Second-harmonic generation and linear electro-optical coefficients of BN nanotubes

A systematic ab initio study of the second-order nonlinear optical properties of BN nanotubes within density functional theory in the local density approximation has been performed. Highly accurate full-potential projector augmented-wave method was used. Specifically, the second-harmonic generation $\left({\chi }_{abc}^{\left(2\right)}\right)$ and linear electro-optical $\left(r_{abc}\right)$ coefficients of a large number of the single-walled zigzag, armchair, and chiral BN nanotubes (BN-NT) as well as the double-walled zigzag (12,0)@(20,0) BN nanotube and the single-walled zigzag (12,0) BN-NT bundle have been calculated. Importantly, unlike carbon nanotubes, both the zigzag and chiral BN-NTs are found to exhibit large second-order nonlinear optical behavior with the ${\chi }_{abc}^{\left(2\right)}$ and $r_{abc}$ coefficients being up to 30 times larger than that of bulk BN in both zinc-blende and wurtzite structures, indicating that BN-NTs are promising materials for nonlinear optical and optoelectric applications. Though the interwall interaction in the double-walled BN-NTs is found to reduce the second-order nonlinear optical coefficients significantly, the interwall interaction in the single-walled BN-NT bundle has essentially no effect on the nonlinear optical properties. The prominant features in the spectra of ${\chi }_{abc}^{\left(2\right)}(-2\omega ,\omega ,\omega )$ of the BN-NTs are successfully correlated with the features in the linear optical dielectric function $\epsilon \left(\omega \right)$ in terms of single-photon and two-photon resonances.

Figure 1

(a) Real and imaginary parts as well as (b) the absolute value of the imaginary part of ${\chi }_{aab}^{\left(2\right)}(-2\omega ,\omega ,\omega )$ of the isolated BN sheet. In (c), ${\epsilon }_a^{″}\left(\omega \right)$ and ${\epsilon }_a^{″}(\omega ∕2)$ (imaginary part of the dielectric function) from Ref. 20 are plotted.

Figure 2

(Color online) Real and imaginary parts of ${\chi }^{\left(2\right)}(-2\omega ,\omega ,\omega )$ of the zigzag (6,0), (12,0), (20,0), and (25,0) BN nanotubes.

Figure 3

Absolute value of the imaginary part of ${\chi }^{\left(2\right)}(-2\omega ,\omega ,\omega )$ (a), (c), (d) as well as ${\epsilon }_a^{″}\left(\omega \right)$ and ${\epsilon }_a^{″}(\omega ∕2)$ (imaginary part of the dielectric function) (b), (e) from Ref. 20 of the zigzag (12,0) BN nanotube.

Figure 4

(Color online) Real and imaginary parts of ${\chi }^{\left(2\right)}(-2\omega ,\omega ,\omega )$ of the chiral (4,2), (6,2), (8,4), and (10,5) BN nanotubes.

Figure 5

Absolute value of the imaginary part of ${\chi }^{\left(2\right)}(-2\omega ,\omega ,\omega )$ (a), (c), (d) and ${\epsilon }_a^{″}\left(\omega \right)$ and ${\epsilon }_a^{″}(\omega ∕2)$ (imaginary part of the dielectric function) (b), (e) from Ref. 20 of the zigzag (6,2) BN nanotube.

Figure 6

(Color online) Real and imaginary parts of ${\chi }^{\left(2\right)}(-2\omega ,\omega ,\omega )$ of the double-walled (12,0)@(20,0) BN nanotube.

Figure 7

(Color online) Real and imaginary parts of ${\chi }^{\left(2\right)}(-2\omega ,\omega ,\omega )$ of the single-walled (12,0) BN-NT bundle.