Effective optical properties of absorbing nanoporous and nanocomposite thin films

Abstract

This paper aims at developing numerically validated models for predicting the through-plane effective index of refraction and absorption index of nanocomposite thin films. First, models for the effective optical properties of such materials are derived from previously reported analysis applying the volume averaging theory (VAT) to Maxwell’s equations. The transmittance and reflectance of nanoporous thin films are computed by solving Maxwell’s equations and the associated boundary conditions at all interfaces using finite element methods. The effective optical properties of the films are retrieved by minimizing the root mean square of the relative errors between the computed and theoretical transmittance and reflectance. Nanoporous thin films made of SiO2 and TiO2 consisting of cylindrical nanopores and nanowires are investigated for different diameters and various porosities. Similarly, electromagnetic wave transport through dielectric medium with embedded metallic nanowires are simulated. The numerical results are compared with predictions from widely used effective property models including (1) the Maxwell-Garnett theory, (2) the Bruggeman effective medium approximation, (3) the parallel, (4) series, (5) Lorentz-Lorenz, and (6) the VAT models. Very good agreement is found with the VAT model for both the effective index of refraction and absorption index. Finally, the effect of volume fraction on the effective index of refraction and absorption index predicted by the VAT model is discussed. For certain values of wavelengths and volume fractions, the effective index of refraction or absorption index of the composite material can be smaller than that of both the continuous and dispersed phases. These results indicate guidelines for designing nanocomposite materials with desired optical properties.

Effective optical properties of highly ordered mesoporous thin films

“…It is evident that the retrieved n ef f and k ef f decreased as porosity increased. As previously reported, both n ef f and k ef f for 2D mesoporous films are accurately predicted by the VAT model for TE polarization [36,37]. For TM polarization however, n ef f is accurately predicted by the 2D MGT model while k ef f is better predicted by the parallel model [38].…”

“…In addition, pore shape and spatial arrangement had a strong effect on the retrieved effective properties. The present study extends our previous investigations of 2D non-absorbing [36] and absorbing nanocomposite films with cylindrical pores [37,38] to 3D absorbing mesoporous thin films with spherical pores. Three-dimensional Maxwell's equations were solved numerically to compute the transmittance and reflectance over the spectral range of 400 to 900 nm.…”

“…For TE polarization, the pore shape and size had no effect on the effective optical properties which were predicted by the VAT model [36,37]. For TM polarization, the parallel model was in good agreement with the retrieved effective optical properties for pores with cylindrical cross-section [38].…”

“…This study expanded our previous studies for 2D mesoporous films with cylindrical pores [36][37][38] by numerically simulating mesoporous films in 3D with spherical pores exposed to TE and TM polarized incident waves. 3D Maxwell's equations were numerically solved to compute the transmittance and reflectance of the mesoporous thin films over the spectral range from 400 to 900 nm.…”

“…Previous studies [36][37][38] established that reflectance and effective optical properties of two-dimensional (2D) mesoporous thin films with cylindrical pores exposed to normally incident transverse electric (TE) and transverse magnetic (TM) waves depended on electro- 3D Maxwell-Garnett Theory n 2 ef f = n 2 c 1 −…”