3D Waveguide Crossings in Photonic Integration

• 3D waveguide crossings are multilayer photonic structures that route optical signals across separate planes to achieve ultra-low crosstalk (<–60 dB) and insertion loss (<0.002 dB per crossing).
• Key architectures include multi-plane dielectric stacks, freeform polymer overpasses, GRIN lenses, and supersymmetric designs, each offering distinct trade-offs in performance, bandwidth, and scalability.
• Advanced fabrication techniques such as CMP-based polishing and two-photon polymerization ensure smooth tapers and precise alignment, enabling efficient mode evolution and low scattering losses.

A three-dimensional (3D) waveguide crossing is a photonic structure in which two or more optical waveguides traverse over or under each other in separate physical planes, substantially reducing crosstalk and insertion loss compared to planar (2D) crossings. 3D crossings are essential for very-large-scale photonic integration (VLSPI), complex on-chip routing, mode-division multiplexing, and highly interconnected optical switch topologies, as they enable dense, low-loss, and low-crosstalk interconnects inaccessible to planar architectures. The rapidly evolving field includes multilayer dielectric waveguide stacks, freeform polymeric overpasses, quasi-conformal transformation optics lenses, and supersymmetric reflectionless intersection designs, each offering distinct scaling, loss, and fabrication properties.

1. Principles of Crosstalk Suppression in 3D Crossings

Crosstalk in waveguide crossings arises from the evanescent overlap between optical modes supported by different guides. Vertical separation between intersecting waveguides exponentially suppresses the coupling coefficient $\kappa$, as described by coupled-mode theory:

$$\mathrm{XT} \approx |\kappa L|^2, \quad \kappa = \frac{\omega}{2} \iint \Delta n(x,y)\, E_1(x,y)\, E_2^*(x,y)\, dx\,dy,$$

where $\omega$ is the angular frequency, $\Delta n(x,y)$ is the refractive index modulation, $E_{1,2}(x,y)$ are normalized transverse optical modes, and $L$ is the effective overlap length at the crossing. By selecting an interlayer spacing $d \gtrsim 1.5\,\mu$m, the spatial overlap $\int E_1 E_2^*\, dx\,dy$ is suppressed exponentially, yielding $\kappa \leq 10^{-3}$ mm$^{-1}$ and crossing crosstalk below –60 dB, as demonstrated in Ta$_2$O$_5$-on-LNOI platforms (Nan et al., 4 Dec 2025). In multi-plane a-Si stacks, interlayer SiO$_2$ spacers (typically 700–900 nm) further decrease evanescent coupling, with measured crossing crosstalk below measurement noise ($<-35$ dB) for second-neighbor plane crossings (Chiles et al., 2017).

In multimode or transformation optics-based crossings, such as those employing Maxwell's fisheye lenses, crosstalk is suppressed via imaging fidelity of the GRIN lens profile and quasi-conformal mapping, achieving crosstalk as low as –72 dB for the fundamental mode (Badri et al., 2019, Badri et al., 2019).

2. 3D Crossing Architectures and Layer Stack Designs

Several prominent 3D crossing architectures exist:

• Multi-plane Dielectric Platforms: Vertically stacked waveguide layers (e.g., a-Si/SiO$_2$ or Ta$_2$O$_5$/SiO$_2$/LNOI) enable out-of-plane crossings. In Ta$_2$O$_5$-on-LNOI, the layer stack comprises: 300 nm Ta$_2$O$_5$ ridge (top), 1.5 μm SiO$_2$ spacer, 600 nm LN ridge (bottom), and 2 μm SiO$_2$ BOX, with both waveguide widths ≈1 μm (Nan et al., 4 Dec 2025). In three-plane a-Si architectures, each plane is separated by 700–900 nm SiO$_2$, with width modulation for phase-velocity mapping (Chiles et al., 2017).
• 3D-Printed Freeform Overpasses: Two-photon polymerization is used to print freeform polymer waveguide overpasses above the silicon photonic layer, providing true 3D routing without planar crossings. Typical cross-section is 1 μm × 1 μm, raised 5 μm above SiP, spanning up to 100 waveguides (Nesic et al., 2019).
• GRIN/Transformation Optics Lenses: Quasi-conformal transformation optics with Maxwell's fisheye or polygonal lenses map multiple input/output channels into a compact, low-loss, multimode crossing region by spatially varying the effective index via thickness grading or photonic crystal patterning, with footprints as small as 3.8×3.8 μm$^2$ (Badri et al., 2019, Badri et al., 2019).
• Supersymmetric Intersection Structures: SUSY optics allows analytic design of reflectionless refractive-index profiles, enabling broadband, back-reflection-free waveguide intersections by constructing separable or nonseparable GRIN profiles (e.g., Pöschl–Teller potential, double Darboux partner) (Longhi, 2014).

3. Fabrication Techniques

• CMP-Based Multilayer Platforms: Layered structures employ chemical mechanical polishing (CMP) to planarize and edge-round waveguides. In Ta$_2$O$_5$-on-LNOI, CMP with polyurethane pads and colloidal silica slurry at 3 psi rounds the SiO$_2$/LN steps into smooth tapers (~5 μm radius), reducing scattering at vertical transitions (Nan et al., 4 Dec 2025). Adiabatic tapers of ≥50 μm ensure mode evolution with minimal bending or mode-mismatch loss.
• 3D Polymer Overpasses: After standard Si photonic processing, negative-tone photoresist is patterned by two-photon polymerization, developed, and encapsulated in low-index cladding. Alignment accuracy is <200 nm, and minimum bend radius (≥40 μm) keeps bending loss below 0.1 dB (Nesic et al., 2019).
• Transformation Optics Implementations: Two primary realization methods exist: (i) graded photonic crystal rods with position-dependent radii, and (ii) continuous slab-thickness grading on SOI for index engineering. Device fabrication may require gray-scale or multi-step etch for smooth thickness transitions (Badri et al., 2019, Badri et al., 2019).
• Supersymmetric/GRIN Index Engineering: Implementation relies on etching subwavelength holes into high-index slabs for effective index tailoring or locally varying the thickness of dielectric layers for desired GRIN profiles (Longhi, 2014).

4. Loss and Crosstalk Performance Metrics

Extensive experimental and simulation data quantify the performance envelope:

Platform/Method	Insertion Loss (dB)	Crosstalk (dB)	Bandwidth (nm)
Ta$_2$O$_5$-on-LNOI 3D (Nan et al., 4 Dec 2025)	0.0017 (per crossing)	< –62	>120
3-plane a-Si (Chiles et al., 2017)	<0.0003 (P1/P3)	< –35	>35
Sq. MFE lens, slab-thick (Badri et al., 2019)	0.24–0.55 (TE$_{0-2}$)	–72 (TE$_0$)	415
Poly. MFE lens, 4×4 (Badri et al., 2019)	<0.5 (all modes)	< –22, < –37	415
3D polymer WOP (Nesic et al., 2019)	1.6–1.9 (per WOP)	< –75	>50
SUSY crossing (theoretical) (Longhi, 2014)	<0.01	< –20	Large (broadband)

Insertion loss in multilayer 3D platforms (Ta$_2$O$_5$-on-LNOI, a-Si stacks) is <0.002 dB per crossing; crosstalk is routinely below –60 dB. Transformation optics crossings offer higher loss (0.2–0.5 dB for TE$_{0-2}$), but with ultrabroad bandwidth and low crosstalk. Freeform polymer overpasses can support crosstalk below –75 dB, but typical loss is 1–2 dB per overpass due to modal mismatch and material absorption. SUSY-based continuous crossings theoretically achieve insertion loss <0.01 dB and broadband, multi-mode transparency.

5. Design Trade-offs and Optimization Criteria

Critical trade-offs are governed by:

• Interlayer Spacing vs. Coupling Efficiency: Increasing vertical gap $d$ reduces crosstalk exponentially, but increases the loss and length of interplane coupling elements (e.g., adiabatic tapers, couplers). There is an optimal $d$ (≈1.5 μm for Ta$_2$O$_5$/LNOI) minimizing total crossing loss while ensuring XT < –60 dB (Nan et al., 4 Dec 2025, Chiles et al., 2017).
• Taper and Edge Rounding: CMP-induced edge rounding (radius ≳5 μm) reduces index-step scattering; vertical taper length (≥50 μm, angle < 0.5°) supports adiabatic mode transfer (Nan et al., 4 Dec 2025).
• Waveguide Width and Index Contrast: Single-mode operation (width ~1 μm) and high index contrast (e.g., Ta$_2$O$_5$/SiO$_2$ with Δ$n$ ≈ 0.7) localize the mode and constrain lateral leakage (Nan et al., 4 Dec 2025).
• Graph-Theoretic Scaling: For $n \times n$ switch-and-select circuits, planar crossing requirement scales as $n^4$, but with 3D waveguide overpasses as $n^2$ (Nesic et al., 2019). The maximum number of crossings along any path drops from $O(n^2)$ (planar) to 1 (WOP approach).

Optimization thus involves balancing insertion/coupling loss, crosstalk suppression, spatial footprint, and fabrication complexity.

6. Advanced Approaches: Multimode and Supersymmetric Crossings

Transformation optics crossings based on Maxwell's fisheye lenses (including polygonal variants) use quasi-conformal mapping to support low-crosstalk, broadband multimode crossings with compact footprints (down to $3.8 \times 3.8$ μm² for 3-mode, square lens). Slab-thickness grading and graded photonic crystal implementations provide near-ideal refractive index profiles for imaging multiple modes. For $N$-mode crossings, the lens is upscaled with $N$, approximately maintaining performance (Badri et al., 2019, Badri et al., 2019).

Supersymmetric optical intersections provide a mathematically rigorous framework for constructing reflectionless, broadband intersections for both continuous (dielectric slab) and discretized (coupled-resonator) photonic lattices. By designing index profiles as SUSY partners, idealized losses $<0.01$ dB and crosstalk $<10^{-2}$ across many guided modes are achievable. These concepts, though primarily explored in 2D, have theoretical extensions to 3D via separable or Moutard-transformation-based index profiles (Longhi, 2014).

7. Applications, Scalability, and Outlook

3D waveguide crossings are critical for VLSPI, photonic switch fabrics, high-radix optical interconnects, mode-division multiplexing networks, and neuromorphic photonic architectures. Three-plane amorphous silicon platforms with ultralow crossing loss and Manhattan-style 3D layout flexibility support on-chip networks requiring thousands of interconnects per node (Chiles et al., 2017). Polymer overpasses reduce the complexity of $n\times n$ switches, converting the crossing count from quartic to quadratic scaling at the expense of higher per-crossing loss (Nesic et al., 2019).

The integration of transformation optics lenses and supersymmetric index engineering enables compact, broadband crossings for advanced mode-multiplexed systems, with continued improvements expected in fabrication precision for graded-index and continuous-thickness structures. A plausible implication is that hybrid platforms incorporating multilayer guides, 3D-printed overpasses, and in-plane transformation optics regions may together push the density and flexibility of photonic VLSI toward its theoretical limits.

Ongoing challenges include minimizing fabrication-induced index variation (critical for transformation optics/supersymmetric crossings), improving per-crossing insertion loss in freeform polymeric structures, and maintaining process scalability. Emerging solutions—such as parallelized direct laser writing, improved CMP for deeper multilayer stacks, and optimized taper/coupler designs—are enabling continued advances in 3D waveguide crossing technologies.