Inverse-Designed Wavelength Multiplexers

• Inverse-designed wavelength division multiplexers are integrated photonic devices that use computational optimization to arrange material distributions for wavelength-selective routing.
• They employ methods such as adjoint-based topology optimization and level-set techniques to achieve compact footprints, low insertion loss, and controlled crosstalk across multiple wavelength channels.
• Fabrication-aware designs have enabled foundry-compatible implementations on platforms like silicon-on-insulator and silicon nitride, expanding applications from telecom to active terahertz systems.

Searching arXiv for the cited papers to ground the article in the current literature. {"query":"Inverse-designed wavelength demultiplexer silicon photonics arXiv 2015 2017 2019 2024 2025", "max_results": 10} {"query":"(Digiorgio et al., 2024, Mason et al., 8 Sep 2025, Chong et al., 1 Sep 2025, Su et al., 2017, Piggott et al., 2015) arXiv", "max_results": 10} Inverse-designed wavelength division multiplexers are integrated photonic devices in which wavelength-selective routing is obtained by solving a Maxwell-constrained design problem over a high-dimensional material distribution, rather than by hand-tuning a small set of parameters in conventional architectures such as arrayed waveguide gratings, ring-resonator banks, or Mach–Zehnder lattices. In the literature, the term encompasses compact in-plane demultiplexers on silicon-on-insulator, wavelength-demultiplexing grating couplers, foundry-fabricated multiport devices, reconfigurable phase-change implementations, metasurface-based and topological variants, and recent terahertz realizations in active quantum-cascade platforms (Piggott et al., 2015, Piggott et al., 2014, Piggott et al., 2019, Digiorgio et al., 2024). Because passive reciprocal structures can generally be operated in reverse, many reported demultiplexers also function as multiplexers, but the design targets are usually posed in demultiplexing form (Piggott et al., 2015).

1. Historical emergence and scope

The early inverse-designed WDM literature established that wavelength routing could be posed directly as a mode-conversion problem. An early example, "Inverse design and implementation of a wavelength demultiplexing grating coupler" (Piggott et al., 2014), specified a vertically incident Gaussian beam and required separation of O-band and C-band light into distinct silicon waveguides. "Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer" (Piggott et al., 2015) then demonstrated a $2.8 \times 2.8~\mu\text{m}$ silicon device that splits $1300~\mathrm{nm}$ and $1550~\mathrm{nm}$ light into different output waveguides, with measured insertion loss $2{-}4~\mathrm{dB}$, contrast $12{-}17~\mathrm{dB}$, and bandwidths $\sim 100~\mathrm{nm}$. The next major step was to move beyond two channels and large wavelength separations: "Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer" (Su et al., 2017) reported three channels at 1500 nm, 1540 nm, and 1580 nm with 40 nm spacing in a $5.5~\mu\text{m} \times 4.5~\mu\text{m}$ footprint.

A parallel development was the transition from research-fabricated proof-of-concept devices to foundry-compatible implementations. "Inverse-designed photonics for semiconductor foundries" (Piggott et al., 2019) demonstrated a 3-channel wavelength demultiplexer fabricated in the AIM Photonics 300 mm MPW process, with target wavelengths 1500 nm, 1540 nm, and 1580 nm and a footprint of $5.5 \times 4.5~\mathrm{\mu m}^2$. More recent work expanded the design space in several orthogonal directions: compact $1\times N$ T-junction systems up to six output ports (Yilmaz et al., 2019), neural-network-assisted inverse design (Yuan et al., 2022), hybrid mode-and-wavelength demultiplexing (Chong et al., 1 Sep 2025), co-optimization with distributed Bragg gratings for sub-$-40$ dB crosstalk at 15 nm spacing (Mason et al., 8 Sep 2025), and reprogrammable wavelength demultiplexing via pixel-level phase-change control (Wu et al., 2024).

The field is therefore broader than a single algorithmic tradition. It includes objective-first inverse design, adjoint-based topology optimization, continuous-to-binary level-set workflows, co-optimization with external filtering structures, and data-driven inverse models. It also spans telecom silicon photonics, silicon nitride, photonic-crystal platforms, metasurface-loaded waveguides, phase-change photonics, terahertz double-metal cavities, and hybrid source-routing systems based on TMDC photoluminescence (Han et al., 2022, Alquliah et al., 2022, Zalogina et al., 24 Jan 2025, Digiorgio et al., 2024).

2. Optimization formulations and computational design methods

A defining feature of inverse-designed WDMs is that the desired device behavior is imposed at the level of electromagnetic fields and port-mode overlaps. In the 2015 silicon demultiplexer, the governing frequency-domain Maxwell constraint is written as

$1300~\mathrm{nm}$0

with modal coupling constraints of the form

$1300~\mathrm{nm}$1

so the design variable is the spatial permittivity $1300~\mathrm{nm}$2, while the performance target is specified in terms of overlap with desired output modes (Piggott et al., 2015). That paper used a staged workflow consisting of objective-first initialization, steepest-descent refinement, binary level-set conversion, and final broadband optimization at 10 wavelengths.

A closely related but more explicit multi-objective telecom formulation appears in the 2017 three-channel demultiplexer (Su et al., 2017). There, the total objective is

$1300~\mathrm{nm}$3

with wavelength-specific overlap constraints enforcing near-unity transmission to the desired output and near-zero transmission to the undesired outputs. That work also introduced self-biasing and neighbor biasing in the continuous stage, then thresholding and fabrication-constrained level-set optimization with a 40 nm minimum radius of curvature and 90 nm minimum hole width.

Other strands of the literature generalize the optimization problem in different ways. Objective-first inverse design was used to produce compact $1300~\mathrm{nm}$4 T-junction WDMs for $1300~\mathrm{nm}$5, alternating between a field subproblem and a material subproblem, then applying either level-set thresholding or a binarization-cost term during optimization (Yilmaz et al., 2019). In terahertz photonics, topology optimization using SPINS with adjoint gradients was used on a $1300~\mathrm{nm}$6 domain to route different THz frequencies to three ports in an active quantum-cascade platform (Digiorgio et al., 2024). The objective was a sum over optimization frequencies, each assigned to one output port, and transmitted power was computed via the squared overlap integral with the desired TM$1300~\mathrm{nm}$7 output mode. A notable point in that paper is that rejection of unwanted frequencies was not explicitly included in the figure of merit; crosstalk suppression emerged from the optimized structure rather than from direct penalty terms (Digiorgio et al., 2024).

Recent work has also explored composite and hybrid workflows. "High-Performance Wavelength Division Multiplexers Enabled by Co-Optimized Inverse Design" (Mason et al., 8 Sep 2025) optimized an inverse-designed routing region together with output distributed Bragg gratings, using

$1300~\mathrm{nm}$8

so desired transmissions and back-reflections are optimized on the full structure rather than in separate stages. "Inverse-Designed On-Chip Terahertz Three-Channel Mode and Wavelength Division Demultiplexer" (Chong et al., 1 Sep 2025) combined a genetic algorithm with adjoint topology optimization, using a broadband multi-channel objective based on power-normalized mode overlaps across wavelength. "Inverse design of nano-photonic wavelength demultiplexer with a deep neural network approach" (Yuan et al., 2022) replaced direct iterative field optimization at inference time with a pre-trained-combined neural network, though its training set itself was generated through 3D-FDTD and modified direct binary search.

3. Platforms, materials, and physical operating mechanisms

The canonical inverse-designed WDM platform is silicon-on-insulator with a 220 nm fully etched silicon device layer. This platform underlies the 2015 broadband 2-channel device (Piggott et al., 2015), the 2017 three-channel narrowband device (Su et al., 2017), the foundry-demonstrated 3-channel demultiplexer (Piggott et al., 2019), and the later co-optimized Bragg-assisted silicon WDMs (Mason et al., 8 Sep 2025). In these devices, the inverse-designed region is a compact, aperiodic scattering volume that redistributes the incoming guided mode through wavelength-dependent interference and modal matching.

Silicon nitride has been used when broader transparency or reconfigurability is required. Metasurface-loaded SiN waveguides supporting TE$1300~\mathrm{nm}$9 and TM$1550~\mathrm{nm}$0 operation were proposed for 2-channel and 3-channel wavelength division demultiplexing over visible-to-infrared bands through TiO$1550~\mathrm{nm}$1 nanorod arrays that locally modify the effective index (Alquliah et al., 2022). Reconfigurable Si$1550~\mathrm{nm}$2N$1550~\mathrm{nm}$3 MMIs overlaid with Sb$1550~\mathrm{nm}$4Se$1550~\mathrm{nm}$5 phase-change films were programmed as $1550~\mathrm{nm}$6 WDMs by writing a binary amorphous/crystalline pixel pattern into a 30 nm PCM layer (Wu et al., 2024). A different Si$1550~\mathrm{nm}$7N$1550~\mathrm{nm}$8 platform supported an inverse-designed $1550~\mathrm{nm}$9 demultiplexer for sorting WS$2{-}4~\mathrm{dB}$0, WSe$2{-}4~\mathrm{dB}$1, and interlayer exciton emission near 620 nm, 750 nm, and 870 nm, respectively (Zalogina et al., 24 Jan 2025).

Alternative physical mechanisms have also been used as structured counterparts or complements to freeform inverse design. Valley photonic crystals on silicon use tunable beard-interface edge states to realize two-channel wavelength routing at 1470–1523 nm and 1548–1609 nm with contrast ratios of 22.4 dB and 24.9 dB (Han et al., 2022). Although that work is not inverse design in the adjoint-topology sense, it is directly relevant as a compact wavelength-routing architecture based on a small set of geometry parameters rather than arbitrary freeform topology.

At terahertz frequencies, the design space changes substantially. "On-chip, inverse-designed active wavelength division multiplexer at THz frequencies" (Digiorgio et al., 2024) implemented the optimized region in a GaAs-based quantum cascade active material embedded in benzocyclobutene within a planarized double-metal cavity. The physical mechanism is still frequency-selective scattering and interference in a compact freeform region, but the device is explicitly active: the inverse-designed region is electrically isolated from the laser section and can act as a spectral amplifier. This suggests a distinction absent from most near-infrared WDM literature: inverse-designed WDMs need not be passive routing blocks.

4. Representative device classes and reported performance

The literature spans broadband two-channel splitters, narrowband multi-channel telecom demultiplexers, compact foundry-compatible routers, active THz multiplexers, and hybrid mode-and-wavelength devices. Selected examples are summarized below.

Work	Platform and function	Reported metrics
(Piggott et al., 2015)	SOI, 2-channel on-chip demultiplexer	$2{-}4~\mathrm{dB}$2; insertion loss $2{-}4~\mathrm{dB}$3; contrast $2{-}4~\mathrm{dB}$4; bandwidths $2{-}4~\mathrm{dB}$5
(Su et al., 2017)	SOI, 3-channel narrowband demultiplexer	$2{-}4~\mathrm{dB}$6; 1500/1540/1580 nm; simulated peak insertion loss $2{-}4~\mathrm{dB}$7; measured peak insertion loss $2{-}4~\mathrm{dB}$8; measured crosstalk under $2{-}4~\mathrm{dB}$9
(Piggott et al., 2019)	AIM Photonics foundry, 3-channel demultiplexer	$12{-}17~\mathrm{dB}$0; insertion loss 3.0 dB, 3.1 dB, 1.2 dB; crosstalk suppression 8.3 dB, 12.6 dB, 12.3 dB
(Yilmaz et al., 2019)	2D silicon/air $12{-}17~\mathrm{dB}$1 T-junction WDMs	$12{-}17~\mathrm{dB}$2: $12{-}17~\mathrm{dB}$3 and $12{-}17~\mathrm{dB}$4, crosstalk $12{-}17~\mathrm{dB}$5 and $12{-}17~\mathrm{dB}$6; $12{-}17~\mathrm{dB}$7: $12{-}17~\mathrm{dB}$8, crosstalk $12{-}17~\mathrm{dB}$9
(Mason et al., 8 Sep 2025)	SOI, 2-channel co-optimized WDM + Bragg gratings	15 nm spacing; measured crosstalk less than $\sim 100~\mathrm{nm}$0; inverse-designed region $\sim 100~\mathrm{nm}$1
(Digiorgio et al., 2024)	THz QCL double-metal platform, active 3-port WDM	2.2–3.2 THz; $\sim 100~\mathrm{nm}$2; $\sim 100~\mathrm{nm}$3 GHz bandwidth; maximum crosstalk $\sim 100~\mathrm{nm}$4; maximum amplification almost 3.5-times (5.4 dB) for port 2

These reported metrics show that inverse-designed WDM performance is not uniform across platforms or problem formulations. Broadband two-channel telecom splitters can achieve very small footprints with moderate insertion loss (Piggott et al., 2015), narrowband multi-channel devices can reach three ports in similar footprint ranges but with only moderate crosstalk (Su et al., 2017, Piggott et al., 2019), and co-optimization with Bragg gratings can push crosstalk far below earlier dielectric inverse-designed WDM levels (Mason et al., 8 Sep 2025). By contrast, the THz active device prioritizes monolithic integration, subwavelength volume, and gain-assisted routing rather than telecom-grade channel isolation (Digiorgio et al., 2024).

A common misconception is that inverse-designed WDMs are intrinsically broadband or intrinsically narrowband. The literature shows both regimes. The 2015 two-channel device was explicitly broadband (Piggott et al., 2015), the 2017 three-channel device was explicitly narrowband (Su et al., 2017), and the 2025 Bragg-assisted design achieved 15 nm channel spacing through co-optimization with external spectral filters (Mason et al., 8 Sep 2025). Another misconception is that “inverse-designed WDM” necessarily means “pure WDM.” Some later devices are hybrid MDM-WDM structures, in which wavelength labels and mode labels are jointly assigned to the outputs (Chong et al., 1 Sep 2025).

5. Fabrication, foundry translation, and experimental realism

Fabrication-aware design has become a central theme because unconstrained inverse-designed layouts often contain sharp corners, sub-resolution gaps, or grayscale material regions. The 2017 three-channel demultiplexer addressed this with neighbor biasing, thresholding, and fabrication-constrained level-set optimization with explicit minimum curvature and minimum hole-width constraints (Su et al., 2017). The 2019 foundry paper used a continuous-permittivity stage followed by level-set boundary optimization and geometric heuristics such as minimum radius of curvature 40 nm and minimum gap 90 nm, then demonstrated reproducible operation in a commercial 193 nm immersion lithography flow (Piggott et al., 2019).

The foundry result is important because it separated two issues that are sometimes conflated. One issue is whether inverse-designed WDMs can be fabricated at all; that was answered positively. The second is whether they already satisfy standard PDK rule decks without waivers; the answer, in that work, was no, because minimum width and minimum separation rules were waived for the demultiplexer (Piggott et al., 2019). This suggests that manufacturability and full foundry signoff are related but distinct goals.

Several papers document performance degradation relative to simulation, usually attributed to etch bias, geometry deviations, or imperfect pattern transfer. The 2017 three-channel device exhibited measured peaks shifted by about 28–29 nm relative to design targets and worse insertion loss and crosstalk than simulation, which the authors attributed primarily to slight underetching and/or overetching (Su et al., 2017). The foundry-demonstrated 3-channel demultiplexer showed nearly identical transmission across three fabricated instances, but measured crosstalk was somewhat higher than in simulation (Piggott et al., 2019). Reconfigurable PCM-based WDMs showed reduced measured extinction ratio relative to simulation because of fabrication imperfections and pattern misalignment (Wu et al., 2024). In the TMDC photoluminescence sorter, discrepancies were associated with binarization effects, mesh-resolution differences, and fabrication imperfections (Zalogina et al., 24 Jan 2025).

Terahertz fabrication poses different constraints. The active THz WDM required dry etching of complex inverse-designed geometries in the quantum cascade active material, BCB planarization, double-metal processing, electrical isolation of sections, and integrated broadband patch-array antennas (Digiorgio et al., 2024). In the hybrid THz MDM-WDM work, manufacturability was built into the pipeline via binarization, process-constrained optimization, periodic circular spatial blurring, and a smallest fabricated feature size larger than $\sim 100~\mathrm{nm}$5, compatible with DRIE through a $\sim 100~\mathrm{nm}$6-thick silicon slab (Chong et al., 1 Sep 2025).

6. Applications, limitations, and current directions

Inverse-designed WDMs now serve several distinct application classes. In telecom and optical interconnects, they provide compact wavelength routers and can be integrated with mode multiplexing or beam emitters in multi-dimensional transmitter architectures (Yang et al., 2021). In foundry silicon photonics, they function as compact passive primitives that could complement or in some cases replace larger semi-analytical components (Piggott et al., 2019). In terahertz photonics, they enable on-chip routing of broadband quantum-cascade-laser comb spectra and active spectral amplification in the 2.2–3.2 THz range (Digiorgio et al., 2024). In hybrid material systems, they act as wavelength sorters for excitonic photoluminescence from TMDC heterostructures (Zalogina et al., 24 Jan 2025). Reconfigurable PCM implementations suggest programmable multiplexing hardware in which the wavelength-routing function is encoded in a rewritable phase pattern rather than in a fixed etched geometry (Wu et al., 2024).

The main limitations are equally clear. Channel isolation in many compact dielectric inverse-designed WDMs remained modest for several years, with measured crosstalk around $\sim 100~\mathrm{nm}$7 in the 2017 three-channel device (Su et al., 2017) and 8.3–12.6 dB suppression in the foundry 3-channel demultiplexer (Piggott et al., 2019). Some methodologies optimize only desired-port transmission and do not explicitly penalize crosstalk, as in the active THz WDM (Digiorgio et al., 2024). Some works are simulated only, especially in metasurface and topological variants (Alquliah et al., 2022, Han et al., 2022). Some devices are not pure WDMs but joint mode-and-wavelength demultiplexers (Chong et al., 1 Sep 2025). Reconfigurable PCM devices have so far demonstrated only two-channel wavelength routing with measured extinction ratio $\sim 100~\mathrm{nm}$8 dB (Wu et al., 2024).

Current directions suggest several converging themes. One is co-optimization of the freeform router with spectrally selective surrounding elements, exemplified by the Bragg-assisted design that reached less than $\sim 100~\mathrm{nm}$9 dB crosstalk at 15 nm spacing (Mason et al., 8 Sep 2025). A second is fabrication-aware optimization from the start, rather than post hoc binarization. A third is extension beyond passive telecom silicon, toward active THz platforms, visible-to-near-IR source integration, and programmable phase-change photonics (Digiorgio et al., 2024, Zalogina et al., 24 Jan 2025, Wu et al., 2024). A plausible implication is that the term “inverse-designed WDM” now denotes not a single device class, but a general design paradigm for compact wavelength-selective routing across multiple material systems, spectral ranges, and levels of programmability.