E.E. Muryumin

Optical second-harmonic generation from two-dimensional hexagonal crystals with broken space inversion symmetry

We propose a microscopic theory of the optical second-harmonic generation (SHG) from π electrons in two-dimensional (2D) honeycomb lattice structures with broken space inversion symmetry, such as graphene epitaxially grown on a SiC substrate and boronitrene (a single sheet of hexagonal boron nitride (h-BN)). The approach developed is based on a simple two-band π-electron tight-binding model combined with the original Genkin-Mednis formalism of the second-order nonlinear optical response theory, detailed in our recent paper (2010 Phys. Rev. B 82 235426). Within the framework of the approach, we derive an explicit expression for the SHG susceptibility χ2(SHG(ω), which involves two distinct contributions originating from a mixture of interband and intraband motion of π electrons. Both the contributions, and, hence, the χ2(SHG(ω) on the whole, are found to tend to zero when the π-electron energy bands involved are treated at the simplest level of approximation, neglecting the effect of their trigonal warping around the corners of the Brillouin zone of the 2D hexagonal lattice. Through numerical calculations, it is shown that this effect, though rather small, leads to a fairly large magnitude of the SHG susceptibility, reaching the order of 10(-4) esu for the graphene/SiC overlayer system and 10(-7) esu for monolayer h-BN, when the pump photon energy ħω approaches half the bandgap energy Eg of those structures. These theoretical findings suggest that SHG can be used as a sensitive optical probe of the electronic structure of the examined 2D hexagonal crystals and simultaneously demonstrate that those crystals may be an appropriate material for practical uses in future optoelectronic nano-devices.

Theoretical calculations of nonlinear refraction and absorption coefficients of doped graphene

In this study, we present the first theoretical predictions concerning the nonlinear refractive and absorptive properties of the doped graphene in which the Fermi energy of charge carriers (noninteracting massless Dirac fermions) is controlled by an external gate voltage. We base our study on the original perturbation theory technique developed by Genkin and Mednis (1968 Sov. Phys. JETP 27 609) for calculating the nonlinear-optical (NLO) response coefficients of bulk crystalline semiconductors with partially filled bands. Using a simple tight-binding model for the π-electron energy bands of graphene, we obtain analytic expressions for the nonlinear refractive index and the nonlinear absorption coefficient of the doped graphene at photon energies above twice the value of the Fermi energy (). We show that in this spectral region, both the nonlinear refraction ant the nonlinear absorption are determined predominantly by the combined processes which simultaneously involve intraband and interband motion of π-electrons. Our calculations indicate that extremely large negative values of n2 (of the order of cm2 W−1) can be achieved in the graphene at a relatively low doping level (of about 1012 cm−2) provided that the excitation frequency slightly exceeds the threshold frequency corresponding to the onset of interband transitions. With a further increase of the radiation frequency, the becomes positive and begins to decrease in its absolute magnitude. The peculiar frequency dispersion of n2 and a negative sign of the (absorption bleaching), as predicted by our theory, suggest that the doped graphene is a prospective NLO material to be used in practical optical switching applications.

Spectral characteristics of the sum-frequency generation from atomically thin hexagonal crystals lacking center-of-inversion symmetry

We calculate the second-order nonlinear optical susceptibility for the sum-frequency generation (SFG) from two-dimensional (2D) hexagonal crystals with broken space inversion symmetry, such as graphene, grown epitaxially on a SiC substrate, and boronitrene (a single atomic layer of hexagonal boron nitride (h-BN)). We show that in the presence of two normally incident pump beams at frequencies and , a remarkably large output signal at frequency is generated in those materials in the two-photon resonant regime where the frequencies and are matched to provide a resonance for the radiated photon energy with the bandgap energy Eg of the materials. In addition, it is found that the absolute magnitude of the is resonantly enhanced when the photon energy of one of the input beams is tuned to the fundamental absorption edge. These resonant behaviors lead to very large values of , reaching the order of 10−4 esu for the graphene/SiC overlayer system and 10−6 esu for monolayer h-BN. Furthermore, even outside the resonances, the magnitude of is fairly large ( esu for the overlying graphene and 10−8 esu for boronitrene), which opens up new opportunities for practical exploitation of the SFG effect in the examined 2D crystals.

Linear Optical Susceptibility of Single‐Walled Boron Nitride Nanotubes

Abstract A simple model based on an effective‐mass approximation is developed to describe the dispersion behavior of the linear optical susceptibility χ1 of an array of aligned, identical single‐walled boron nitride nanotubes (BNNTs) in the spectral range where interband π‐electron transitions dominate. An analytic closed‐form expression for χ(1) valid in the low‐frequency part of the spectrum is obtained in terms of the band gap Δ g of BNNTs and the π‐electron transfer integral V ppπ. To the best of our knowledge, the present analytic calculation is the first for such nanotubes.