Waveguide Multiplexing (WM)

• Waveguide Multiplexing (WM) is a strategy that exploits the modal, spatial, spectral, and temporal degrees of freedom in waveguides to facilitate parallel, low-crosstalk transmission.
• WM employs mode-division, frequency-division, and hybrid multiplexing techniques using engineered couplers, subwavelength gratings, and digital equalization to achieve high data rates and robust performance.
• WM is pivotal in on-chip interconnects, quantum communications, and advanced wireless systems, with ongoing research addressing scalability, energy efficiency, and precise fabrication constraints.

Waveguide Multiplexing (WM) encompasses a set of physical-layer strategies that utilize the modal, spatial, spectral, and temporal degrees of freedom in guided-wave structures for parallel, interference-suppressed multi-channel transmission. WM enables simultaneous propagation of independent data streams, quantum states, or particle signals by mapping each stream onto an orthogonal channel defined by the electromagnetic eigenmodes, frequency bands, polarization states, or physical paths within an integrated or distributed waveguide substrate. This resource-multiplexing is foundational to contemporary high-capacity optical interconnects, quantum networking, on-chip photonic devices, and advanced wireless infrastructures.

1. Physical Principles and Modal Basis

WM is fundamentally reliant on the orthogonality and confinement properties of waveguide eigenmodes $\psi_m(x, y)$, which solve the vector Helmholtz equation with boundary conditions set by the waveguide geometry and material indices. In arrangements supporting multiple guided modes (e.g., TE$_0$, TE$_1$, TE$_2$, ...), the crucial orthogonality relations

$$\iint \psi_m^*(x, y) \, \varepsilon(x, y) \psi_n(x, y) \, dx dy = 0 \quad (m \neq n)$$

and corresponding vanishing of mutual coupling in ideal lossless, reciprocal structures ensure each mode carries information independently (Huang et al., 2020, Wu et al., 2017, Stranden et al., 2 Dec 2025).

WM is not restricted to spatial modes; frequency bands (via frequency-selective structures), temporal wavepacket orthogonality, orbital angular momentum (OAM), and polarization can be used as independent channels. Any linear combination of modes that remains mutually orthogonal and robust under propagation supports distinct streams with negligible modal cross-talk in the ideal case (Mohanty et al., 2016, Peñas et al., 2024, Hong et al., 2022).

2. Mode-Division and Frequency-Division Multiplexing

Mode-Division Multiplexing (MDM)

MDM encodes parallel data streams onto orthogonal spatial/mode indices in multimode waveguides. In silicon photonic platforms, MDM has reached up to 11 spatial channels per SOI waveguide using engineered couplers, subwavelength gratings, and sophisticated MIMO equalization (Huang et al., 2020). Each mode's capacity is determined by its SNR, and total aggregate rate is additive across modes:

$$C_\mathrm{total} = \sum_{i=1}^N B \log_2(1 + \mathrm{SNR}_i)$$

Typical insertion losses are $<$0.6 dB/mode, crosstalk is $<-27$ to $-72$ dB (for first three TE modes through an advanced Maxwell fisheye-based crossing), and pulse fidelity factors can exceed 0.98, supporting $>$100 Gb/s per mode (Badri et al., 2019).

Frequency-Division Multiplexing (FDM)

FDM assigns each data stream to a distinct frequency channel, physically realized via frequency-selective structures such as Bragg gratings, epsilon-near-zero (ENZ) waveguide sections, or integrated photonic add-drop multiplexers. In metallic ENZ waveguides, sub-bands of $\sim1$ GHz width with $Q$ up to 39 and insertion loss $<$1.8 dB per channel can be achieved, with adjacent channel isolation at $<$–15 dB (Hong et al., 2022). In THz platforms, modular Bragg/coupler elements enable up to four or more channels, with aggregate bandwidths determined by component fabrication and GVD constraints (Cao et al., 2021).

Hybrid Approaches and Alternative Multiplexing

Other WM protocols exploit temporal (orthogonal pulse shaping), OAM (via PT-symmetric plasmonic structures), or polarization multiplexing. Frequency-temporal hybrid multiplexing supports $N \sim 60$ qubits with $\lesssim 10^{-4}$ global error in quantum networks, given optimized spacing and bandwidth (Peñas et al., 2024).

3. WM Implementation in Photonics, Quantum, and Wireless Systems

Integrated Photonics

SOI and Si$_3$N$_4$ platforms have demonstrated WM using asymmetric directional couplers for mode multiplexers/demultiplexers, subwavelength or photonic crystal grating-based structures for mode conversion and filtering, and transformation optics-based lenses (e.g., Maxwell’s fisheye) for ultra-low-loss, broadband crossings that preserve modal selectivity (Huang et al., 2020, Badri et al., 2019, Mohanty et al., 2016). Multi-plane light conversion (MPLC) further enables efficient mapping between free-space and on-chip spatial modes (Stranden et al., 2 Dec 2025).

Quantum Photonic and Atom-Photon Systems

WM is employed for parallel quantum state delivery using spatial-waveguide-mode encoding and temporal or frequency division of single photons. Photonic circuits using multi-mode waveguides and reconfigurable beamsplitters enable quantum interference, NOON state preparation, and scalable high-dimensional entanglement (Mohanty et al., 2016). In neutral atom quantum networks, arrays of glass-integrated single-mode waveguides spatially multiplex emissions from individual atom traps, supporting >10 parallel low-crosstalk channels and scalable up to hundreds with advanced mode-field engineering (Maeda et al., 25 Dec 2025).

Wireless and PASS Frameworks

In the pinching-antenna system (PASS), WM refers to the simultaneous use of $K$ waveguides with $N$ position-tunable pinching antennas. WM supports joint baseband and spatial (pinching) beamforming, enabling simultaneous multi-user transmission with superior minimum-rate fairness over conventional MIMO. Performance optimization relies on large-scale nonconvex formulations (e.g., penalty dual decomposition, alternating optimization with SCA and PSO), targeting objectives such as minimum-rate maximization, secrecy rate, spectral–energy efficiency trade-offs, and robustness to spatial user distributions (Zhao et al., 20 Aug 2025, Shan et al., 19 Jun 2025, Zhu et al., 8 Jan 2026, Zhu et al., 18 Apr 2025). WM is particularly advantageous for multicast and dense deployments, achieving higher aggregate rates or secrecy by leveraging joint digital and PINching-layer design.

4. Performance Metrics and System Scalability

The effectiveness of WM is quantified by metrics including:

• Insertion Loss (IL): Typically $<$1 dB/mode for advanced crossings in silicon (Badri et al., 2019), $<$1.8 dB per channel in ENZ and THz circuits (Hong et al., 2022, Cao et al., 2021).
• Crosstalk (XT): $<-72$ dB for TE$_0$, $<-27$ dB for TE$_2$ in Maxwell fisheye crossings; $<$–14 dB for higher-order mode interfaces (Badri et al., 2019, Stranden et al., 2 Dec 2025).
• Return Loss (RL): Up to 54 dB for TE$_0$ in lens-based crossings (Badri et al., 2019).
• Fidelity Factor (FF) / Quantum Interference Visibility: $>$0.98 for ultrafast, low-distortion pulse propagation; NOON-state visibilities $>$86% (Badri et al., 2019, Mohanty et al., 2016).
• Aggregate Data Rate: Exceeding 1 Tb/s per wavelength in 11-mode MDM with advanced DSP (Huang et al., 2020).
• Scaling Limitations: Channel count limited by modal overlap, coupling efficiency, fabrication precision, and bandwidth constraints. An increase in lateral waveguide size or number of phase planes enables higher spatial channel counts, with demonstrated scalability to >10 modes in both integrated and free-space-coupled photonics (Stranden et al., 2 Dec 2025, Mohanty et al., 2016).

5. Algorithmic and Fabrication Methodologies

WM architectures frequently involve the co-optimization of hardware layout (mode profiles, antenna positions, coupling elements) and signal processing (beamforming, digital equalization). State-of-the-art optimization exploits:

• Penalty Dual Decomposition (PDD): Used to handle the coupled nonconvex baseband/pinching variables in PASS for max-min fairness (Zhao et al., 20 Aug 2025).
• Successive Convex Approximation (SCA): Applied to baseband beamforming and secrecy-rate subproblems, simplifying nonconvex rate- or SR-based constraints (Zhu et al., 8 Jan 2026, Zhu et al., 18 Apr 2025).
• Particle Swarm Optimization (PSO): Utilized for position optimization of pinching antennas in continuous WM frameworks (Zhu et al., 18 Apr 2025, Zhu et al., 8 Jan 2026).
• Majorization-Minimization (MM) with Projected Adaptive Gradient Descent: Addresses non-smooth multicast objectives in joint beamforming/position tuning (Shan et al., 19 Jun 2025).

Fabrication advances include the use of quasi-conformal transformation optics for creating compact, broadband multimode crossings (Badri et al., 2019), thick-SOI rib waveguides for high-mode-count interfaces (Stranden et al., 2 Dec 2025), and 3D-printed THz circuits for tunable multi-channel FDM (Cao et al., 2021).

6. Application Domains and Emerging Architectures

WM is now foundational in:

• On-Chip Interconnects: Terabit/s-level data rates in high-density integrated circuits for data center and high-performance computing (HPC) environments (Huang et al., 2020, Wu et al., 2017).
• Quantum Networks: High-fidelity quantum state transfer and entanglement delivery, atomic arrays mapped to multiplexed PICs, and quantum photonic logic with multimode elements (Mohanty et al., 2016, Maeda et al., 25 Dec 2025, Peñas et al., 2024).
• Wireless/Fiber-Wireless Integration: High-Q multi-channel THz and mmWave modules, reconfigurable antennas for multi-user beamforming and secure communications in PASS (Zhao et al., 20 Aug 2025, Zhu et al., 8 Jan 2026, Zhu et al., 18 Apr 2025).
• Multifunctional Nanophotonics: Simultaneous realization of Fano, EIT-like, and Lorentzian transmission responses in a single waveguide via photonic spin–orbit engineering, enabling advanced active circuit responses (Cheng et al., 2023).

WM paradigms continue to advance towards higher scalability, robustness to fabrication and environmental perturbations, and seamless integration of digital and analog front ends.

7. Limitations, Trade-offs, and Future Challenges

Trade-offs in WM center on the balance between spectral efficiency, energy consumption, system complexity, and robustness. In PASS networks, WM maximizes spectral efficiency at the cost of higher RF-chain activation and digital processing power, whereas time-sharing approaches (e.g., waveguide switching) deliver higher energy efficiency at reduced throughput (Zhu et al., 8 Jan 2026). Channel count is fundamentally bounded by modal confinement, fabrication tolerances, and system-level DSP complexity.

Future challenges include pushing toward low-cross-talk, low-loss interfaces for >100 spatial channels, further miniaturization and adaptive control (e.g., via digital metasurfaces), and robust algorithmic co-design for fully integrated quantum and classical multimode network platforms.