Oblique scattering from non-Hermitian optical waveguides

A judicious design of gain and loss leads to counterintuitive wave phenomena that are inaccessible by conservative systems. Notably, such designs can give rise to laser-absorber modes and anisotropic transmission resonances. Here, we analyze the emergence of these phenomena in an optical scatterer with sinusoid gain-loss modulation that is subjected to monochromatic oblique waves. We derive an analytical solution to the problem, with which we show how the scatterer parameters, and specifically the modulation phase and incident angle, constitute a real design space to access these phenomena.Comment: 23 pages, 10 figure

Homogenized estimates for soft fiber-composites and tissues with two families of fibers

The macroscopic response of hyperelastic fiber composites is characterized in terms of the behaviors of their constituting phases. To this end, we make use of a unique representation of the deformation gradient in terms of a set of transversely isotropic invariants. Respectively, these invariants correspond to extension along the fibers, transverse dilatation, out-of-plane shear along the fibers, in-plane shear in the transverse plane, and the coupling between the shear modes. With the aid of this representation, it is demonstrated that under a combination of out-of-plane shear and extension along the fibers there is a class of nonlinear materials for which the exact expression for the macroscopic behavior of a composite cylinder assemblage can be determined. The macroscopic response of the composite to shear in the transverse plane is approximated with the aid of an exact result for sequentially laminated composites. Assuming no coupling between the shear modes, these results allow to construct a closed-form homogenized model for the macroscopic response of a fiber composite with neo-Hookean phases. A new variational estimate allows to extend these results to more general classes of materials. The resulting explicit estimates for the macroscopic stresses developing in composites and connective tissues with one and two families of fibers are compared with corresponding finite element simulations of periodic composites and with experimental results. Estimates for the critical stretch ratios at which the composites loose stability at the macroscopic level are compared with the corresponding numerical results too. It is demonstrated that both the primary stress–strain curves and the critical stretch ratios are in fine agreement with the corresponding numerical results

Fundamental principles for generalized Willis metamaterials

Metamaterials that exhibit a constitutive coupling between their momentum and strain, show promise in wave manipulation for engineering purposes and are called Willis materials. They were discovered using an effective-medium theory, showing that their response is nonlocal in space and time. Recently, we generalized this theory to account for piezoelectricity, and demonstrated that the effective momentum can depend constitutively on the electric field, thereby enlarging the design space for metamaterials. Here, we develop the mathematical restrictions on the effective properties of such generalized Willis materials, owing to passivity, reciprocity, and causality. The establishment of these restrictions is of fundamental significance, as they test the validity of theoretical and experimental results-and applicational importance, since they provide elementary bounds for the maximal response that potential devices may achieve.This research was supported by the Israel Science Foundation, funded by the Israel Academy of Sciences and Humanities (Grant No. 2061/20), the United States - Israel Binational Science Foundation (Grant No. 2014358), and the Ministry of Science and Technology (Grant No. 880011)