Failure mechanisms of graphene under tension

Recent experiments established pure graphene as the strongest material known to mankind, further invigorating the question of how graphene fails. Using density functional theory, we reveal the mechanisms of mechanical failure of pure graphene under a generic state of tension. One failure mechanism is a novel soft-mode phonon instability of the $K_1$-mode, whereby the graphene sheet undergoes a phase transition and is driven towards isolated benzene rings resulting in a reduction of strength. The other is the usual elastic instability corresponding to a maximum in the stress-strain curve. Our results indicate that finite wave vector soft modes can be the key factor in limiting the strength of monolayer materials

Non-paraxial Split-step Finite-difference Method for Beam Propagation

A method based on symmetrized splitting of the propagation operator in the finite difference scheme for non-paraxial beam propagation is presented. The formulation allows the solution of the second order scalar wave equation without having to make the slowly varying envelope and one-way propagation approximations. The method is highly accurate and numerically efficient. Unlike most Padé approximant based methods, it is non-iterative in nature and requires less computation. The method can be used for bi-directional propagation as well

Comparison of vector finite-difference techniques for modal analysis

We compare a vector finite-difference method that correctly applies the boundary conditions at both horizontal and vertical dielectric interfaces (but not at corners or slanted interfaces) to algorithms that only approximately satisfy these boundary conditions. We find, rather unexpectedly, that for strongly guiding waveguides the boundary conditions imposed at the refractive- index discontinuities typically affect the calculated field distributions less than the procedure employed to assign the refractive index at a computational grid point. In fact, locally averaging the refractive index around each grid point transforms the precision of the most straightforward finite-difference models to that of far more sophisticated techniques. Further, H- and E-field formalisms exhibit identical accuracy

Reconstruction Of The Permittivity Profile Of A Stratified Dielectric Layer

A numerical procedure is given for the reconstruction of the permittivity profile of a dielectric slab on a perfect conductor. Profiles not supporting guided modes are reconstructed from the complex reflection amplitude for TE-polarized, monochromatic plane waves incident from different directions using the Marchenko theory. The contribution of guided modes is incorporated in the reconstruction procedure through the Gelfand-Levitan equations. An advantage of our approach is that a unique solution for the permittivity profile is obtained without the use of complicated regularization techniques. Some illustrative numerical examples are presented

An analysis of the linewidth and spectral behaviour of DBR lasers

Using recently developed techniques for calculating the linewidths of lasers with arbitrary external feedback, it is shown that distributed Bragg reflector lasers with long grating lengths can exhibit sharply reduced linewidths. Several effects of the dependence of the refractive index on carrier density, such as the large sensitivity of the linewidth and threshold current to the roundtrip phase change in the active region, are discussed. Such linewidth and threshold variations are especially pronounced for long grating lengths