this manuscript is suitable for publication after addressing the above comments and questions.", "reviewer_2": "This work presents a system that enables efficient coupling and multi-dimensional parallel data transmission among various types of SDM optical fibers (SMF, FMF, MCF, OAMF) and silicon photonic chips through a fiber-chip-fiber heterogeneous integration approach. The authors demonstrate a high-capacity transmission of 30 Tbit/s across 288 channels. The paper presents a clear overall framework and provides a technically detailed implementation. Overall, it effectively highlights the synergistic advantages of femtosecond-laser-inscribed 3D glass chips combined with large-scale silicon-photonic ROADM architectures. Several concerns need to be addressed:\nQ.1. The author mentioned using the ‘under-coupled’ state of MRR to obtain broadened 3-dB bandwidth. However, this property generally appears in ‘over-coupled’ state. A detailed explanation should be provided.\nQ.2. In Fig. 3d, the simulated transmission spectrum of mode-compressing waveguide shows a clear ripple, while the measured one is flat. Could the author explain the reason?\nQ.3. There are a few errors in figure captions and their corresponding text throughout the manuscript; please proofread the manuscript again to catch the remaining errors.\nQ.4. The measured spectra of tuned MRR are presented in Fig. 3d (Large-scale 2D silicon ROADM) with poor loss uniformity. Please explain the reason.\nQ.5. Please clearly describe the function of the fiber-chip-fiber system management. Is it possible to achieve switching between different spatial modes?\nQ.6. A summarized loss decomposition for the data transmission experiment should be added.\nQ.7. Please discuss the effect of the fiber disturbance to the signal quality.\nQ.8. In Fig. 3h, the transmission spectra between the fiber and the multimode waveguide are presented. Please provide the structure parameters of the waveguide.\nQ.9. The authors should include a table for large-capacity, multi-dimensional parallel data-transmission systems, comparing the key metrics of past work with those of the present work."}, "author_response": "Manuscript ID: NCOMMS-25-84090\nTitle: Towards universal multi-dimensional parallelization communications by direct diverse fiber/3D/2D chip\nhybrid integration\nAuthor: Kang Li, Chengkun Cai, Guofeng Yan,Bing Han, Hang Chen,Guangze Wu, and Jian Wang\nDear reviewers of Nature Communications,\nWe have carefully revised our paper (Manuscript ID: NCOMMS-25-84090) according to the valuable\ncomments of reviewers. Enclosed please find the detailed point-by-point responses. We would like to thank\nyou for the constructive comments and helpful suggestions.\nSincerely yours,\nKang Li, Chengkun Cai, Guofeng Yan,Bing Han, Hang Chen,Guangze Wu, and Jian Wang\n******************************************************************************************\nPoint-by-point response to the comments of the reviewers #1\n******************************************************************************************\nOverall Remarks:\nIn this study, the authors present a universal architecture that overcomes the critical challenge of mode\nmismatch in space-division multiplexing systems. By innovatively combining fiber-chip hybrid\nintegration with femtosecond-laser processing, they demonstrate highly efficient couplers compatible\nwith various fiber types. Most remarkably, the authors achieve a 288-channel parallel communication\nsystem with 30 Tbit/s total capacity, establishing a versatile platform for next-generation multi-\ndimensional data transmission and paving the way for future high-capacity communication systems.\nThe manuscript is well-structured and validated by comprehensive experimental results. It holds\nsignificant interest for audiences in optics, photonics, and communications. Overall, I recommend its\npublication in Nature communications after addressing the following minor comments:\nOverall Remarks:\nWe sincerely thank you for the positive comments. Following your helpful suggestions, we have\ncarefully addressed your minor comments to further improve our work in the revised paper. Please find\nour point-by-response attached.\n(1) Reviewer Comment:\nThe authors have presented a highly impressive and innovative work. The heterogeneous integration\napproach between the fiber and chip is pivotal to the success of this architecture and deserves to be\nmore clearly elaborated for the reader.\n(1) Response:\nYour comment is very helpful in improving the quality of our manuscript. Heterogeneous integration\ninvolves directly integrating different materials onto a common substrate or within a single chip, typically\nvia bonding or epitaxial growth, to form a monolithic device. This process requires all components to\nbe compatible with high-volume factory production and poses significant challenges in processing\ncompatibility, often making it difficult to fully retain the optimal performance of each individual\ncomponent. In contrast, hybrid integration combines devices made from different materials or on\nseparate chips through optical coupling or packaging, while maintaining their fabrication processes\nindependently. This approach allows each component to fully leverage its superior performance, and it\nis less demanding in terms of the individual component yield. Following the reviewer's suggestion, we\nhave re-evaluated our integration strategy and concluded that our approach aligns with hybrid\nintegration. Consequently, we have updated the entire manuscript and all relevant figures to\nconsistently refer to it as “hybrid integration”. We sincerely thank the reviewer for this valuable insight.\n(1) Revision:\nOwing to the extensive revisions made, we have not enumerated each modification individually.\n(2) Reviewer Comment:\nThe hybrid integration technology presented in this work is highly significant and represents a valuable\napproach that could benefit the research community. To fully enable readers to appreciate and learn\nfrom this key methodological advancement, it would be greatly beneficial if the authors could provide\na more detailed description of the integration process, either within the main manuscript or as\nsupplementary information.\n(2) Response:\nThank you for the reviewer’s constructive suggestion. The hybrid integration comprises two critical\ncoupling procedures: silica-to-silicon chip coupling and fiber-to-silica chip coupling.\nFor the silica-to-silicon chip coupling, two six-axis alignment stages are employed to achieve\noptimal interfacial contact. The silica chip, mounted on carrier substrate #1 and secured to the six-axis\nstage #1, is coarsely aligned with the single-mode waveguide array on the silicon chip using a single-\nmode fiber and a visible infrared laser. The silicon chip is fixed to a PCB via gold wire bonding and\nmounted on the chip holder with a custom fixture. On the opposite side, the six-axis stage #2 couples\nlight vertically into the grating couplers on the silicon chip. By injecting light into gratings of different\nspatial channels, the optical field patterns emerging at the multimode port of the silica chip can be\nobserved via a CCD camera, enabling fine positional adjustment of the silica chip.\nThe fiber-to-silica chip coupling begins by assembling the target fiber and substrate #1 (with the\nfixed silica chip) into a back-to-back fiber transmission setup. Once optimal coupling is confirmed, the\nfiber is permanently fixed to substrate #2 using UV-curable adhesive to preserve its cross-section. This\nback-to-back setup and UV curing procedure is repeated to sequentially couple subsequent fibers to\nan additional substrate #3. Both substrate #2 and substrate #3 are individually controlled by dedicated\nsix-axis stages #3, #4, with the aid of a single-mode red laser for precise alignment. Following full\nsystem assembly, all six-axis stages are coordinately fine-tuned based on power meter readings to\nglobally optimize coupling efficiency.\nIt should be noted that due to spatial constraints within the setup, only one input and one output\nfiber can be coupled at a time. However, simultaneous multi-fiber input and output can be achieved in\nthe future through custom-designed fiber arrays, thereby enhancing system integration density.\nThe above responses have been appropriately incorporated into the revised supplementary information.\n(2) Revision:\n(Section S3 of supplementary information) “Owing to the multiplicity of components, the hybrid\nintegration procedure will be elaborated upon in the following section. The hybrid integration comprises\ntwo critical coupling procedures: silica-to-silicon chip coupling and fiber-to-silica chip coupling.\nFor the silica-to-silicon chip coupling, two six-axis alignment stages are employed to achieve optimal\ninterfacial contact. The silica chip, mounted on carrier substrate #1 and secured to the six-axis stage\n#1, is coarsely aligned with the single-mode waveguide array on the silicon chip using a single-mode\nfiber and a visible infrared laser. The silicon chip is fixed to a printed circuit board (PCB) via gold wire\nbonding and mounted on the chip holder with a custom fixture. On the opposite side, the six-axis stage\n#2 couples light vertically into the grating couplers on the silicon chip. By injecting light into gratings of\ndifferent spatial channels, the optical field patterns emerging at the multimode port of the silica chip\ncan be observed via a CCD camera, enabling fine positional adjustment of the silica chip.\nThe fiber-to-silica chip coupling begins by assembling the target fiber and substrate #1 (with the fixed\nsilica chip) into a back-to-back fiber transmission setup. Once optimal coupling is confirmed, the fiber\nis permanently fixed to substrate #2 using UV-curable adhesive to preserve its cross-section. This\nback-to-back setup and UV curing procedure is repeated to sequentially couple subsequent fibers to\nan additional substrate #3. Both substrate #2 and substrate #3 are individually controlled by dedicated\nsix-axis stages #3, #4, with the aid of a single-mode red laser for precise alignment. Following full\nsystem assembly, all six-axis stages are coordinately fine-tuned based on power meter readings to\nglobally optimize coupling efficiency.\nIt should be noted that due to spatial constraints within the setup, only one input and one output fiber\ncan be coupled at a time. However, simultaneous multi-fiber input and output can be achieved in the\nfuture through custom-designed fiber arrays, thereby enhancing system integration density.”\n(3) Reviewer Comment:\nThe use of a single AWG for 36 transmitters implies that odd/even wavelengths carry identical signals.\nThe role of this division is unclear, especially since no decorrelation is applied.\n(3) Response:\nThank you for the reviewer’s constructive comment. The reviewer is correct. 36 wavelengths divided\ninto odd and even channels are designed to emulate real-world communication scenarios, where\nadjacent wavelength channels carry different data streams. A four-channel arbitrary waveform\ngenerator (AWG: Keysight M8199A) simultaneously drives two independent IQ modulators to generate\ndistinct signals for the odd and even channels. In our experiment, an optical delay line is used to\ndecorrelate the odd and even optical signals, thereby avoiding underestimation of the bit-error ratio\n(BER) in WDM systems. Due to an oversight in the drawing, this delay line was forgotten to be marked.\nThank you very much for pointing this out.\nThe above responses have been appropriately incorporated into the revised manuscript.\n(3) Revision:\n(Page 13 of the revised manuscript) “To simulate practical communication scenarios, the 36 ECLs are\ndivided into odd and even groups, and a four-channel arbitrary waveform generator (AWG: Keysight\nM8199A) is used to drive two in-phase/quadrature (I/Q) modulators to independently modulate 28-GBaud\n16-QAM signals. To prevent the underestimation of the bit-error ratio (BER) in WDM system, an optical\ndelay line is employed to decorrelate the odd and even optical signals.”\n(Figure 5 of the revised manuscript) “\n”\n(4) Reviewer Comment:\nIn fig.4d, the wavelength spacing does not appear to be strictly aligned. Please explain why this is the\ncase.\n(4) Response:\nThank you for the valuable feedback. Following the reviewer’s kind suggestion, we have quantified the\nwavelength shift caused by the limited precision of laser control. The maximum observed shift is less\nthan 0.1 nm. This shift can be further minimized by employing lasers with higher tuning precision, or\ncompletely mitigated by using optical frequency combs to maintain stable wavelength spacing.\nTherefore, the impact of wavelength shift on overall system performance remains negligible.\n(4) Revision:\n(Page 13 of the revised manuscript) “The observed non-uniform channel spacing, resulting from laser\ntuning inaccuracies, directly contributes to performance fluctuations in inter-wavelength crosstalk and bit-\nerror ratio (BER).”\n(5) Reviewer Comment:\nThe statement \"... capability of 20 Tbit/s\" in discussion seems somewhat inaccurate in terms of\nnumbers.\n(5) Response:\nThank you for your valuable feedback. In response to the reviewer's suggestion, we have conducted a\nthorough review of the entire manuscript. Both the text and figures have been carefully revised and\npolished accordingly.\n(5) Revision:\n(Page 13 of the revised manuscript) “By transmitting 28-Gbaud 16-QAM signals, our diversified fiber-chip\nsystem achieves a groundbreaking data transmission and management capability of 30 Tbit/s.”\n(6) Reviewer Comment:\nIn conclusion, I believe this manuscript is suitable for publication after addressing the above comments\nand questions.\n(6) Response:\nThank you very much for the positive feedback.\n******************************************************************************************\nPoint-by-point response to the comments of the reviewers #2\n******************************************************************************************\nOverall Remarks:\nThis work presents a system that enables efficient coupling and multi-dimensional parallel data\ntransmission among various types of SDM optical fibers (SMF, FMF, MCF, OAMF) and silicon photonic\nchips through a fiber-chip-fiber heterogeneous integration approach. The authors demonstrate a high-\ncapacity transmission of 30 Tbit/s across 288 channels. The paper presents a clear overall framework\nand provides a technically detailed implementation. Overall, it effectively highlights the synergistic\nadvantages of femtosecond-laser-inscribed 3D glass chips combined with large-scale silicon-photonic\nROADM architectures. Several concerns need to be addressed:\nOverall Remarks:\nThank you for the helpful comments and valuable suggestions. We truly appreciate the significant\namount of time and effort you dedicated to this review. In the revised manuscript, we have included\ndesign and experimental details and carefully proofread the manuscript. Please find our point-by-point\nresponse attached.\n(1) Reviewer Comment:\nQ.1. The author mentioned using the ‘under-coupled’ state of MRR to obtain broadened 3-dB\nbandwidth. However, this property generally appears in ‘over-coupled’ state. A detailed explanation\nshould be provided.\n(1) Response:\nWe are very grateful for the reviewers’ valuable feedback. In response to the reviewer’s suggestion,\nwe have included a detailed explanation of the ‘under-coupled’ MRR in the supplementary information.\nThe following analysis will use the transfer matrix model to examine the spectral properties of an\nadd-drop microring resonator (MRR). As shown in Fig. R1a, the overall structure consists of a lower\nstraight waveguide for input coupling, an upper straight waveguide for output, and a microring\nwaveguide. Resonance occurs when the round-trip optical path in the microring equals an integer\nmultiple of the wavelength, leading to constructive interference between the circulating and input light.\nThe resonant wavelength of the microring satisfies the following relation:\nm2Rn\neff\nWhere m represents the resonant order, λ is the optical wavelength, R is the radius of the microring,\nand n is the effective refractive index of the waveguide mode in the resonator. For a deeper\neff\nunderstanding of the operational mechanism, the transfer matrix model can be used for further\nderivation. As illustrated in Fig. R1a, the key aspect of the transfer matrix analysis involves the coupling\nbetween the straight waveguide and the microring, which can be expressed using a 2×2 matrix:\nE    iE \nth  1 1 in\n    \n E  i   E \n1 1 1 4\nE    i E \n drop   2 2  add \n E  i   E \n3 2 2 2\nwhere τ and τ are the coupling coefficients at the through port of the straight waveguide and the\n1 2\nmicroring, respectively, while κ and κ are the coupling coefficients between the waveguides. Under\n1 2\nthe lossless condition, τ2 + κ2 = 1 (i = 1, 2). E denotes the amplitude of the input field, E is the\ni i in th\namplitude at the through port, E and E represent the amplitudes at the drop port and add port,\ndrop add\nrespectively. E , E , E , and E correspond to the field amplitudes at four positions inside the microring.\n1 2 3 4\nAs light completes one round-trip in the microring, it accumulates a phase shift and experiences\namplitude attenuation. Thus, the recursive relationship among E , E , E , and E can be expressed as:\n1 2 3 4\n \ni i\nE  e 2E ,E  e 2E\n2 1 4 3\nWhere α denotes the round-trip loss factor of the microring. The phase change is given by θ = 2πn\neff\nL/λ, where L is the microring circumference. Assuming no input at the add port, the transfer functions\nfor the microring internal field, through-port output, and drop-port output can be derived as:\n \ni i\n e 2 k k e 2\nE  1 2 E ,E  1 2 E\nth 1ei in drop 1ei in\n1 2 1 2\nThe output light intensity can be obtained by taking the absolute square:\n2 2\nE 2 22 2cos E k2k 2\nth  1 2 1 2 , drop  1 2\nE 1222 2cos E 1222 2cos\nin 1 2 1 2 in 1 2 1 2\nAs indicated by the formulas above, when the resonance condition (θ being an integer multiple of 2π)\nis met, the drop-port output power is maximized while the through-port power is minimized, thereby\nenabling wavelength-selective filtering. Depending on the relationship between the waveguide coupling\ncoefficients and the round-trip loss factor, the MRR can operate in three characteristic coupling regimes.\nIn the critical coupling regime, where τ = ατ = t , the resonant wavelength experiences the strongest\n1 2 c\nfield suppression, yielding the highest extinction ratio at the through port. If τ > ατ , the device is under-\n1 2\ncoupled; conversely, if τ < ατ , it becomes over-coupled, resulting in a reduced extinction ratio. Fig.\n1 2\nS11b displays the drop-port transmission spectrum for τ = t – dt*i (i = 0:5). The plot reveals that as τ\n1 c 1\ndecreases, the drop-port loss increases and the 3-dB bandwidth broadens, with exact values provided\nin Fig. S11c. Therefore, to support higher-speed signal transmission, a broader 3-dB bandwidth is\nnecessary, but this is achieved at the cost of increased optical loss.\nFig. R1. MRR Analysis. (a) Structural diagram. (b) Transmission spectra of MRR drop ports under different\ncoupling efficiencies τ = t – dt*i (i = 0:5). (c) Insertion loss of resonant wavelength and 3-dB bandwidth.\n1 c\nThe above responses have been appropriately incorporated into the revised supplementary information.\n(1) Revision:\n(Page 22 of manuscript) “A detailed 3-dB analysis of the MRR is provided in Supplementary Information S7.”\n(Section S7 of supplementary information) “S7: 3-dB Bandwidth Analysis of Microring Resonators\nAn optical resonator refers to a cavity that allows light waves to reflect back and forth, thereby\nproviding feedback. The microring resonator (MRR), as one type of optical resonator, can perform\nfunctions such as optical filtering and switching, and is often used as a basic component in building\ncomplex photonic integrated devices. While their specific roles may differ, MRRs generally function by\nselecting light of specific frequencies while suppressing others. The following analysis will use the\ntransfer matrix model to examine the spectral properties of an add-drop MRR. As shown in Fig. S11a,\nthe overall structure consists of a lower straight waveguide for input coupling, an upper straight\nwaveguide for output, and a microring waveguide. Resonance occurs when the round-trip optical path\nin the microring equals an integer multiple of the wavelength, leading to constructive interference\nbetween the circulating and input light. The resonant wavelength of the microring satisfies the following\nrelation:\nm2Rn\neff\nWhere m represents the resonant order, λ is the optical wavelength, R is the radius of the microring,\nand n is the effective refractive index of the waveguide mode in the resonator. For a deeper\neff\nunderstanding of the operational mechanism, the transfer matrix model can be used for further\nderivation. As illustrated in Fig. S11a, the key aspect of the transfer matrix analysis involves the\ncoupling between the straight waveguide and the microring, which can be expressed using a 2×2 matrix:\nE    iE \nth  1 1 in\n    \n E  i   E \n1 1 1 4\nE    i E \n drop   2 2  add \n E  i   E \n3 2 2 2\nwhere τ and τ are the coupling coefficients at the through port of the straight waveguide and the\n1 2\nmicroring, respectively, while κ and κ are the coupling coefficients between the waveguides. Under\n1 2\nthe lossless condition, τ2 + κ2 = 1 (i = 1, 2). E denotes the amplitude of the input field, E is the\ni i in th\namplitude at the through port, E and E represent the amplitudes at the drop port and add port,\ndrop add\nrespectively. E , E , E , and E correspond to the field amplitudes at four positions inside the microring.\n1 2 3 4\nAs light completes one round-trip in the microring, it accumulates a phase shift and experiences\namplitude attenuation. Thus, the recursive relationship among E , E , E , and E can be expressed as:\n1 2 3 4\n \ni i\nE  e 2E ,E  e 2E\n2 1 4 3\nWhere α denotes the round-trip loss factor of the microring. The phase change is given by θ = 2πn\neff\nL/λ, where L is the microring circumference. Assuming no input at the add port, the transfer functions\nfor the microring internal field, through-port output, and drop-port output can be derived as:\n \ni i\n e 2 k k e 2\nE  1 2 E ,E  1 2 E\nth 1ei in drop 1ei in\n1 2 1 2\nThe output light intensity can be obtained by taking the absolute square:\n2 2\nE 2 22 2cos E k2k 2\nth  1 2 1 2 , drop  1 2\nE 1222 2cos E 1222 2cos\nin 1 2 1 2 in 1 2 1 2\nAs indicated by the formulas above, when the resonance condition (θ being an integer multiple of 2π)\nis met, the drop-port output power is maximized while the through-port power is minimized, thereby\nenabling wavelength-selective filtering.\nFig. S11. MRR Analysis. (a) Structural diagram. (b) Transmission spectra of MRR drop ports under\ndifferent coupling efficiencies τ = t – dt*i (i = 0:5). (c) Insertion loss of resonant wavelength and 3-dB\n1 c\nbandwidth.\nDepending on the relationship between the waveguide coupling coefficients and the round-trip loss\nfactor, the MRR can operate in three characteristic coupling regimes. In the critical coupling regime,\nwhere τ = ατ = t , the resonant wavelength experiences the strongest field suppression, yielding the\n1 2 c\nhighest extinction ratio at the through port. If τ > ατ , the device is under-coupled; conversely, if τ <\n1 2 1\nατ , it becomes over-coupled, resulting in a reduced extinction ratio. Fig. S11b displays the drop-port\n2\ntransmission spectrum for τ = t – dt*i (i = 0:5). The plot reveals that as τ decreases, the drop-port\n1 c 1\nloss increases and the 3-dB bandwidth broadens, with exact values provided in Fig. S11c. Therefore,\nto support higher-speed signal transmission, a broader 3-dB bandwidth is necessary, but this is\nachieved at the cost of increased optical loss. ”\n(2) Reviewer Comment:\nQ.2. In Fig. 3d, the simulated transmission spectrum of mode-compressing waveguide shows a clear\nripple, while the measured one is flat. Could the author explain the reason?\n(2) Response:\nWe appreciate the reviewer's attention to the transmission spectrum of the mode-compressing\nwaveguide. After carefully examining the simulation setup, we identify that the spectral ripples result\nfrom an insufficient simulation time. This short duration causes the algorithm's auto shutoff to trigger at\na residual level of 1e−4, rather than allowing it to converge fully to the target value of 1e−5. To address\nthis, the simulation time is extended to achieve a steady-state condition. As shown in the revised Fig.\n3d, the spectrum now exhibits a flat response across the C-band. We are grateful for the reviewer's\nvaluable comments, which have helped us correct the simulation results.\nThe above responses have been appropriately incorporated into the revised manuscript.\n(2) Revision:\n(Fig 3d of manuscript) “\n”\n(3) Reviewer Comment:\nQ.3. There are a few errors in figure captions and their corresponding text throughout the manuscript;\nplease proofread the manuscript again to catch the remaining errors.\n(3) Response:\nThank you for your valuable feedback. In response to the reviewer's suggestion, we have conducted a\nthorough review of the entire manuscript. Both the text and figures have been carefully revised and\npolished accordingly.\n(3) Revision:\nOwing to the extensive revisions made, we have not enumerated each modification individually.\n(4) Reviewer Comment:\nQ.4. The measured spectra of tuned MRR are presented in Fig. 3d (Large-scale 2D silicon ROADM)\nwith poor loss uniformity. Please explain the reason.\n(4) Response:\nThank you very much for the valuable feedback. The reviewer is correct. A certain degree of\ninconsistency is observed in the measured spectra of the MRRs, which can be attributed to two main\nfactors.\nFirst, the 36 MRRs in each spatial channel are connected in a cascade configuration. This results in\nthe lowest insertion loss for the first MRR and the highest for the 36th. Theoretically, the optical power\nat the resonant wavelength is expected to decrease progressively along the cascade, which is\nconsistent with the overall trend observed in the measured spectra of all 36 MRRs. Additionally, careful\nexamination reveals that the resonant wavelengths of the later MRRs are slightly higher than those of\nthe earlier ones, primarily due to fabrication variations.\nSecond, variations across different spatial channels result in a loss fluctuation of approximately 2 dB\nfor MRRs at the same cascade position. This is mainly caused by the cumulative effect of minor loss\nvariations in individual components due to fabrication tolerances. The loss of each MRR is derived by\nsubtracting the losses of other components from the total link loss. The link includes an edge coupler\narray, waveguide and MZI array placed before the MRR array, as well as a grating array placed\nafterward. Moreover, the MRRs themselves are subject to variations caused by fabrication tolerances.\nConsequently, the 2 dB power fluctuation observed for MRRs across different spatial channels arises\nfrom the accumulation of these minor loss variations in each component along the optical path.\nThe above responses have been appropriately incorporated into the revised manuscript.\n(4) Revision:\n(Page 11 of manuscript) “The inconsistency in MRR insertion loss originates from two main factors. First, the\ncascaded structure inherently causes the loss at the resonant wavelength to increase along the chain. Second,\nthe MRR insertion loss is extracted by subtracting the losses of other components from the total link loss, and\nthe cumulative effect of fabrication-induced variations across different channels contributes to a power\nfluctuation of approximately 2 dB in the MRR response.”\n(5) Reviewer Comment:\nQ.5. Please clearly describe the function of the fiber-chip-fiber system management. Is it possible to\nachieve switching between different spatial modes?\n(5) Response:\nThank you very much for the constructive feedback. In our fiber-chip-fiber system, switching between\ndifferent spatial modes has been successfully implemented. Each spatial channel from an eight-core\nfiber is transformed into three LP modes in a few-mode fiber, three OAM modes in a vortex fiber, and\nthe fundamental mode in two single-mode fibers. Since the silica chip is fixed, the corresponding mode\ntransformation mapping is also fixed. By fabricating other 3D chips, different spatial optical field\nconversions can also be achieved. Alternatively, a multi-channel non-blocking silicon optical switch can\nbe integrated into the silicon chip to enable dynamic spatial field transformation.\nThe above responses have been appropriately incorporated into the revised manuscript.\n(5) Revision:\n(Page 10 of manuscript) “As in our previous work, incorporating multi-channel non-blocking optical\nswitches enables reconfigurable mapping and conversion of structured light fields. Thus, each core channel\nof the 8-core fiber can be dynamically mapped onto various higher-order or fundamental modes in other\nfibers. Tailored 3D chips can be designed and fabricated to enable the desired spatial light field conversion.”\n(6) Reviewer Comment:\nQ.6. A summarized loss decomposition for the data transmission experiment should be added.\n(6) Response:\nThank you very much for the valuable feedback. The maximum loss for the dropping function system\nis 25 dB, consisting of the following components: a silica fan-in chip (< 3 dB), an 8-core fiber segment\n(< 1 dB), a hybrid integrated coupler (< 4.5 dB), a silicon MZI (< 1 dB), a MRR array (< 9 dB), a grating\n(< 4.5 dB), and multiple bends and crossings (< 2 dB). For the adding function system, the maximum\nloss is 27.5 dB. Compared to the dropping system, the adding system exhibits an extra 2.5-dB loss\ndue to the 1.2-cm-long waveguide loop integrated in the silicon chip.\nThe above responses have been appropriately incorporated into the revised manuscript.\n(6) Revision:\n(Page 14 of manuscript) “The amplified WDM signal is divided into eight parts and further decorrelated via\ndifferent optical delay lines. Eight EDFAs are used to compensate for the losses in the fiber-chip-fiber system.\nThe maximum loss for the dropping function system is 25 dB, consisting of the following components:\na silica fan-in chip (< 3 dB), an 8-core fiber segment (< 1 dB), a hybrid integrated coupler (< 4.5 dB),\na silicon MZI (< 1 dB), a MRR array (< 9 dB), a grating (< 4.5 dB), and multiple bends and crossings (<\n2 dB). For the adding function system, the maximum loss is 27.5 dB. Compared to the dropping system,\nthe adding system exhibits an extra 2.5-dB loss due to the 1.2-cm-long waveguide loop integrated in\nthe silicon chip.”\n(7) Reviewer Comment:\nQ.7. Please discuss the effect of the fiber disturbance to the signal quality.\n(7) Response:\nThank you very much for the helpful feedback from the reviewer.In a \"fiber chip fiber\" multidimensional\n(mode, polarization, wavelength) multiplexing system, external fiber disturbances (such as bending,\n- -\nvibration, temperature variations, and stress changes) represent a fundamental challenge to\nsignal transmission performance. Such systems rely on multiple physical dimensions, including mode,\npolarization, and wavelength, to establish parallel independent channels. Any disturbance along the\n- fiber can degrade the orthogonality and stability of these dimensions during propagation, leading to\ncomplex cross dimensional crosstalk. Generally, the wavelength dimension maintains relatively high\nstability under normal conditions; only under extreme disturbances can nonlinear effects induce\n- noticeable channel drift or power fluctuations. In contrast, the mode and polarization dimensions are\nfar more sensitive to disturbances: even slight environmental variations can cause energy coupling\nbetween spatial modes, alter dispersion characteristics, or trigger rapid polarization state rotation and\ndynamic polarization mode dispersion, substantially complicating signal processing at the receiver. The\n- combined impact of these effects markedly increases the system bit error rate, limits overall\n- - transmission capacity, and imposes stringent demands on real time signal processing algorithms.\nTo address such challenges, for routine minor disturbances, a progressive self configuration\n- - approach based on feedback mechanisms has been demonstrated as an effective strategy for\n- controlling integrated optical grids. This method can compensate in real time for mode evolution and\npolarization rotation induced by fiber transmission. Notably, when thermo optic phase shifters are\nemployed, the reconfiguration speed of photonic processors can reach the microsecond level, whereas\n- electro optic phase shifters enable nanosecond scale response. These capabilities make it feasible to\nimplement dynamic, real time management of high dimensional fiber systems through on chip\n- - integrated photonic processors, offering a practical pathway toward enhancing system robustness in\n- - - complex operational environments.\n(7) Revision:\n(Page 18 of manuscript) “Real-time configuration of silicon photonic processors is crucial for fiber-optic\ncommunication systems, as the demands of optical clients dynamically adjust according to practical\napplications and changing external environments. Under conditions of relativelyminor disturbances, the\nmode and polarization dimensions in optical fibers exhibit greater sensitivity than the wavelength dimension:\ndisturbances readily induce optical energy coupling between spatial modes, leading to inter-mode crosstalk\nand altered dispersion properties.Such disturbances can trigger dynamic polarization mode dispersion and\nrapid polarization state rotation, resulting in failure of polarization demultiplexing at the receiver and decision\nerrors. The combined effect of these factors significantly increases the BER, thereby limiting communication\ntransmission capacity. Fortunately, the progressive self-configuration method with feedback has been\ndemonstrated to be a straightforward and efficient approach for demodulating single-fiber optical fields. This\nmethod is capable of handling arbitrary mode evolution and polarization rotation following fiber transmission.\nNotably, when employing thermo-optic phase shifters, the configuration speed of photonic processors can\nreach approximately 10 microseconds, while the use of electro-optic phase shifters enables sub-\nnanosecond reconfiguration speeds. These advances pave the way for the future real-time management of\nhigh-dimensional fiber systems through integrated photonic processors, offering a promising solution to\naddress dynamic fiber disturbances.”\n(8) Reviewer Comment:\nQ.8. In Fig. 3h, the transmission spectra between the fiber and the multimode waveguide are presented.\nPlease provide the structure parameters of the waveguide.\n(8) Response:\nThank you very much for the constructive feedback. The silicon multimode waveguide has a width\nof 1.2 μm and a height of 0.22 μm.\nThe above responses have been appropriately incorporated into the revised manuscript.\n(8) Revision:\n(Page 11 of manuscript)\n“The silicon multimode waveguide has a width of 1.2 μm and a height of 0.22 μm.”\n(9) Reviewer Comment:\nQ.9. The authors should include a table for large-capacity, multi-dimensional parallel data-transmission\nsystems, comparing the key metrics of past work with those of the present work.\n(9) Response:\nThank you very much for the constructive feedback. We have added the references about large-\ncapacity, multi-dimensional parallel data-transmission systems in the revised manuscript and revised\nsupplementary information. Table S1 and Table S2 summarize the reported fiber-chip systems and\nfiber transmission systems, respectively. The reported characteristics include fiber type, total capacity,\ndimension, number of channels, system function, and operating wavelength. As evident from Table S1,\nexisting fiber-chip systems typically exhibit relative limitations in both channel count and system\ncapacity. Furthermore, the system functions they are capable of performing are quite restricted.\nSignificantly, these systems are generally limited to supporting only a single type of optical fiber for\nconnection and management. In contrast, our proposed scheme is designed to deliver not only a\nsubstantially larger channel count and greater system capacity, but also the ability to execute a richer\nvariety of functions. Crucially, our solution enables the simultaneous, parallel operation of multiple types\nof optical fibers.\nTable S2 illustrates the characteristics of conventional fiber transmission systems that utilize bulk\ncomponents. These systems are also generally limited to supporting a single type of SDM fiber.\nHowever, when factors like integration density and power consumption are disregarded, these bulk-\noptic transmission systems achieve massive scale, demonstrating tens of thousands of channels and\nsystem capacities reaching up to 10 Pbit/s.\nIn summary, while conventional optical transmission systems utilizing bulk optical components and\nfiber-to-chip optical transmission and management systems belong to two distinct technological\nparadigms, there is significant potential for mutual reference between them. Specifically, the massive\ncapacity and channel count achieved by bulk-optic transmission systems can provide critical guidance\nfor the further scaling of fiber-to-chip integrated systems.\nThe above responses have been appropriately incorporated into the revised manuscript and revised\nsupplementary information.\n(9) Revision:\n(Pages 17, 18 of manuscript) “While this fiber-chip optical transmission and management system has\nachieved significant increases in channel count and system capacity, it still falls far short of the scale and\ncapacity of multi-dimensional optical transmission systems using bulk components. A detailed comparison\nof the tables can be found in Supplementary Information S8. Looking ahead, with the continuous\nadvancement of integrated photonic technologies, the throughput of fiber-chip interfaces and photonic\nprocessing devices holds the potential to eventually rival the capacity of optical transmission systems based\non bulk optical components. Firstly, realizing direct and efficient interconnection between various optical\nfibers and silicon chips requires the development of a greater number and higher-order (de)multiplexers,\nminimizing channel loss and crosstalk. For the approach that increases channel count via core-division\nmultiplexing, 3D silica chips can leverage the excellent fabrication capabilities of femtosecond direct writing\ntechnology to realize FIFO device for high-core-count fibers (e.g., 19-core or 24-core fibers). Higher-order\nmode multiplexer can be implemented through specialized structural designs. Managing such a large\nnumber of channels requires more optical management equipment, which may necessitate further\nimprovements in the performance of integrated optical management components. In the wavelength\ndimension, parameter optimization is expected to allow 3D silica devices to operate across the entire C+L\nband. Furthermore, the smallest reported MRR currently boast a FSR of 93 nm, enabling them to process\nmore wavelengths through cascading54. Crucially, the design of the silicon chip can be optimized to eliminate\npolarization dependency, achieving polarization-independent optical management and thereby increasing\nthe overall data throughput55. Therefore, by integrating these numerous cutting-edge technologies, the\nrealization of Pbit/s fiber-chip optical transmission and processing systems is a foreseeable prospect.”\n(S8 of supplementary information) “ S8: Comparisons of various fiber and fiber-chip systems\nTable S1 and Table S2 summarize the reported fiber-chip systems and fiber transmission systems,\nrespectively. The reported characteristics include fiber type, total capacity, dimension, number of channels,\nsystem function, and operating wavelength. As evident from Table S1, existing fiber-chip systems typically\nexhibit relative limitations in both channel count and system capacity. Furthermore, the system functions\nthey are capable of performing are quite restricted. Significantly, these systems are generally limited to\nsupporting only a single type of optical fiber for connection and management. In contrast, our proposed\nscheme is designed to deliver not only a substantially larger channel count and greater system capacity,\nbut also the ability to execute a richer variety of functions. Crucially, our solution enables the simultaneous,\nparallel operation of multiple types of optical fibers.\nTable S1 Comparison of the state-of-the-art fiber-chip systems.\nCapacity Number of Wavelength Ref.\nFiber types Dimension1 Functions\n[bit/s] channels (nm) (year)\nTransmission, [34]\nFMF 160 G M 4 1542.1 – 1557.1\nmultiplexing (2020)\nTransmission, [35]\nFMF 400 G M 2 1520 - 1610\nmultiplexing (2020)\nTransmission, [37]\nFMF 192 G M 4 1570\nmultiplexing (2020)\nTransmission, [38]\nFMF 4.36 T M, P, W 98 ~ 1538 - 1565\nmultiplexing (2022)\nTransmission, [36]\nFMF 1.12 T M, W 28 1540 - 1565\nmultiplexing (2022)\nTransmission, [30]\nFMF 256 G M, P, W 16 1570 - 1582\nmultiplexing (2022)\nTransmission, [29]\nFMF 580.8 G M 4 1550.12\nmultiplexing (2023)\nTransmission, [15]\nFMF 5.38 T M, P, W 96 1547.3 – 1558.9\nmultiplexing, switching (2023)\nTransmission,\n[14]\nFMF 4.032 T M, P, W 96 multiplexing, 1547.3 – 1558.9\n(2024)\nadding/dropping\nTransmission,\nOAMF, FMF, multiplexing, This\n30. T S, M, P, W 288 1530 - 1544\nMCF, SMF, equalizing, work\nadding/dropping\nMCF: multi-core fiber; OAMF: orbital angular momentum fiber; FMF: few-mode fiber; SMF: single-mode fiber; MMI:\nmultimode interferometer. 1Dimensions includes mode(M), polarization(P), space(S), and wavelength(W). The\nassociated reference labels are from the Ref. [14,15, 29, 30, 34-38] of the main text.\nTable S2 Comparison of the reported fiber transmission systems with capacity more than 1 Pbit/s.\nCapacity Number of Ref.\nFiber types Dimension1 Functions Wavelength (nm)\n[bit/s] channels (year)\n~ 1527.7 - [45]\n6-mode 19-core 2.05 P S, M, P, W 41040 Transmission\n1563.7 (2015)\n[46]\n6-mode 19-core 10.16 P S, M, P, W 84246 Transmission 1527.4 - 1608.4\n(2018)\n[47]\n3-mode 4-core 1.2 P S, M, P, W 4416 Transmission 1528.9 - 1610\n(2019)\n[48]\n3-mode 38-core 10.66 P S, M, P, W 27048 Transmission ~ 1530 - 1560\n(2018)\n[11]\n15-mode 1.01 P M, P, W 5730 Transmission 1528 - 1610\n(2021)\n[49]\n7-core OAM 1.02 P S, M, P, W 24960 Transmission 1538.19 - 1602.1\n(2022)\nTable S2 illustrates the characteristics of conventional fiber transmission systems that utilize bulk\ncomponents. These systems are also generally limited to supporting a single type of SDM fiber. However,\nwhen factors like integration density and power consumption are disregarded, these bulk-optic transmission\nsystems achieve massive scale, demonstrating tens of thousands of channels and system capacities\nreaching up to 10Pbit/s.\nIn summary, while conventional optical transmission systems utilizing bulk optical components and fiber-\nto-chip optical transmission and management systems belong to two distinct technological paradigms, there\nis significant potential for mutual reference between them. Specifically, the massive capacity and channel\ncount achieved by bulk-optic transmission systems can provide critical guidance for the further scaling of\nfiber-to-chip integrated systems.”\nThanks again for your valuable comments and helpful suggestions."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Thank you for the detailed revisions. The manuscript in its current form can be accepted.", "reviewer_2": "All concerns raised by the reviewer have been addressed."}, "author_response": ""}]

Decision letter