Waveguide Division: Architectures & Applications

• Waveguide Division is a family of architectures that leverage the waveguide as an intrinsic resource to divide channels, power, or frequency across various platforms.
• In integrated photonics, WD exploits distinct guided modes for on-chip modal multiplexing and switching, achieving low crosstalk and minimal insertion loss.
• Alternative embodiments in microwave, magnonic, and PASS systems demonstrate WD’s versatility in deterministic power splitting and optical frequency division.

Waveguide Division (WD) is a context-dependent term used in several research communities to denote architectures that partition, multiplex, route, or divide signals by exploiting a waveguide as the primary physical resource. In integrated photonics, WD refers to multiplexing and switching multiple independent data channels that co-propagate within a single on-chip waveguide by using its distinct, orthogonal guided modes, making it functionally equivalent to mode-division multiplexing (MDM) and associated switching within one physical bus (Liu, 2017). In other literatures, the same abbreviation denotes deterministic guided-path power splitting for filters and antenna feeds, optical frequency division implemented on an integrated photonic platform, or transmission structures in which each dielectric waveguide serves as a distinct radio resource in pinching-antenna systems (PASS) (Choi et al., 22 May 2025). This usage pattern suggests that WD is best understood as a family of waveguide-centered division mechanisms rather than a single universally fixed concept.

1. Terminological scope

The literature uses “Waveguide Division” in multiple, technically distinct senses. The common element is not a single governing equation or hardware template, but the use of the waveguide itself as the dimension along which channels, power, frequencies, or users are separated.

Area	Meaning of WD	Representative papers
Integrated photonics	Mode-division multiplexing and switching within one multimode waveguide	(Liu, 2017, Zhao et al., 2023)
Guided-path photonic networks	Deterministic power splitting and phase-controlled feed distribution among waveguide branches	(Choi et al., 22 May 2025, Banerjee et al., 2022, He et al., 2016)
Integrated frequency synthesis	Optical frequency division from an optical reference to microwave or mmWave repetition rates	(Sun et al., 2023)
PASS wireless systems	One stream, user, or cluster per dielectric waveguide as a radio resource	(Shan et al., 19 Jun 2025, Zhao et al., 25 Feb 2025, Xue et al., 3 Dec 2025)
Magnonic and diffractive platforms	Frequency-, mode-, wavelength-, or polarization-selective separation in a shared guiding structure	(Zhang et al., 2019, Wang et al., 2024)

A recurrent source of confusion is that the abbreviation “WD” does not preserve one invariant meaning across fields. In on-chip photonics it is usually modal; in microwave networks it is often power division; in integrated metrology it denotes optical frequency division; and in PASS it denotes a transmission structure or access architecture. The surveyed works therefore support a taxonomic reading of WD rather than a monolithic one.

2. Mode-division WD in integrated photonics

In integrated photonics, WD refers to multiplexing and switching multiple independent data channels that co-propagate within a single on-chip waveguide by using its distinct, orthogonal guided modes such as TE0, TE1, and TE2. In this interpretation, the “division” dimension is the set of spatial modal states supported by the waveguide, so WD is functionally equivalent to MDM and its associated switching within one physical bus. Because each guided mode is an orthogonal solution of Maxwell’s equations, low-crosstalk and low-mode-dependent-loss operation allows each mode to act as an independent lane, and compatibility with wavelength-division multiplexing yields the aggregate-capacity relation $$C_{total} = N_{modes} \times N_{\lambda} \times R_{per\,channel}$$ (Liu, 2017).

A representative implementation is the phase-tunable mode converter introduced in “Flexible on-chip mode-division switching with a new mode converter design” (Liu, 2017). Its topology uses a central multimode transport waveguide with tapered-width sections and two parallel single-mode side arms. For the TE0→TE1→TE2 examples, the central bus widths are tapered through $0.45\,\mu\text{m}$, $0.93\,\mu\text{m}$, and $1.41\,\mu\text{m}$, while the side-arm gaps are $250\,\text{nm}$, $200\,\text{nm}$, and $200\,\text{nm}$. The operating principle is interferometric: the upper and lower side arms excite the multimode bus with a controlled phase difference, so constructive and destructive interference select even- or odd-symmetry modes at the designated coupling sections. The design is described through phase matching $\Delta \beta \approx 0$, a coupling coefficient $\kappa$, conversion efficiency $\eta_{m\to n}=\sin^2(\kappa L)$, and phase tuning $0.45\,\mu\text{m}$0.

That paper also formulates two switching architectures. The first combines a mode multiplexer, one mode converter, and a demultiplexer, but is blocking because the converter acts on one modal state at a time. The second assigns one programmable converter per input port and is non-blocking, allowing simultaneous multi-input operation. In 3D FDTD simulations across the C-band, reported conversion insertion losses are approximately $0.45\,\mu\text{m}$1 for TE0→TE0, $0.45\,\mu\text{m}$2 for TE0→TE1, $0.45\,\mu\text{m}$3 for TE0→TE2, and $0.45\,\mu\text{m}$4 for TE2→TE1. The demonstrated operation is TE-specific, and the paper emphasizes that bends, tapers, multiple coupling sections, and phase errors dominate loss. It also identifies adiabatic tapering, apodized coupling sections, inverse design, larger bend radii, and precise multi-point phase control as mitigation strategies.

3. Alternative photonic embodiments of division

Mode-selective division has also been realized without tapered multimode buses. In “Integrated Broadband Mode Division Demultiplexer in Waveguide Arrays” (Zhao et al., 2023), a 20-waveguide, $0.45\,\mu\text{m}$5-long lithium-niobate-on-insulator array demultiplexes TE0, TE1, and TE2 by exploiting mode-dependent Bloch dispersion and group-velocity tilt. The relevant relations are $0.45\,\mu\text{m}$6, $0.45\,\mu\text{m}$7, $0.45\,\mu\text{m}$8, and $0.45\,\mu\text{m}$9. Experimentally validated wavelengths are $0.93\,\mu\text{m}$0, $0.93\,\mu\text{m}$1, $0.93\,\mu\text{m}$2, and $0.93\,\mu\text{m}$3. At $0.93\,\mu\text{m}$4, the mode-division angles for TE0, TE1, and TE2 are $0.93\,\mu\text{m}$5, $0.93\,\mu\text{m}$6, and $0.93\,\mu\text{m}$7 for theory versus experiment. Propagation FDTD simulations give a demultiplexing efficiency of approximately $0.93\,\mu\text{m}$8 for “middle waveguide” excitation of TE2 at $0.93\,\mu\text{m}$9, and approximately $1.41\,\mu\text{m}$0 for “boundary waveguide” excitation.

A different modal embodiment appears in “Broadband mode division multiplexing of OAM-modes by a micro printed waveguide structure” (Schulz et al., 2023). There, five single-mode inputs evolve adiabatically into a ring-like OAM-supporting guide using a photonic-lantern-like transition combined with a twist that acts as an artificial magnetic field. The printed IP-Dip structure uses $1.41\,\mu\text{m}$1, an initial array radius of $1.41\,\mu\text{m}$2 reduced to $1.41\,\mu\text{m}$3, a final core diameter of approximately $1.41\,\mu\text{m}$4, diameter detuning ramped up to $1.41\,\mu\text{m}$5 and then removed, and a twist rate $1.41\,\mu\text{m}$6. The demonstrated mode set is $1.41\,\mu\text{m}$7. Scalar BPM simulations indicate broadband operation from approximately $1.41\,\mu\text{m}$8 to $1.41\,\mu\text{m}$9, while fabricated $250\,\text{nm}$0 MUX/DEMUX structures show diagonal-dominant crosstalk matrices when the effective magnetic field is applied.

Wavelength-selective variants extend the same logic from mode channels to spectral channels. “Integrated Metasurface-based Wavelengths Division Demultiplexers” reports SiN ridge waveguides loaded with all-dielectric $250\,\text{nm}$1 nanorod metasurfaces that locally modify the effective refractive index and create subwavelength, Bragg-reflection, or radiation regimes depending on period and wavelength. Two- and three-channel devices are demonstrated for TE00 and TM00 inputs from the visible to the infrared, with maximum transmission of $250\,\text{nm}$2, lowest simulated crosstalk below $250\,\text{nm}$3 for TE00 two-channel designs, and footprints in the few-micron range (Alquliah et al., 2022).

A more general programmable route is presented in “Optimizing Structured Surfaces for Diffractive Waveguides,” where cascaded transmissive diffractive surfaces perform spatial-mode filtering, mode splitting, spectral filtering, spectral splitting, and mode-specific polarization maintenance (Wang et al., 2024). For trained modes, a single unit yields coupling efficiency at least $250\,\text{nm}$4 and energy efficiency at least $250\,\text{nm}$5; for unseen higher modes, coupling efficiency is at least $250\,\text{nm}$6 and energy efficiency at least $250\,\text{nm}$7. In a 10-unit cascade, coupling efficiency remains at least $250\,\text{nm}$8 while energy efficiency stays above $250\,\text{nm}$9. The same framework reports a 1550 nm single-mode design with greater than $200\,\text{nm}$0 coupling efficiency and greater than $200\,\text{nm}$1 energy efficiency using 4-bit phase depth and $200\,\text{nm}$2 lateral resolution.

4. Guided-path power division and integrated frequency division

In another strand of the literature, WD means deterministic power splitting between guided paths. “Rapid adiabatic couplers with arbitrary split ratios for broadband DWDM interleaver application” defines WD in dense wavelength-division multiplexing interleavers as the power division stage that sets amplitude weights in cascaded filters (Choi et al., 22 May 2025). The rapid adiabatic coupler uses coupled-waveguide supermodes, a mixing angle $200\,\text{nm}$3, and the design rule $200\,\text{nm}$4 with $200\,\text{nm}$5. Fabricated splitters with target ratios $200\,\text{nm}$6, $200\,\text{nm}$7, $200\,\text{nm}$8, $200\,\text{nm}$9, and $200\,\text{nm}$0 achieve power splitting within $200\,\text{nm}$1 of the design target; four of these ratios remain within $200\,\text{nm}$2 across $200\,\text{nm}$3–$200\,\text{nm}$4. Using these couplers, the authors implement an 8-channel DWDM interleaver with $200\,\text{nm}$5 channel spacing, crosstalk below $200\,\text{nm}$6 for the center 8 channels, flat-top passbands with $200\,\text{nm}$7 bandwidth greater than $200\,\text{nm}$8, and crosstalk below $200\,\text{nm}$9 across more than 40 channels over $\Delta \beta \approx 0$0–$\Delta \beta \approx 0$1.

Microwave hardware uses the same division idea at larger scale. “Development of four kinds of waveguide power divider for S band” compares four rectangular-waveguide splitters at $\Delta \beta \approx 0$2 and selects a matching-rod design after CST simulation (He et al., 2016). For model 4, the simulated VSWR at center is $\Delta \beta \approx 0$3, the bandwidth for VSWR $\Delta \beta \approx 0$4 is $\Delta \beta \approx 0$5, $\Delta \beta \approx 0$6, the phase difference is $\Delta \beta \approx 0$7, and the maximum internal electric field is $\Delta \beta \approx 0$8. The fabricated device yields measured VSWR $\Delta \beta \approx 0$9 at $\kappa$0, bandwidth $\kappa$1 for VSWR $\kappa$2, $\kappa$3, and output phase difference $\kappa$4. In a related X-band feed-network application, “An Integrated, Phase-Controlled Power Divider for Metasurface Array Antennas” distributes power from one hollow-metal main waveguide into eight branch waveguides through inclined slots with angles $\kappa$5 through $\kappa$6, targeting equal power and prescribed phase offsets over $\kappa$7–$\kappa$8; at $\kappa$9, the simulated input return loss is $\eta_{m\to n}=\sin^2(\kappa L)$0 and per-output insertion is approximately $\eta_{m\to n}=\sin^2(\kappa L)$1 in the 16-port CST representation (Banerjee et al., 2022).

A still different meaning appears in “Integrated optical frequency division for stable microwave and mmWave generation,” where WD denotes optical frequency division implemented entirely on an integrated photonics platform (Sun et al., 2023). The architecture combines a $\eta_{m\to n}=\sin^2(\kappa L)$2 SiN coil cavity, two PDH-locked lasers, a Si$\eta_{m\to n}=\sin^2(\kappa L)$3N$\eta_{m\to n}=\sin^2(\kappa L)$4 micro-ring with $\eta_{m\to n}=\sin^2(\kappa L)$5 free spectral range, and two-point optical locking so that

$\eta_{m\to n}=\sin^2(\kappa L)$6

Within the lock bandwidth, phase noise scales as $\eta_{m\to n}=\sin^2(\kappa L)$7, or equivalently $\eta_{m\to n}=\sin^2(\kappa L)$8. The paper validates division ratios $\eta_{m\to n}=\sin^2(\kappa L)$9; for $0.45\,\mu\text{m}$00, the repetition-rate phase noise lies about $0.45\,\mu\text{m}$01 below the reference-laser noise up to approximately $0.45\,\mu\text{m}$02 offset. The best optical-domain repetition-rate phase noise reaches $0.45\,\mu\text{m}$03 at $0.45\,\mu\text{m}$04 offset for a $0.45\,\mu\text{m}$05 carrier, the electrically measured $0.45\,\mu\text{m}$06 mmWave reaches approximately $0.45\,\mu\text{m}$07 at $0.45\,\mu\text{m}$08, and the charge-compensated MUTC photodiode produces up to $0.45\,\mu\text{m}$09 at $0.45\,\mu\text{m}$10.

5. WD in pinching-antenna systems

In PASS, WD denotes a transmission architecture in which each dielectric waveguide is treated as a distinct communication resource. In the multigroup multicast formulation of “Multigroup Multicast Design for Pinching-Antenna Systems: Waveguide-Division or Waveguide-Multiplexing?”, WD assigns one data stream to one waveguide, so $0.45\,\mu\text{m}$11, and the baseband beamformer becomes diagonal,

$0.45\,\mu\text{m}$12

Pinching beamforming is realized by optimizing the activated positions of pinching antennas along each waveguide, with the spacing constraint $0.45\,\mu\text{m}$13. The resulting received signal contains desired radiation from the dedicated waveguide and interference from all others, and the optimization is solved by alternating between log-sum-exp projected gradient descent for power allocation and element-wise sequential optimization for pinching positions (Shan et al., 19 Jun 2025).

“Waveguide Division Multiple Access for Pinching-Antenna Systems” specializes this idea to multi-user access by allocating each user a dedicated waveguide (Zhao et al., 25 Feb 2025). The framework distinguishes continuous PA activation from practical discrete activation. The sum-rate maximization is decomposed into an SCA-based power-allocation step and a pinching-beamforming step solved either by penalty-based gradient ascent for the continuous case or by a matching-theory-based algorithm for the discrete case. Under the paper’s baseline setting of $0.45\,\mu\text{m}$14, $0.45\,\mu\text{m}$15, $0.45\,\mu\text{m}$16, and $0.45\,\mu\text{m}$17, the discrete matching algorithm achieves approximately $0.45\,\mu\text{m}$18 of exhaustive-search performance at $0.45\,\mu\text{m}$19; the gap between discrete and continuous activation shrinks further, with the matching method reaching approximately $0.45\,\mu\text{m}$20 of continuous GAA at $0.45\,\mu\text{m}$21 and approximately $0.45\,\mu\text{m}$22 at $0.45\,\mu\text{m}$23.

The same architectural principle has been extended to security and NOMA. In the secure dual-waveguide case, one waveguide carries legitimate data and the other carries artificial noise; the secrecy-rate maximization uses a two-stage algorithm with PA-wise successive tuning for pinching and SCA for power splitting between $0.45\,\mu\text{m}$24 and $0.45\,\mu\text{m}$25 (Zhu et al., 18 Apr 2025). In PASS-enabled NOMA, each user cluster is served by one dedicated waveguide, and a Matching–PDD pipeline jointly optimizes user-to-waveguide assignment, powers, and PA positions; for $0.45\,\mu\text{m}$26, $0.45\,\mu\text{m}$27, and $0.45\,\mu\text{m}$28, the reported sum rate is approximately $0.45\,\mu\text{m}$29 for WD-PASS-NOMA versus approximately $0.45\,\mu\text{m}$30 for WD-PASS-OMA (Xue et al., 3 Dec 2025). Comparative PASS studies further report that WM is more robust in dense deployments, while WD excels when groups or users are geographically isolated; in multi-waveguide max–min fairness simulations, when the inter-waveguide distance reaches approximately $0.45\,\mu\text{m}$31, WD achieves nearly the same performance as WM (Zhao et al., 20 Aug 2025).

6. Cross-domain extensions, constraints, and recurring design problems

WD concepts also appear outside photonics. In “Spin-Wave frequency division multiplexing in an yttrium iron garnet microstripe magnetized by inhomogeneous field,” a $0.45\,\mu\text{m}$32-wide, $0.45\,\mu\text{m}$33-thick YIG stripe is placed $0.45\,\mu\text{m}$34 from a $0.45\,\mu\text{m}$35-wide Py stripe under an in-plane field of $0.45\,\mu\text{m}$36 (Zhang et al., 2019). The Py stray field creates a lateral $0.45\,\mu\text{m}$37 gradient that maps different spin-wave frequencies to different transverse positions within the same waveguide. Micro-focused BLS imaging shows simultaneous $0.45\,\mu\text{m}$38 and $0.45\,\mu\text{m}$39 channels propagating on opposite sides of the YIG stripe, with the dual-frequency maps matching the linear superposition of the corresponding single-frequency maps. Here WD is not modal multiplexing in the optical sense, but frequency-dependent spatial partitioning inside one shared magnonic guide.

A related constraint-driven interpretation appears in dielectric-waveguide interconnects. “A Low-Dispersion Depressed Core Waveguide for Dielectric Waveguide Interconnects” addresses multimode rectangular dielectric waveguides used for WD interconnects by wrapping the guide with a material of higher dielectric constant than both the core and the cladding (Elsawaf et al., 16 Feb 2026). The aim is to increase the confinement factor of the fundamental mode, suppress coupling to parasitic higher-order cladding modes during taper excitation, and improve group delay. With a $0.45\,\mu\text{m}$40 linear taper, the unwrapped guide shows approximately $0.45\,\mu\text{m}$41 coupling to the Ex,13 mode, measured group delay around $0.45\,\mu\text{m}$42, and strong oscillations; the wrapped guide yields more than $0.45\,\mu\text{m}$43 isolation, measured group delay around $0.45\,\mu\text{m}$44, and much closer agreement with the simulated fundamental-mode value of $0.45\,\mu\text{m}$45. The corresponding wrap-thickness constraints are expressed through

$0.45\,\mu\text{m}$46

which are used to keep the first wrap-confined modes above cutoff across the operating band.

Across these otherwise disparate literatures, the same design pressures recur. The data consistently identify crosstalk, higher-order-mode management, fabrication sensitivity, phase calibration, thermal or environmental drift, and scaling complexity as central constraints. In on-chip modal WD, these issues motivate adiabatic tapering, apodized coupling sections, inverse design, larger bend radii, and closed-loop phase control; in guided-path power division they motivate adiabatic supermode evolution and offset engineering; in PASS they motivate alternating optimization, projected gradient descent, matching, PDD, and SCA; and in interconnect or magnonic settings they motivate field-gradient shaping or confinement engineering (Liu, 2017). A plausible implication is that future uses of “Waveguide Division” will continue to proliferate in form, while remaining unified by one engineering premise: the waveguide is treated ոչ merely as a passive conduit, but as the structure in which channel separation itself is physically synthesized.