The random arrangement of dielectrics and nanostructures in disordered photonic crystals produces strong Anderson localization effect and does not require high-precision nanomaterials and structures. In the previous study, we reported photonic crystal organic films with disordered nanoparticles, which were a roll-to-roll expandable material for various applications in aerospace, automotive, construction, and apparel. However, the design parameters of disordered photonic crystals still need to be optimized. This paper aims to investigate the effect of fill factor, particle size distribution, and structural symmetry of nanoparticles on the light-insulation properties by using a finite-difference time-domain (FDTD) method. The discrete nanoparticle system of organic polymer films should be further designed by analyzing the light transport properties in the microstructure.

Organic film samples of discrete nanoparticles are prepared by using the tape casting method. The microstructure of TiO₂ particles is observed by scanning electron microscopy and modeled in the FDTD. The nanostructure is simplified to a two-dimensional (2D) disordered photonic crystal in the non-polarized plane, with the particle size and the fill factor set according to experimental measurements. Electromagnetic field calculation is carried out by the FDTD method to analyze the microscopic electric field spatial distribution and macroscopic optical characteristic curves. Then the effect of different design parameters on the optical transmission characteristics is investigated. On the basis of SEM photographs, models of hierarchical size and agglomerated structures are established, and the electric field distribution of light waves in three typical structures is calculated and compared with the experimental transmittance curves. Floquet periodicity boundary conditions are set to investigate the propagation characteristics of polarized lights at different incident angles, and the wide-angle light-blocking capability is verified.

The effects of the fill factor and particle diameter of TiO₂ particles on the film spectra are investigated, and the spatial distribution of the electric field is used to describe the transmission characteristics of light waves in disordered TiO₂ photonic crystals. At a fill factor of M_f=10%, the forbidden band width is wider in the range of 200-1500 nm, and the transmittance is higher. However, when M_f is larger than 45%, the forbidden band width is narrower in the wavelength range of 200-1100 nm, and the reflectance is higher at 1000 nm compared with that at a low fill factor. The results suggest that the optimal fill factor for TiO₂ particles shall fall in the range of 35%-45%, so as to produce the best spectral forbidden band effect. As the nanoparticle diameter increases, the forbidden band region shifts towards the long wavelength band, and the reflection peaks become redshifted, in contrast to the blue shift observed when the fill factor increases. For a wavelength of 200 nm, the spatial electric field distribution is confined to the upper region of the array for nanoparticle diameter of 100 nm. The light of 800 nm propagates to the bottom surface of the film in the array with three particle sizes, but the phases are not synchronous. For electromagnetic waves with a length of 1600 nm, their propagation is unobstructed in the array of 100 nm, and the phase of the light reaching the bottom surface almost always reaches the wave peak, while the light reaching the bottom surface in the arrays of 200 nm and 300 nm undergoes multiple scattering and results in reduced transmittance. When the light wavelength is 3000 nm, much larger than the nanoparticle diameter, the light propagates through the film without scattering effects, the spatial distribution of the electric field is no longer influenced by the TiO₂ particles, and the light transmission properties are consistent with those in a homogeneous polymer matrix. The effects of hierarchical particle size and structural aggregation on the light transmission properties are further investigated and compared with experimental results, which result in a 54% reduction in near-infrared (NIR) light transmission. Finally, the wide-angle light-blocking capability of the films is evaluated. Then the transmittance profiles and electric field spatial distribution at polarized waves are analyzed. For TE- and TM-mode polarized light, efficient band-blocking properties are achieved over a wide incidence angle range of 0°-70° for wavelengths of 200-600 nm. For a wavelength of 300 nm similar to the particle size, the light propagates only to the shallow layers of the film over a wide range of incidence angles. For a wavelength of 2000 nm, which is well beyond the particle size, TiO₂ particles have difficulty in blocking light. This study provides theoretical support for the optimal design of parameters for disordered photonic crystals, especially for the preparation of organic films of TiO₂ nanoparticles.

The preparation of disordered photonic crystal organic films is the key to achieving mass production of light-insulation materials. In this paper, hierarchically disordered photonic crystal structured organic films are designed by using thermoplastic polyurethane as the film substrate and titanium dioxide particles as the reflective barrier material filling the substrate. Simulations are carried out by using the FDTD method, and the results show that the increase in fill factor causes a blue shift in the reflection peak and spectral forbidden band, while the increase in particle diameter causes a red shift in the spectral forbidden band. Compared with arrays with a uniform distribution and a single diameter, the effects of hierarchical particle size and structural aggregation on NIR waves are analyzed. For both transverse electric and transverse magnetic waves, efficient forbidden band effects are achieved over a wide incidence angle range of 0°-70°. Such organic films containing disordered photonic crystal structures provide a reference for wide-angle light-insulation materials.