Mode-Domain Multiplexing

• Mode-domain multiplexing is a technique that utilizes orthogonal spatial eigenmodes to transmit multiple independent data channels over one waveguide.
• Innovative devices such as inverse-designed metamaterials, multi-plane light converters, and integrated photonic circuits enable low loss and low crosstalk for scalable implementations.
• MDM enhances applications ranging from high-capacity fiber-optic links to quantum communication by extending bandwidth and reducing system complexity.

Mode-domain multiplexing (MDM)—also known as mode-division multiplexing—is a physical-layer technique for transmitting multiple independent data channels over a single waveguide or fiber by utilizing its orthogonal spatial eigenmodes. Each mode acts as a parallel, non-interacting channel, enabling the system to circumvent the single-mode bandwidth limit by scaling aggregate capacity linearly with the number of supported modes. MDM spans free-space, fiber, and on-chip photonics, and is increasingly important for interconnect technology, long-haul communications, quantum light processing, and integrated photonic circuits. Leading MDM approaches exploit engineered devices such as metamaterial-based multiplexers, multi-plane light converters, and photonic integrated circuits, targeting low insertion loss (IL), low inter-mode crosstalk (CT), and broad bandwidth for efficient, scalable optical transmission (Liu et al., 2018, Kruk et al., 2017, Bade et al., 2018, Zhou et al., 2023, Melati et al., 2016, Mojaver et al., 2024).

1. Theoretical Principles and Modal Orthogonality

MDM is predicated on the orthogonality of eigenmodes in waveguides and fibers. In a weakly guiding fiber or silicon waveguide, the electromagnetic field decomposes into spatial modes—e.g., TE₀, TE₁, TE₂ (transverse electric modes), LP₀₁, LP₁₁, LP₂₁ (linearly polarized modes), or more generally Hermite–Gaussian (HG) or Laguerre–Gaussian (LG) modes. These satisfy

$\int E_i(x, y) E_j^*(x, y) \, dx\,dy = \delta_{ij}$

which implies independent propagation in the absence of perturbations. Each mode supports an independent data channel; the total channel capacity under ideal conditions scales as

$$C_{\text{total}} = \sum_{m=1}^{M} B \cdot \log_2(1+\text{SNR}_m)$$

where M is the number of modes, and SNRₘ is the signal-to-noise ratio in mode m (Wu et al., 2017).

Orthogonality is preserved unless broken by imperfections—waveguide bends, crossings, surface roughness, or index perturbations. Mode-coupling theory describes scattering between modes via the overlap integral of perturbations with mode profiles. In strong coupling regimes (e.g., long-haul MMF), the fiber acts as a random linear MIMO channel with statistical MDL (mode-dependent loss), group-delay spread, and crosstalk (Zia et al., 2024, Vijay et al., 10 May 2025).

2. Multiplexer Architectures and Device Designs

MDM requires devices for selective excitation, routing, and detection of modes. Major device categories include:

a. Inverse-Designed Metamaterial Bends and Crossings

Subwavelength meta-structures (digitized silicon/air pixel lattices) are inverse-optimized to enable ultra-compact (e.g., 3.9 μm radius bends; 8×8 μm² crossings) and low-loss 3-mode routing. Direct binary search tailors the local index to maximize overlap with TE₀–TE₂ and suppress inter-mode radiation and crosstalk. Experimental results: insertion loss (IL) ≈ 0.7–0.9 dB, CT < –20 dB over 1500–1580 nm (Liu et al., 2018).

b. Multi-Plane Light Conversion (MPLC)

MPLC implements an arbitrary N×N unitary mapping between SMF inputs and MMF (LP or HG) eigenmodes by cascading a sequence of phase planes (binary/analog). For a 45-mode system, a separable Hermite–Gaussian basis reduces the needed reflections to ≈11, yielding average IL = 4 dB, CT = –28 dB, and <4 dB mode-dependent loss (MDL) over the C-band. MPLC is also robust to fiber bending and supports modular upgrades to higher mode counts (Bade et al., 2018, Labroille et al., 2014).

c. Dielectric Metasurfaces and Grating Couplers

Transparent dielectric nanopillar metasurfaces, designed for broadband modal phase conversion, enable LP₀₁ → LP₁₁/LP₂₁ with ER > 22 dB, <0.5 dB Q-factor penalty for 100 G PAM4 signals, and unity passband transmission. Two-dimensional multimode grating couplers (MMGCs) with subwavelength-index Mikaelian lenses achieve ultra-compact (35×35 μm²) and low-loss coupling (–3.6 ~ –5.5 dB) to FMF modes up to LP₂₁, enabling dense integration (Zhou et al., 2023, Kruk et al., 2017).

d. Integrated Photonic Circuits (PICs)

Silicon and InP-based PICs employ symmetric/asymmetric directional couplers, multi-mode interferometers (MMIs), and cascaded Y-junctions. Example: a cascaded Y-junction/4×4 MMI MUX achieves <1.2 dB IL, CT < –20 dB, and >160 nm bandwidth for 3+ mode multiplexing (González-Andrade et al., 2023, Mojaver et al., 2024). Reconfigurable MUX/DEMUX with thermo-optic phase shifters allow dynamic mode switching (Melati et al., 2016).

3. Performance Metrics: Insertion Loss, Crosstalk, and Scalability

Key figures of merit include:

	Inverse-Designed Meta	MPLC	Dielectric Metasurface	Grating/Integrated
IL (dB)	0.7–0.9 (per element)	3–4 (per system)	<1 (device)	0.3–1 (per comp.)
CT (dB)	<–20 to <–30	<–28	>22 ER	<–17 (typ., MMIs)
Bandwidth	80 nm	C-band	S/C/L bands	50–100 nm
Mode count	3–4	up to 45+	2–3 (current)	2–4 (current)

Scalability is ultimately set by mode-dependent loss, crosstalk control, group-delay spread (which dictates MIMO equalizer complexity), and device footprint. Advanced designs employ SWG-metamaterials, inverse design, and hybrid approaches to extend the mode count and bandwidth without sacrificing isolation (González-Andrade et al., 2023, Mojaver et al., 2024).

4. Applications: Communication, On-Chip Networking, and Quantum Optics

MDM is deployed in multiple domains:

• High-capacity fiber-optic links: SDM/MDM increases per-fiber throughput linearly with the number of guided modes. For example, a 45-mode C-band MPLC system provides a 45× capacity multiplier with standard SMF transceivers (Bade et al., 2018).
• Integrated photonic networks: Intra-chip and inter-chip interconnects utilize MDM (e.g., silicon microring MUX/DEMUX, hybrid MDM + WDM filters) for Tb/s-scale datacenter links (Wu et al., 2017, Mojaver et al., 2024).
• Quantum-classical hybrid links: Simultaneous modal multiplexing of quantum and classical signals in FMF with low SNR penalty (e.g., >10 dB quantum SNR after 8 km, group crosstalk < –10 dB), extending QKD to SDM backbones (Zia et al., 2024).
• Nonlinear and multidimensional optics: Free-space and fiber-based mode-multiplexers are used for modal encoding in CARS microscopy, high-dimensional QKD, and continuous-variable measurement-based quantum computation (Yoshikawa et al., 2016, Mansuryan et al., 2023).

5. Signal Processing and Channel Modeling

Transmission over multimode waveguides/fibers is modeled as a linear M×M MIMO channel: $$\mathbf{y}(t) = \mathbf{H}(t) \mathbf{x}(t) + \mathbf{n}(t)$$ $\mathbf{x}(t)$ and $\mathbf{y}(t)$ are input/output modal vectors; $\mathbf{H}(t)$ captures random linear mixing due to mode coupling; $\mathbf{n}(t)$ is noise (Huang et al., 2021, Barbosa et al., 2022, Vijay et al., 10 May 2025). Key properties:

• Group-delay spread (σ_GD): Modal dispersion scales MIMO channel memory and DSP complexity.
• Mode-dependent loss (MDL)/gain: Fluctuations reduce finite-outage capacities; mitigated by frequency diversity (signal bandwidth B ≫ MDL coherence bandwidth B_c) (Ho et al., 2011).
• Crosstalk and random coupling: Impact channel estimation, equalization. Principal modes and MIMO equalizers are used to compress channel memory and reduce front-end requirements (Barbosa et al., 2022, Huang et al., 2021).
• Compensation techniques: Periodic mode permutation or fiber-type alternation can reduce group-delay spread, with closed-form scaling laws for effective system design (Vijay et al., 10 May 2025).

6. Engineering Challenges and Future Directions

Principal challenges in MDM scale-up include:

• Managing group-delay spread and MDL as the number of multiplexed modes increases (practical for ~45 in current systems, challenging beyond).
• Integrated mode manipulation with low IL and CT for 5+ modes, especially for on-chip and fiber-chip transitions.
• Robustness to fabrication errors, modal dispersion, and environmental perturbations in both integrated and fiber systems (Vijay et al., 10 May 2025, Mojaver et al., 2024).
• Real-time, reconfigurable, and large-scale MIMO-DSP for random mode-coupled channels, including fast tracking and principal-mode adaptation (Barbosa et al., 2022).
• Integration of MDM with quantum optics, advanced modulation (QAM, PAM, DP-QPSK), and hybrid multiplexing (WDM + MDM + polarization) for Tb/s-scale interconnects (Kruk et al., 2017, Yoshikawa et al., 2016, Zia et al., 2024).

Prospects include dynamically tunable meta-devices, higher-density PDK-compatible mode libraries, and the convergence of MDM with high-dimensional quantum information processors and analog photonic computation platforms (Mojaver et al., 2024, Yoshikawa et al., 2016). The field continues to progress rapidly toward higher mode counts, tighter footprints, and sub-dB loss/isolation across broad spectral bands.