Dual-Polarization 2D Grating Couplers

• The paper demonstrates dual-polarization 2D grating couplers achieving sub-decibel fiber-chip coupling via innovative topology and double-layer designs.
• It employs full-vectorial 3D simulations and eigenmode analysis to optimize modal overlap, minimize polarization-dependent loss, and ensure CMOS compatibility.
• Experimental results highlight broadband performance, low crosstalk, and compact device footprints, making them ideal for data centers and quantum photonics applications.

Dual-polarization two-dimensional (2D) grating couplers are integrated photonic structures engineered to interface with optical fibers regardless of the polarization state of the incident light. Unlike conventional one-dimensional (1D) grating couplers, which are inherently polarization-selective, 2D grating couplers employ geometrically complex periodic patterns—often with multipolar symmetry, double-layer structures, or topology-optimized arrangements—to achieve polarization-diversity coupling. This enables robust, efficient, and broadband coupling of both transverse electric (TE) and transverse magnetic (TM) modes between chips and fibers, which is critical for advanced WDM, SDM, and quantum photonics platforms. Their performance hinges on precise control of modal overlap, scattering directionality, polarization-dependent loss, and fabrication tolerances, with recent demonstrations reporting sub-decibel coupling efficiencies and ultra-compact footprints using CMOS-compatible processes (Huang et al., 17 Oct 2025, Zhou et al., 19 Jul 2024).

1. Physical Principles and Governing Equations

Dual-polarization 2D grating couplers operate fundamentally by manipulating guided-wave to radiation-mode transformations through engineered spatial permittivity modulations. The electromagnetic problem is governed by time-harmonic Maxwell's equations:

$$\nabla \times \nabla \times \mathbf{E} - k^2 \varepsilon(\mathbf{r}) \mathbf{E} = 0$$

where $k = 2\pi/\lambda_0$ and $\varepsilon(\mathbf{r})$ captures the 2D refractive index distribution. Accurate modeling requires full-vectorial simulations to resolve both TE and TM polarizations and capture multipolar modal symmetries. For grating-based coupling to LP fiber modes, phase matching obeys the generalized Bragg condition:

$\beta + \frac{2\pi}{\Lambda} = k_0 \sin \theta$

where $\Lambda$ is the grating period and $\theta$ is the diffraction angle (Wohlfeil et al., 2014). In dual-polarization architectures, input waveguides and grating geometries are arranged so $\mathbf{E}(\mathbf{r})$ can overlap with both $\mathrm{LP}_{01}$-type fiber modes for arbitrary polarization.

2. Structural Architectures and Optimization Strategies

Recent advances encompass various structural motifs aimed at dual-polarization efficacy:

• Double-Layer Bi-Level Gratings: A shallow-etched hole array in silicon overlain by deposited polycrystalline silicon teeth enhances field confinement and upward directionality. The vertical asymmetry and multipolar resonance excitation in these structures minimize PDL to sub-0.3 dB and achieve –2.54 dB peak efficiency (Zhou et al., 19 Jul 2024).
• Topology Optimization and Inverse-Designed Pixelated Arrays: The material profile $\rho(x, y) \in [0, 1]$ discretizes the design region and is optimized via adjoint 3D-FDTD and gradient-based algorithms (e.g., L-BFGS-B), maximizing the modal overlap figure of merit:

$$\text{FoM}_{ij} = \frac{|\int_S \mathbf{E}_{ij}^* \mathbf{E}_{\text{wg}}\, dS|^2}{\int_S |\mathbf{E}_{ij}|^2\, dS \int_S |\mathbf{E}_{\text{wg}}|^2\, dS}$$

This strategy has yielded 14 μm × 14 μm SOI 2D couplers with –0.86(13) dB measured efficiency per polarization at normal incidence (Huang et al., 17 Oct 2025).

• Adjoint Shape Optimization for Polarization Splitting: Scatterer shapes are parameterized by Fourier expansions with aspect ratios modulated via 2D Chebyshev polynomials, spatially apodizing the grating and balancing coupling for orthogonal polarizations. Simulations report 1.2 dB peak loss and PDL below 0.01 dB without bottom reflectors (Sun et al., 2022).
• Sheared Grating Geometries: Control of the waveguide-to-grating shear angle and perturbation depth regulates polarization splitting. Splitting ratios and extinction ratios for QPSK and QAM modulation formats are analytically determined as functions of cross-polarization leakage (Georgieva et al., 2020).

3. Numerical Methods and Convergence Criteria

Accurate prediction of dual-polarization coupler performance relies on:

• Eigenmode Analysis (2D): Computing effective indices for both TE and TM modal sets using higher-order finite elements (polynomial degree $p \geq 4$ with adaptive mesh refinement) (Wohlfeil et al., 2014).
• Full-vectorial 3D Simulations (FDTD/FEM): Complete device modeling (coupler, substrate, superstrate) with prismatoidal mesh or adjoint FDTD, leveraging bottom reflectors or metal mirrors to enhance upward directionality and suppress substrate leakage (Huang et al., 17 Oct 2025, Lomonte et al., 2023). Convergence studies monitor the relative error in electromagnetic energy and overlap integrals; with $p>2$, numerical errors are typically controlled below 1% (Wohlfeil et al., 2014).
• Efficiency Measures: The modal overlap is the primary metric, sometimes complemented by coupling efficiency $$\eta = 10\log_{10}\left( \frac{P_{\text{out}}}{P_{\text{in}}} \right)$$ (Ruiz et al., 2021), and directionality $D = P_{\text{up}}/P_{\text{total}}$.
• Polarization-Dependent Loss (PDL): $$\text{PDL (dB)} = |10\log_{10}(T_\text{max}/T_\text{min})|$$ quantifies uniformity across polarizations (Zhou et al., 19 Jul 2024).

4. Experimental Results and Performance Metrics

Empirical demonstrations highlight several key metrics:

Device Structure	Peak Coupling Efficiency	PDL	Bandwidth
Topology-optimized 2D SOI, bottom reflector (Huang et al., 17 Oct 2025)	–0.86(13) dB	<0.2 dB*	~30 nm*
Bi-level SOI, poly-Si tooth (Zhou et al., 19 Jul 2024)	–2.54 dB	<0.3 dB	23.4 nm
Compact 2D SOI, multicore fiber (Ruiz et al., 2021)	–4.3 dB	0.54 dB	48 nm
PSGC, adjoint shape opt. (Sun et al., 2022)	1.2 dB (sim.)	<0.01 dB	~10 nm*

*Context-value; not directly measured or may vary between samples.

These results establish that modern dual-polarization 2D grating couplers routinely offer sub-decibel fiber–chip coupling, bandwidth approaching 50 nm, and PDL levels below 0.3 dB. Competition between fabrication tolerances and design-dependent effects is reflected in device-to-device variability. Implementation with standard DUV lithography and SOI foundry compatibility underscore scalability and integration readiness (Zhou et al., 19 Jul 2024).

5. Material Platforms and Integration Considerations

2D dual-polarization grating couplers have been realized on various platforms:

• Silicon-on-Insulator (SOI): CMOS compatibility, demonstrated minimal feature sizes of 180 nm and scalable DUV lithography processing for volume manufacturing (Zhou et al., 19 Jul 2024).
• Low-index platforms (SiN, LN): Apodized self-imaging designs and metal back-reflectors overcome limited grating strength, with measured –0.55 dB coupling efficiency on SiN and broadband performance (Lomonte et al., 2023, Krasnokutska et al., 2019).
• Backend-of-line amorphous Si:H: Enables hybrid transmitter integration and demonstrated O-band extension (Georgieva et al., 2022).

Fabrication steps include shallow etching, bottom metal mirror (via DRIE), and overlap alignment for multi-layer architectures. Device footprint remains critical for photonic circuit density; designs as small as 200 μm² per fiber core have been implemented (Ruiz et al., 2021).

6. Polarization-Diversity, Multiplexing, and Advanced Functionality

Dual-polarization 2D couplers now support features beyond polarization-insensitive coupling:

• Multipolar Mode Excitation and Demultiplexing: Carefully arranged input gratings and superimposed excitation patterns enable selective excitation of LP modes (LP₀₁, LP₁₁ₐ, LP₁₁_b, LP₂₁ₐ) in both TE and TM states, valuable for SDM and multimode systems (Wohlfeil et al., 2014).
• Polarization-Splitting and Chiral Routing: PSGC designs efficiently split incoming light by polarization into independent waveguide arms with virtually zero PDL (Sun et al., 2022). Plasmonic gratings further support routing of TE/TM modes in opposite waveguide directions as a function of input circular polarization handedness, realizing effective polarization-division multiplexers with routing efficiencies up to 95% (Fradkin et al., 2023).
• Bandwidth and Crosstalk: Low inter-core crosstalk (–42.7 dB) in multicore-fiber couplers and robust bandwidth (>20 nm) confirm suitability for high-speed optical interconnects (Ruiz et al., 2021, Zhou et al., 19 Jul 2024).

7. Applications and Outlook

Dual-polarization 2D grating couplers address demands for efficient fiber-chip interfaces in data centers, SDM transmission, coherent communication systems (minimizing BER in DP-QAM formats (Georgieva et al., 2020)), and integrated quantum photonics (quantum key distribution, teleportation, low-loss quantum state transfer (Huang et al., 17 Oct 2025)). Scalability, compactness, and low PDL enable their deployment in dense photonic integrated circuits, polarization-diversity transceivers, and advanced multiplexing platforms.

A plausible implication is continued adoption of topology optimization and adjoint shape design methodologies—leveraging their process-independent physical insights—for future coupler generations, together with integration of 2D couplers into larger on-chip networks including beam splitters and interferometers. This suggests that further reductions in device footprint, enhancements in directionality, and full polarization independence (down to single-digit millidecibel PDL) are realistic targets for next-generation photonic systems.