Objective High-speed coherent optical communication, driven by 5G/6G, data-center interconnects, and ultra-high-definition video transmission, requires advanced modulation formats such as QPSK and high-order QAM, which impose stringent demands on integrated 90° optical hybrids. These devices perform coherent mixing of signal and local oscillator (LO) light, converting the in-phase (I) and quadrature (Q) components into optical intensity signals. Their insertion loss, channel crosstalk, phase error, and splitting uniformity directly determine receiver sensitivity and error vector magnitude (EVM). Currently, most integrated 90° optical hybrids are fabricated on planar platforms such as silica-based PLC and SOI. Restricted by two-dimensional geometry, the I and Q arms must be arranged within the same plane, leading to severe crosstalk from waveguide crossings and large device footprints—the overall chip area far exceeds that of the core functional units. In contrast, femtosecond laser direct writing offers true three-dimensional (3D) fabrication capability, enabling arbitrary waveguide geometries inside transparent materials and overcoming planar layout limitations. This work exploits this 3D capability to propose a compact, high-performance 90° optical hybrid with ultra-low crosstalk and low polarization-dependent phase error.

Methods A fully symmetric 3D orthogonal architecture is proposed based exclusively on 2×2 directional couplers for both splitting and phase shifting. The theoretical analysis is grounded in coupled-mode theory. For a lossless 2×2 directional coupler, the through and cross port outputs satisfy E_through = E_incos(κL) and E_cross = E_injsin(κL), where κ is the coupling coefficient, L is the coupling length, and j is the imaginary unit corresponding to the intrinsic 90° phase shift. This phase difference is determined solely by coupled-mode theory and has no direct dependence on κ or L, making it highly robust against process fluctuations. Even when input polarization varies and causes κ to fluctuate, the 90° phase difference remains stable. Moreover, the I and Q interferometric arms adopt completely symmetric spatial layouts and identical fabrication parameters, ensuring that for any polarization state, the propagation phase difference remains zero. Based on this theory, the I and Q arms are inscribed at depths of 250 µm and 300 µm, respectively, with a 50 µm vertical separation to virtually eliminate evanescent-wave crosstalk. Identical writing parameters and symmetric paths maintain amplitude balance and phase orthogonality, while a waveguide trimming structure (ΔL) provides precise optical-path-length matching. Fabrication uses a Yb:KGW femtosecond laser system (1030 nm, 100 kHz, 197 fs) with second-harmonic generation at 515 nm through a BBO crystal. The 515 nm pulses are focused by a 20× objective (NA = 0.75), and the process is monitored in real time by a CCD camera.

Results and Discussion Systematic optimization of fabrication parameters is performed. Under optimized conditions (56 mW, 0.1 mm/s), waveguides achieve stable single-mode transmission at 1550 nm with a minimum propagation loss of 0.16 dB/cm. Performance at different depths (250 µm and 300 µm) shows excellent consistency, with a loss difference below 0.02 dB/cm and a mode-field overlap integral of 0.986, demonstrating outstanding process stability across depths. The directional coupler splitting characteristics are systematically characterized. With a coupling gap of 12 µm, a coupling length of 1.712 mm achieves 1∶1 uniform splitting at 1550 nm. The coupling coefficient κ deviation between the two depths is less than 0.5%, confirming that core functional units do not require separate design adjustments for different depths, significantly simplifying fabrication. The crosstalk between the I and Q arms, measured by the end-face injection method, is below −72 dB—far superior to the −20 to −40 dB levels of most reported devices. This fully verifies that the 3D orthogonal layout effectively suppresses evanescent-wave crosstalk. In practice, due to measurement system limitations, the actual crosstalk does not exceed −72 dB. The fabricated device exhibits a compact footprint of 25 mm × 90 µm and an insertion loss of 2.3 dB. The splitting amplitude imbalance is maintained within 0.95–1.05, achieving near-ideal 1:1 uniformity. Phase demodulation performance is evaluated using Lissajous ellipse fitting. Under vertical polarization (V-light), the phase error is −0.35° with an amplitude imbalance of 1.04; under 30° polarization, −0.83° and 1.10; under 60° polarization, −3.53° and 1.26; and under horizontal polarization (H-light), −3.37° and 1.26. Across the full polarization range, the phase error remains within ±5°, demonstrating significant suppression of polarization-dependent phase errors by the symmetric interferometric arm structure. A digital calibration matrix is derived from the measured transmission matrix. After applying a single fixed calibration matrix, the residual phase error across the full polarization range is reduced to within 2°, and the amplitude imbalance is controlled within 1 ± 10%. The calibrated Lissajous ellipses converge to nearly perfect circles that almost completely overlap with the ideal unit circle, with no observable rotation or axis deviation. This intuitively verifies that the digital calibration method effectively compensates for amplitude imbalance and phase errors, requiring only a single calibration to achieve near-ideal quadrature demodulation across the full polarization range.

Conclusions This work demonstrates a novel paradigm for high-performance 90° optical hybrids using femtosecond-laser 3D photonic integration. By synergistically combining a 3D orthogonal waveguide layout with a fully symmetric directional-coupler-based architecture, the device simultaneously achieves ultra-low crosstalk (<−72 dB), minimal polarization-dependent phase error (<±5° across the full polarization range, and <2° after calibration), and an extremely compact form factor (25 mm × 90 μm). The device offers a high-performance, rapidly prototypable 3D integration solution for high-speed coherent optical communication systems, and also provides new design concepts for the application of femtosecond laser direct writing technology in 3D integrated photonic signal processing and quantum optics.