Optical third harmonic generation in black phosphorus

We present a calculation of Third Harmonic Generation (THG) for two-band systems using the length gauge that avoids unphysical divergences otherwise present in the evaluation of the third order current density response. The calculation is applied to bulk and monolayer black Phosphorus (bP) using a non-orthogonal tight-binding model. Results show that the low energy response is dominated by mixed inter-intraband processes and estimates of the magnitude of THG susceptibility are comparable to recent experimental reports for bulk bP samples.Comment: 9 pages, 5 figure

Iterative approach to arbitrary nonlinear optical response functions of graphene

Two-dimensional materials constitute an exciting platform for nonlinear optics with large nonlinearities that are tunable by gating. Hence, gate-tunable harmonic generation and intensity-dependent refraction have been observed in e.g. graphene and transition-metal dichalcogenides, whose electronic structures are accurately modelled by the (massive) Dirac equation. We exploit on the simplicity of this model and demonstrate here that arbitrary nonlinear response functions follow from a simple iterative approach. The power of this approach is illustrated by analytical expressions for harmonic generation and intensity-dependent refraction, both computed up to ninth order in the pump field. Moreover, the results allow for arbitrary band gaps and gating potentials. As illustrative applications, we consider (i) gate-dependence of third- and fifth-harmonic generation in gapped and gapless graphene, (ii) intensity-dependent refractive index of graphene up to ninth order, and (iii) intensity-dependence of high-harmonic generation.Comment: 6 pages, 5 figures. Supplemental material: 6 pages, 2 figure

Linear and nonlinear optical response of crystals using length and velocity gauges: Effect of basis truncation

We study the effects of a truncated band structure on the linear and nonlinear optical response of crystals using four methods. These are constructed by (i) choosing either length or velocity gauge for the perturbation and (ii) computing the current density either directly or via the time-derivative of the polarization density. In the infinite band limit, the results of all four methods are identical, but basis truncation breaks their equivalence. In particular, certain response functions vanish identically and unphysical low-frequency divergences are observed for few-band models in the velocity gauge. Using hexagonal boron nitride (hBN) monolayer as a case study, we analyze the problems associated with all methods and identify the optimal one. Our results show that the length gauge calculations provide the fastest convergence rates as well as the most accurate spectra for any basis size and, moreover, that low-frequency divergences are eliminated.Comment: 11 pages, 7 figure

VUCA and the future of the global mobile telco industry

The disruption global digitally based firms are imposing on the positions of established multinational telcos is not just in degree, but also in kind. As such, the telcos are entering a period of VUCA. Although digitally based competitors could suffer from liabilities of ‘outsidership’, employing the telco Telenor as a case, we argue that the physical presence of telcos in local markets will be insufficient to avoid a future as utilities or dumb-pipes. One significant issue as they confront VUCA is therefore whether telcos are able to develop and apply dynamic capabilities

The digital challenge for multinational mobile network operators. More marginalization or rejuvenation?

Multinational mobile network operators (MNOs) rapidly emerged in the early 1990s and for a decade and a half were the dominant actors in their industry. We analyze the development and competitiveness of a typical MNO, Telenor. With the introduction of 4G in 2010, we show that Telenor, like other MNOs largely failed to respond to the opportunity that connectivity provided to develop digital services. Instead, these were developed by technology platform companies such as Amazon, Google and Microsoft. Telenor became a marginalized supplier of standardized internet connectivity. We argue that the ‘decade of lost opportunity’ (2010-2020) for Telenor was a product of a lack of ‘recombinant firm-specific advantages’ (FSARs). With the launch of 5G, an emerging global digital infrastructure, this sidelining is set to intensify unless Telenor responds to this new opportunity by developing B2B digital services. We analyze the FSARs that are necessary for a successful transition of capturing the value that 5G provides and the degree to which they are present, or potentially present, in Telenor

The geochemistry of iodine and bromine in sediments of the Panama Basin

The areal and vertical distribution of iodine, bromine and organic carbon has been examined in a suite of sediment cores from the Panama Basin. Both halogens are approximately correlative with organic carbon in surface sediments. The concentrations of all three elements vary sympathetically but considerably with depth, especially in equatorial carbonate oozes where a distinct mid-depth (40-80 cm) concentration maximum is observed...

Oxygen minimum zone expansion in the eastern tropical North Pacific during deglaciation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95396/1/grl21420.pd

Nonlinear optical response of doped mono- and bilayer graphene: length gauge tight-binding model

We compute the nonlinear optical response of doped mono- and bilayer graphene using the full dispersion based on tight-binding models. The response is derived with the density matrix formalism using the length gauge and is valid for any periodic system, with arbitrary doping. By collecting terms that define effective nonlinear response tensors, we identify all nonlinear Drude-like terms (up to third-order) and show that all additional spurious divergences present in the induced current vanish. The nonlinear response of graphene comprises a large Drude-like divergence and three resonances that are tightly connected with transitions occurring in the vicinity of the Fermi level. The analytic solution derived using the Dirac approximation captures accurately the first- and third-order responses in graphene, even at very high doping levels. The quadratic response of gapped graphene is also strongly enhanced by doping, even for systems with small gaps such as commensurate structures of graphene on SiC. The nonlinear response of bilayer graphene is significantly richer, combining the resonances that stem from doping with its intrinsic strong low-energy resonances.Comment: Revised manuscript 18 pages, 6 figure

Observations of electron gyroharmonic waves and the structure of the Io torus

Narrow-banded emissions were observed by the Planetary Radio Astronomy experiment on the Voyager 1 spacecraft as it traversed the Io plasma torus. These waves occur between harmonics of the electron gyrofrequency and are the Jovian analogue of electrostatic emissions observed and theoretically studied for the terrestrial magnetosphere. The observed frequencies always include the component near the upper hybrid resonant frequency, (fuhr) but the distribution of the other observed emissions varies in a systematic way with position in the torus. A refined model of the electron density variation, based on identification of the fuhr line, is included. Spectra of the observed waves are analyzed in terms of the linear instability of an electron distribution function consisting of isotropic cold electrons and hot losscone electrons. The positioning of the observed auxiliary harmonics with respect to fuhr is shown to be an indicator of the cold to hot temperature ratio. It is concluded that this ratio increases systematically by an overall factor of perhaps 4 or 5 between the inner and outer portions of the torus