# Large Second-Harmonic Generation and Linear Electro-Optic Effect in Trigonal Selenium and Tellurium

## TL;DR

This study uses ab initio calculations to reveal that trigonal selenium and tellurium exhibit exceptionally large second-harmonic generation and electro-optic effects, surpassing common materials like GaN, with potential applications in nonlinear optics.

## Contribution

The paper provides the first systematic ab initio analysis of the nonlinear optical properties of trigonal selenium and tellurium, highlighting their giant SHG and LEO coefficients compared to GaN.

## Key findings

- Tellurium exhibits SHG coefficients up to 3640 pm/V, much larger than GaN.
- Selenium shows LEO coefficients over six times larger than GaN.
- Calculated optical properties align well with experimental data.

## Abstract

Trigonal selenium and tellurium crystalize in helical chain-like structures and thus possess interesting properties such as current-induced spin polarization, gyrotropic effects and nonlinear optical responses. By performing systematic ab initio calculations based on density functional theory in the generalized gradient approximation plus scissors correction, we study their linear and nonlinear optical (NLO) properties. We find that the two materials exhibit significant second-harmonic generation (SHG) and linear electro-optic (LEO) effect. In particular, the SHG coefficients of tellurium are huge in the photon energy range of 0 ~ 3 eV, with the magnitudes of SHG(xxx) being as large as 3640 pm/V, which are about sixteen times larger than that of GaN, a widely used NLO material. On the other hand, trigonal selenium is found to possesses large LEO coefficients r(xxx,0) which are more than six times larger than that of GaN.Therefore, trigonal tellurium and selenium may find valuable applications in NLO and LEO devices such as frequency conversion, electro-optical switch and light signal modulator.The energy positions and shapes of the principal features in the calculated optical dielectric functions of both materials agree rather well with the available experimental ones, and are also analyzed in terms of the calculated band structures especially symmetries of the involved band states and dipole transition selection rules.