Carbon nanotubes (CNT) have been grown in a honeycomb configuration on silicon substrates using nanosphere self-assembly and plasma enhanced chemical vapor deposition. The optical properties of the arrays were also studied. Diffraction efficiency was found to be a function of the wavelength, angle of incidence and state of polarization of incident light. The unique optical properties of the arrays combined with the excellent mechanical and electrical properties of carbon nanotubes indicates that these materials may find many uses in the field of optoelectronics. In addition to their optical properties, periodic CNT arrays have a host of other unique electromagnetic and mechanical properties that may be exploited for numerous applications. Polarization measurements indicate that the intensity of both the diffracted light and diffusely scattered light is dependent on wavelength and angle of incidence. These arrays not only reflect and diffract light, but can also have a photonic band gap in, or around, the visible frequency range. The precise frequency location and size of this gap can be controlled by the structural and material parameters of the arrays.