Fig. 1. Theoretical basis of polarized light^[33]. (a) Relationship among unpolarized light, linearly and circularly polarized light; (b) schematic illustration of linearly polarized luminescence; (c) schematic illustration of circularly polarized luminescence

Fig. 2. Linear polarization characteristics of a single β-NaYF₄∶Yb³⁺/Tm³⁺ nanocrystal^[32]. (a) SEM image of β-NaYF₄∶Yb³⁺/Tm³⁺ nanorods with doping Gd³⁺ mole fraction of 30%; (b) SEM image of β-NaYF₄∶Yb³⁺/Tm³⁺ nanodisks; (c)‒(g) polar plots of the upconversion peak intensity as a function of the emission polarization angle, which is corresponding to the transitions of Tm³⁺: (c) ¹G₄→³F₄, (d) ³F₃→³H₆, (e) ¹D₂→³F₃, (f) ¹G₄→³H₅, and (g) ³H₄→³H₆; (h) composite effect of two orthogonal linearly polarized emissions

Fig. 3. Linear polarization characteristics of a single β-NaYF₄∶Yb³⁺/Pr³⁺ microcrystal^[44]. (a) π-configuration, in which light propagates perpendicularly to the crystal c-axis with a polarization perpendicular to the a-axis; (b) σ-configuration, in which light propagates perpendicularly to the crystal a-axis with a polarization perpendicular to the c-axis; (c)(d) electron cloud distribution of Y³⁺/Yb³⁺/Pr³⁺ in the hexagonal NaYF₄ structure by density functional theory calculations, observed in π- and σ-configuration; (e)(f) upconversion photoluminescence spectra and corresponding fluorescence microscopy images in two excitation configurations of a single β-NaYF₄∶20%Yb³⁺, 10%Pr³⁺ microcrystal in π- and σ-configuration, recorded at excitation polarization angles varying from 0° to 360°

Fig. 4. Linear polarization characteristics of Eu³⁺ in LaPO₄ structures. Polarized emission spectra of the aligned nanorod films of LaPO₄∶5%Eu in (a) rhabdophane phase without annealing and (b) monazite phase annealed at 1000 ℃ (λ_ex=394.5 nm, 77 K)^[46]; (c) SEM images of the aligned LaPO₄∶5%Eu nanorod films for different final annealing temperatures (scale bars 200 nm)^[46]; (d) polarized photoluminescence spectra of an aligned thin film of LaPO₄∶Eu nanorods fabricated by the shear-directed assembly, in which the inset is SEM image of the film (scale bar, 200 nm)^[49]; (e) schematic illustration of the microfluidic channel used for the local shear rate measurement^[49]

Fig. 5. Circular polarization characteristics of rare earth ions-doped materials^[51]. (a) Schematic representation of upconverted circularly polarized luminescence (UC-CPL) based on achiral Er or Tm-doped upconversion nanoparticles (UCNPs) and chiral nanotubes at excitation wavelength of 980 nm; (b) UC-CPL emission spectra of co-gels excited by 980 nm laser, and the circular dichroism value in the bottom spectrum stands for fluorescence intensity; (c) illustration of the possible mechanism for the UC-CPL, in which the unassembled state of chiral monomer (LGAm)/UCNPs was achieved form a chlorobenzene solution, and achiral monomer (BAm) with similar structure was synthesized to illustrate the importance of chirality from gelator