This article reviews the basic theoretical aspects of graphene in order to contribute to making teaching easier and more understandable for those who still cannot understand it in an abstract way. This work presents the basic aspects of sp2 hybridization concepts from a quantum approach, which consists in obtaining the states for the sigma bonds from the orientation of the carbon atoms close to another carbon atom that is our reference point in the crystal lattice. Furthermore, we calculate the band structure of graphene by using the Tight-Binding Model, which can give us a good approximation to the energy levels as a function of the wave vector. This is for students interested in the topics of the solid-state and is approached in a simple and understandable way step by step to nally obtain the structure of bands of the primitive cell of one monolayer of graphene. Additionally, we calculate the High Symmetry points of the rst Brillouin zone and the analysis around the K points to obtain the well-known Dirac cones. The intention of this work is to show that this topic can be less abstract than it seems.
In recent years, nonlinear optics field is in constant growth, particularly on the characterization and study of optical properties of glass compounds. In this sense, the plasmonic effect caused by silver nanoparticles (SNP) on the nonlinear optical (NLO) properties of different materials was studied. Furthermore, we report the experimental absorption spectra, the emission spectra, Z-scan measurements in both closed and open apertures and scanning transmission electron microscopy (STEM) to show the morphology of the matrices and the nucleation of SNP. Moreover, some NLO parameters were calculated, such as the NL refraction index and NL coefficient absorption of lithium tetraborate (Li2B4O7) glass activated with rare earths (Dy3+ and Yb3+), as well as study of the effect of different concentrations of SNP. From the results obtained, it has been ascertained that the plasmon resonance caused by the presence of SNP enhances the NL refraction index value, as well as most of its linear optical properties in the matrix of Li2B4O7.
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