  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.
