Orientation tomography of lanthanide-doped nanoprobes by polarization-resolved micro-spectroscopy

Abstract Quantifying three-dimensional (3D) orientation is critical for understanding self-assembly and collective behavior in soft matter and biological systems. Moreover, orientational analysis of anisotropic particles can characterize locally applied forces in fluids. We present a methodology for 3D orientation tomography based on polarization-resolved spectroscopy of lanthanide-doped nanorods exhibiting multiple emission dipoles, enabling 3D orientation measurements from a single viewing angle. We develop a confocal imaging setup optimized for lanthanide luminescence and a theoretical framework to extract both the local director and order parameter in nanorod assemblies. The technique achieves 0.5 μm lateral and 1 μm axial spatial resolution and is demonstrated in dense nematic liquid-crystal assemblies, resolving complex 3D topological structures, and in microfluidic flows, mapping alignment under hydrodynamic shear. This approach provides a versatile platform for quantitative studies of collective orientation, self-assembly mechanics, and alignment induced by external forces, and can be extended to other lanthanide-labeled particles and molecular probes.