Orthogonally stacked dye-doped liquid crystal modulators: a coupled complex Jones matrix model and synergistic optimization of transmittance and contrast ratio

Dye-doped liquid crystal (DDLC) modulators are critical for smart windows and automotive displays, yet suffer from an inherent trade-off between transmittance and contrast ratio. Conventional optical models neglect the coupling between polarisation rotation and anisotropic absorption of dichroic dyes in twisted nematic (TN) structures, causing large theory-experiment discrepancies and leaving device design reliant on empirical trial-and-error. Herein, we develop a unified complex Jones matrix model incorporating these coupled effects and introduce two physically intuitive parameters: the absorption enhancement factor S1 and the light leakage amplification factor S2, revealing the degradation mechanism in TN DDLC devices. Using a commercial dye mixture (dichroic ratio 6.35), we systematically characterise six typical device configurations based on electrically controlled birefringence (ECB) and TN modes. Orthogonally stacked dual-ECB and anti-handed dual-TN structures overcome the 50% intrinsic optical loss of conventional polarisers, simultaneously optimising transmittance and contrast. The dual-ECB structure delivers a transmittance modulation of 32.21% at a 5-μm cell gap (48.2% higher than ECB with a single polariser) and a contrast ratio of 23.72 at a 10-μm cell gap. This work establishes a quantitative mapping between dichroic dye properties, device architecture, and optical performance, enabling rational design of high-performance DDLC modulators.