Second-order nonlinear optical response of zigzag BN single-walled nanotubes

A theory based on the two-band tight-binding approximation for pi electrons is developed to describe the second-order nonlinear optical (NLO) properties of arrays of uniformly sized and well-aligned boron-nitride single-walled nanotubes (BN-SWNTs) with a zigzag achiral structure. It is assumed that the coherent light beam at frequency omega, incident upon the nanotube sample, is linearly polarized along the symmetry axis of the nanotubes. The long-axis NLO susceptibility chi((2))(omega) of those nanotubes is calculated within the independent nanotube approximation and in neglecting local-field effects. Using the perturbation-theory formalism in the crystal-momentum representation, we derive an explicit analytic expression for the chi((2))(omega) and apply it to study three distinct second-order NLO effects possible in the BN-SWNTs due to their noncentrosymmetric structure-namely, second-harmonic generation (SHG), linear electro-optical (LEO) effect, and nonlinear optical rectification (NOR). The theory is illustrated by numerical model calculations of the SHG, LEO, and NOR susceptibility spectra for several representative BN-SWNT ensembles consisting of large-diameter nanotubes. The calculated SHG spectra are found to be dominated by the highly peaked 2 omega resonance at half the band-gap energy of the BN-SWNTs, where the absorption of light is negligible. Distinct features are also found in the LEO and NOR susceptibility spectra, e. g., a sudden switching of the susceptibility from a positive peak value to a negative peak one in the near vicinity of the fundamental absorption edge. A fairly large magnitude of those susceptibilities, reaching the order of 10(-7) esu under off-resonant conditions and up to 10(-6) esu in the resonant case, suggests that BN-SWNTs are a promising material for various electro-optical device applications.