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We present the numerical simulation results of a model granular assembly formed by spherical particles with Hertzian interaction subjected to a simple shear in the athermal quasi-static limit. The stress-strain curve is shown to separate into smooth, elastic branches followed by a subsequent plastic event. Mode analysis shows that the lowest-frequency vibrational mode is more localized, and eigenvalues and participation ratios of low-frequency modes exhibit similar power-law behavior as the system approaches plastic instability, indicating that the nature of plastic events in the granular system is also a saddle node bifurcation. The analysis of projection and spatial structure shows that over 75% contributions to the non-affine displacement field at a plastic instability come from the lowest-frequency mode, and the lowest-frequency mode is strongly spatially correlated with local plastic rearrangements, inferring that the lowest-frequency mode could be used as a predictor for future plastic rearrangements in the disordered system jammed marginally.

The far-field superlens based on surface plasmon polaritons (SPP) has shown great application potential, but it is difficult and time-consuming to reconstruct the far-field image. We derive a near-field optical transfer function (NOTF) of a silver slab and analyse its validity so that accurate information of nano-scale object in the near-field can be computed rapidly. The NOTF is helpful not only for analysing the super-resolution imaging process in far-field, but also for providing a track to describe the transmission of optical information from near-field to far-field by using the optical transfer functions theory only.