Compact deterministic liquid-crystal polarization controller with single-measurement direct control

The gist: A compact deterministic liquid-crystal polarization controller (LC-PC) with a single-measurement direct-calculation algorithm achieves deterministic polarization modulation over the full Poincaré sphere with an angular error below 2 degrees.

Device Performance and Design

The proposed device is a compact liquid-crystal polarization controller (LC-PC) with dimensions of 30 × 12.7 × 13 mm3 The device exhibits low insertion loss (< 1 dB), low driving voltage (< 6 V), and full Poincaré sphere coverage It achieves a fiber-to-fiber insertion loss of approximately 0.97 dB and a PDL of only 0.04 dB The structure consists of three miniature LC cells with fast-axis orientations of 0°, 45°, and 0° Each LC cell has dimensions of 6.5mm × 5mm × 1.1mm and consists of a nematic liquid-crystal layer sandwiched between two indium tin oxide (ITO)-coated glass substrates To suppress temperature-induced performance variations, integrated thermistors and thermoelectric coolers (TECs) are employed for active thermal stabilization The package is subsequently hermetically sealed using parallelseam welding technology, providing enhanced mechanical robustness and environmental reliability

Theoretical Basis of Deterministic Control

Liquid crystals exhibit anisotropic dielectric and optical properties due to their elongated molecular structure, resulting in polarization-dependent propagation characteristics When polarized light propagates through a liquid-crystal layer, it can be decomposed into ordinary and extraordinary components By adjusting the amplitude of the applied electric field, the orientation of liquid-crystal molecules changes, leading to a voltage-dependent birefringence and consequently an electrically controllable phase retardation The liquid-crystal cell can therefore be modeled as a voltage-controlled linear retarder Based on Jones calculus, its polarization transformation matrix can be expressed as MLC(δ, θ) = [cos2theta + e-iδ sin2theta cos θ sin theta(1 − e-iδ) cos θ sin theta(1 − e-iδ) sin2theta + e-iδ cos2θ] Simulations of the Jones matrices for liquid crystal cells with fast axes at 0° and 45° reveal their polarization modulation characteristics on the Poincaré sphere Under a fixed liquid crystal cell fast-axis orientation, the modulation characteristics were analyzed for different input SOPs As shown in Fig. 3(a), the polarization modulation characteristics of the three channels form circular paths on the Poincaré sphere The trajectories generated by the two cells are mutually orthogonal, as are their normal vectors n0 and n45 This deterministic phaseretardation-to-rotation relationship forms the physical basis for the proposed single-measurement direct-calculation polarization control algorithm

Single-Measurement Direct Calculation Algorithm

The core innovation is a direct-calculation control algorithm that requires only a single SOP measurement to compute driving voltages, achieving convergence with angular error less than 2◦ This strategy is based on the physical insight that the LC-PC is not a black-box polarization transformer, but rather a cascade of three deterministic rotations with fixed and well-defined axes The problem is reformulated as a geometric rotation synthesis problem on the Poincaré sphere Let the initial and target SOPs be denoted by points A and D The transformation from A to D is decomposed into three successive rotations corresponding to the LC channels CH1, CH2, and CH3 The initial state A and the CH1 rotation axis n1 define a circular trajectory constraint on the Poincaré sphere The target state D and the CH3 axis n3 define another one The CH2 axis n2 provides the intermediate rotational constraint that couples these two fixed-axis evolutions into a continuous trajectory By simultaneously solving the corresponding geometric constraints, two sets of intermediate intersection points, B (or B′) and C (or C′), can be obtained Since the initial SOP, target SOP, and three rotation axes are known, the intermediate SOPs B and C can be directly solved without iterative optimization Once the intermediate SOPs are determined, the required rotation angles of the three LC channels can be calculated from the angular displacement between the corresponding points along their respective circular trajectories on the Poincaré sphere These rotation angles are subsequently converted into driving voltages according to the experimentally characterized voltage-to-rotation relationships of the three LC channels

Experimental Validation and Comparison

To experimentally demonstrate the single-measurement direct-calculation polarization control enabled by the deterministic LC-PC, polarization control experiments were performed using the fabricated device Ten randomly selected initial SOPs were tested, and all were successfully transformed to the target SOP located at (−0.958, 0.129, 0.275) For each case, only a single measurement of the initial SOP was required, after which the driving voltages were directly calculated and applied without further optimization The control accuracy was evaluated by the angular separation between the measured and target SOPs on the Poincaré sphere For all test cases, the Poincaré sphere angle error was maintained below 2◦, demonstrating that arbitrary input SOPs can be accurately transformed to the desired target state using the proposed direct-calculation method The resulting SOPs were measured and compared with the target state

Comparative Analysis

The proposed LC-PC achieves a favorable balance among optical performance, electrical driving requirements, and compactness Compared with waveplate- and fiber-squeezer-based PCs [13, 19], the proposed device eliminates mechanical moving components and provides electronically controlled polarization modulation with improved compactness and stability Compared with integrated PCs based on thin-film lithium niobate (TFLN) [23] and silicon photonics (SOI) [32, 33], the proposed LC-PC avoids additional fiber-tochip coupling loss by maintaining a fiber-to-fiber optical path, which is advantageous for insertion-loss-sensitive applications such as quantum key distribution systems (QKD) The combination of the compact deterministic LC-PC and the single-measurement control scheme provides an efficient solution for size-, weight-, and loss-constrained polarization-sensitive photonic systems The primary limitation of the device remains the ∼100 ms response time, governed by nematic LC switching dynamics Future work will focus on adopting fast-response LC materials (e.g., ferroelectric LCs)[34] and optimized cell/packaging designs to further improve response speed and compactness The deterministic polarization response of the LC-PC is exploited to establish a geometric rotation model The SOP-independent trajectory normal vectors of the LC channels provide fixed rotational axes on the Poincaré sphere, enabling an analytical mapping between polarization states and phase retardations Therefore, the required driving voltages can be directly calculated from a single measured input SOP, avoiding multi-state channel characterization and iterative optimization The proposed device and control algorithm are highly synergistic The combination of the compact deterministic LC-PC and the single-measurement direct-calculation algorithm provides an efficient solution for size-, weight-, and loss-constrained polarization-sensitive photonic systems.

1. textbfDirect-Calculation Control Algorithm Implementation in AI Systems: Enables real-time polarization state determination with minimal input data, as it requires only a single SOP measurement to compute driving voltages. This allows AI systems to instantly determine the necessary control signals for polarization management without needing iterative optimization or complex Mueller matrix reconstruction, drastically reducing latency in quantum communication and sensing applications.

2. textbfDeterministic Polarization Mapping for Robust State Estimation: The paper's finding that the rotation angle is uniquely determined by the phase retardation and remains independent of the input SOP allows AI models to create a deterministic mapping between applied voltage and resulting polarization state, ensuring highly predictable control outcomes even under environmental disturbances. This enables AI systems to maintain high signal fidelity in quantum key distribution by accurately compensating for SOP fluctuations using this fixed geometric relationship.

3. textbfCompact Hardware Integration for Resource-Constrained Environments: The demonstration of a compact deterministic LC-PC (30 × 12.7 × 13 mm3) with "low insertion loss (<1 dB), low driving voltage (<6 V)" provides a viable, small form factor solution for polarization management in embedded AI hardware. This allows AI systems designed for size-weight constraints, such as QKD terminals or optical sensors, to incorporate precise polarization control without sacrificing system compactness or incurring significant power consumption from high-voltage drivers.

Polarization controllers (PCs) and their control algorithms are critical for compensating environmental disturbances and maintaining signal fidelity in polarization-sensitive photonic systems. However, existing controllers often involve trade-offs among key performance metrics,while associated control algorithms either converge inefficiently or require multiple state-of-polarization (SOP) measurements. This work presents a compact deterministic liquid-crystal polarization controller (LC-PC) with balanced overall performance, featuring low insertion loss (<1 dB), low driving voltage (<6 V), and full Poincaré sphere coverage. The device exhibits highly predictable and repeatable polarization modulation characterized by SOP-independent trajectory normal vectors, enabling a single-measurement direct-calculation algorithm using pre-characterized rotation axes and voltage-to-rotation relationships, with degree-level polarization control accuracy. The combination of this compact deterministic LC-PC and its efficient control scheme provides a practical solution for polarization management in quantum key distribution, optical sensing, and advanced photonic systems.