On the reflection and diffraction of carbon nanotube array thin film

A theory for determining the effective refraction index of carbon nanotube array thin film is developed based on Fresnel's equation of wave normals. Here, the theory of a metallic film is used to determine the reflectivity and then to analyze the results of previous experiments on the optical properties of vertically aligned carbon nanotube arrays for different polarized incident lights. Both transverse electric-polarized lights and transverse magnetic-polarized lights are investigated, and the results agree well with the available experimental data. In a different case, when considering the weighted average of the polarized lights, the theoretical reflectivity for a non-polarized incident light is in excellent agreement with the experimental data. The refraction efficiency of a grating-patterned carbon nanotube array thin film is also investigated using the Fraunhofer diffraction theory. Based on the comparison of the theoretical and experimental results, it is concluded that the proposed theoretical model reveals the optical behavior of a carbon nanotube array thin film.