V. A. Margulis

Third-order optical nonlinearity of semiconductor carbon nanotubes: third harmonic generation ☆

Abstract Within the framework of a two-band model of the electronic structure of semiconductor carbon nanotubes (CNs) we have studied the third-order nonlinear optical susceptibility χ THG (3) ( ω ) responsible for the effect of the third harmonic generation. We have obtained a theoretical expression for χ THG (3) ( ω ) which takes into account the contributions to the susceptibility due to purely interband transitions of π-electrons and combined intraband–interband motion of the latter. A detailed analysis of the dispersion dependence of χ THG (3) ( ω ) has been carried out in a wide range of frequencies involving those which are much smaller than the bandgap energy and those equal to it by the order of magnitude. The nonlinear-optical spectra of χ THG (3) ( ω ) are calculated numerically for nonchiral single-shell nanotubes with different radii. The results show that at the expense of the increase of the radius of the nanotubes one can achieve a giant enhancement of the power of radiation generated at the third harmonic frequency in the three-photon resonance regime. It is also shown that the magnitude of the resonant optical susceptibility of CNs can exceed the resonance values of χ (3) THG for the fullerenes C 60 and C 70 by several orders. The results obtained allow us to give a positive prognostic estimate of CNs as a new class of materials for nonlinear optics.

QUADRATIC ELECTRO-OPTIC EFFECTS IN SEMICONDUCTOR CARBON NANOTUBES

Abstract We investigate the third-order nonlinear optical susceptibility χ (3) ( ω ) responsible for the quadratic electro-optic effects (electro-absorption and the DC Kerr effect) in single-shell semiconductor carbon nanotubes. Distinct new features in the dispersion behaviour of χ (3) ( ω ) (e.g. change of sign) are found, which are of fundamental importance to the electro-optic device potential of nanotubes.

Hybrid–impurity resonances in anisotropic quantum dots

The absorption of electromagnetic radiation of an anisotropic quantum dot is theoretically investigated taking into account the processes associated with simultaneous scattering from ionized impurities. It is shown that the scattering of electrons by impurities leads to the resonance absorption even if we have only one impurity in the quantum dot. Explicit formula is derived for the absorption coefficient. The positions of the resonances peaks are found. The effects of external magnetic field on the resonance absorption are studied.

Effect of surface curvature on magnetic moment and persistent currents in two-dimensional quantum rings and dots

The effect of the surface curvature on the magnetic moment and persistent currents in two-dimensional quantum rings and dots is investigated. It is shown that the surface curvature decreases the spacing between neighboring maxima of de Haas\char21{}van Alphen type oscillations of the magnetic moment of a ring and decreases the amplitude and period of Aharonov-Bohm type oscillations. In the case of a quantum dot, the surface curvature reduces the level degeneracy at zero magnetic fields. This leads to a suppression of the magnetic moment at low magnetic fields. The relation between the persistent current and the magnetic moment is studied. We show that the surface curvature decreases the amplitude and the period of persistent current oscillations.

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.

Quantum Hall effect on the Lobachevsky plane

The Hall conductivity of an electron gas on the surface of constant negative curvature (the Lobachevsky plane) in the presence of an orthogonal magnetic field is investigated. It is shown that the surface curvature decreases the quantum Hall plateau widths and shifts the steps in the Hall conductivity to higher magnetic fields (or to lower values of the chemical potential). An increase of temperature results in smearing of the steps.

Nature of near-infrared absorption in single-wall carbon nanotubes

Abstract A simple one-electron theory is proposed for linear optical properties of a bundle of diameter-distributed and aligned single-wall carbon nanotubes (SWCNs), which is in excellent agreement with both the position and spectral shape of the fundamental absorption edge recently observed in SWCN thin films.

Dielectric function of single-wall carbon nanotubes

The optical dielectric function for a bundle of aligned single-wall carbon nanotubes (SWCNs) with randomly distributed diameters has been calculated in the one-electron approximation. It is shown that the superposition of the spectral lines corresponding to the interband transitions in SWCNs of different sizes results in a strong broadening, intensity decrease, and red (respectively, blue) shift of the resonant peak in the spectrum of the real (respectively, imaginary) part of the response function. The implication of the findings for understanding the optical properties of realistic SWCN samples is discussed.

Optical third-harmonic generation from an array of aligned carbon nanotubes with randomly distributed diameters

Abstract The optical susceptibility for third-harmonic generation (THG) from an array of aligned carbon nanotubes (CNs) is theoretically studied, taking into account the diameter distribution of CNs. The average THG susceptibility is calculated for three different types of distribution of CNs: Gaussian, rectangular and triangular ones. The results clearly demonstrate a strong broadening, intensity decrease, and red shift of the main three-photon resonant peak in the THG spectrum. It is shown that, in spite of the overall suppression of the average THG intensity, the amplitude of the peak strongly enhances with an increase of the average radius ( R av ) of CNs in a sample achieving record values up to ∼10 −4 e.s.u. at R av =5.2 nm for a typically occurring normal distribution of CNs. The enhancement of the height of the peak is accompanied by the shift of the top of the peak towards lower frequencies. Both the resonance frequency and magnitude of enhancement are found to be dependent on the type of distribution of CNs. Our results thus indicate the possibility of using THG measurement as an experimental tool to extract information about the prevailing type of CN distribution in a sample.