Second-harmonic generation and linear electro-optical coefficients of SiC polytypes and nanotubes

The second-order nonlinear optical susceptibility $\left[{\chi }_{abc}^{\left(2\right)}\right]$ and linear electro-optical coefficient $\left(r_{abc}\right)$ of a large number of single-walled zigzag, armchair, and chiral silicon carbide (SiC) nanotubes (SiC NTs), as well as bulk SiC polytypes (2H-, 4H-, 6H-, and 3C-SiC) and single graphitic SiC sheet have been calculated from the first principles. The calculations are based on the density-functional theory in the local-density approximation where the highly accurate full-potential projector augmented-wave method was used. Both the zigzag and chiral SiC NTs are found to exhibit large second-order nonlinear optical behaviors with the ${\chi }_{abc}^{\left(2\right)}$ and $r_{abc}$ coefficients being up to ten times larger than that of bulk SiC polytypes and also being up to thirteen times larger than the counterparts of the corresponding BN NTs, indicating that SiC NTs are promising materials for nonlinear optical and optoelectric applications. The features in the spectra of ${\chi }_{abc}^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ of the SiC NTs are discussed in terms of the single- and two-photon resonances and also related to the features in the linear dielectric function $\epsilon \left(\omega \right)$.

Figure 1

(Color online) Real and imaginary parts of ${\chi }^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ of the hexagonal SiC polytypes.

Figure 2

(Color online) Real and imaginary parts of ${\chi }_{xyz}^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ of SiC in the zinc-blende (3C) structure. Previous calculations by Adolph and Bechstedt (Ref. 41) are also displayed for comparison.

Figure 3

(Color online) Imaginary parts of ${\chi }^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ of SiC in the wurtzite (2H) structure. Previous calculations by Adolph and Bechstedt (Ref. 41) are also displayed for comparison.

Figure 4

(Color online) (a) Real and imaginary parts as well as (b) the absolute value of the imaginary part of ${\chi }_{aab}^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ of the isolated SiC sheet. In (c) ${\epsilon }_a^{″}\left(\omega \right)$ and ${\epsilon }_a^{″}\left(\omega /2\right)$ (imaginary part of the dielectric function) from Ref. 28 are plotted.

Figure 5

(Color online) Real (dotted line) and imaginary (solid line) parts of ${\chi }^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ of the zigzag (6,0), (12,0), (20,0), and (24,0) SiC NTs.

Figure 6

(Color online) Absolute value of the imaginary part of ${\chi }^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ (a)–(d) as well as ${\epsilon }^{″}\left(\omega \right)$ and ${\epsilon }^{″}\left(\omega /2\right)$ (imaginary part of the dielectric function) (b)–(e) from Ref. 28 of the zigzag (12,0) SiC NT.

Figure 7

(Color online) Real (dotted line) and imaginary (solid line) parts of ${\chi }^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ of the chiral (4,2), (6,2), (8,4), and (10,4) SiC NTs.

Figure 8

(Color online) Absolute value of the imaginary part of ${\chi }^{\left(2\right)}\left(-2\omega ,\omega ,\omega \right)$ (a)–(d) and ${\epsilon }^{″}\left(\omega \right)$ and ${\epsilon }^{″}\left(\omega /2\right)$ (imaginary part of the dielectric function) (b)–(e) from Ref. 28 of the zigzag (8,4) SiC NT.