# Poster Session and Reception

Tuesday, March 14, 2017 - 4:05pm - 6:00pm

Lind 400

**Modeling of Individual and Arrayed Nanoantennas in the Quantum Plasmonic Regime**

Pai-Yen Chen (Wayne State University (Detroit, MI, US))

We put forward here design and semiclassical modeling of nonlinear and reconfigurable optical metasurfaces formed by arrayed nanoantennas with nano/subnano-scale feed-gaps, where the photon-assisted tunneling results in a set of linear/nonlinear quantum conductivities. We show that optical nonlinearities sourced from higher-order quantum conductivities may be boosted by the plasmonic resonance and the large local field enhancement in the load region of nanoantenna. We discuss three exciting applications of the proposed nanoantenna-based devices: efficient frequency multiplication at the nanoscale, optical rectification (subbandgap photodetection and energy harvesting), and dynamic resistive switching.**Field Patterns in Space-time Microstructures**

Ornella Mattei (The University of Utah)

The study of space-time microstructures was initiated in the Fifties, with particular attention to wave propagation. Focusing only on space-time microstructures in one spatial dimension plus time, one has that every time a wave hits a space-time boundary it splits into a transmitted wave and a reflected wave, and if the space-time geometry is not suitably chosen this, in general, evolves into a complicated cascade of disturbances which is very difficult to keep track of, thus leading to complex numerical simulations. With the aim of overcoming such a disadvantage we introduce the brand-new theory of field patterns: the space-time microstructure is chosen in such a way that its geometry is, in a sense, related to the slope of the characteristic lines so that the disturbance does not evolve into a cascade of disturbances but rather concentrates on a pattern of characteristic lines: this is the field pattern. An example of such a space-time microstructure is a two-phase checkerboard geometry in which the wave speeds of the components are identical.

As a consequence of the special geometry of the space-time microstructures chosen, the discrete dynamic network on which the field pattern lives turns out to be periodic both in space and time, thus allowing one to solve the problem on the unit cell of such a discrete network, rather than on the whole space-time domain. Specifically, the global solution is recovered by introducing a suitable transfer matrix that relates the solution at a certain time to the solution after one time period. In general, the eigenvalues of the transfer matrix have either modulus one (in this case the corresponding mode is a propagating mode), or modulus greater (less) than one, thus corresponding to modes that blow up (decrease) exponentially with time. Some special space-time microstructures have only propagating modes.**Nonlinear Graphene Metasurfaces with Enhanced Electromagnetic Functionalities**

Christos Argyropoulos (University of Nebraska)

The conductivity of graphene at THz and infrared (IR) frequencies is dominated by intraband transitions and can be characterized by the Drude model. Strong surface plasmons can be excited at the surface of graphene in this frequency regime. Even stronger resonance conditions in the transmission or reflection spectrum can be obtained when graphene is patterned to periodic rectangular patches or strips forming new planar graphene metasurfaces. It is interesting that the third-order nonlinear conductivity of graphene is much larger compared to the nonlinear properties of thin metallic and dielectric layers measured at the same frequency range. We will employ the enhanced nonlinear properties of graphene metasurfaces to boost several relative weak THz and IR optical nonlinear processes, such as third-harmonic generation and four-wave mixing. In addition, we will use nonlinear graphene metasurfaces to demonstrate tunable negative refraction and coherent perfect absorption.**Consistency of Dirichlet Partitions**

Todd Reeb (The University of Utah)

A Dirichlet k-partition of a domain U is a collection of k pairwise disjoint open subsets such that the sum of their first Laplace-Dirichlet eigenvalues is minimal. A discrete version of Dirichlet partitions has been posed on graphs and used in data analysis, while the continuum problem has been used to model mixtures of distinct species of Bose-Einstein condensates. We extend results of N. Garcia Trillos and D. Slepcev to show via Gamma-convergence that there exist solutions of the continuum problem arising as limits to solutions of a sequence of discrete problems. Our results imply the statistical consistency statement that Dirichlet partitions of geometric graphs converge to partitions of the sampled space in the Hausdorff sense. This is joint work with Braxton Osting.**High-Order Finite-Difference Time-Domain Simulation of Electromagnetic Waves at Complex Interfaces Between Dispersive Media**

Michael Jenkinson (Rensselaer Polytechnic Institute)

We propose a new numerical scheme for the simulation of electromagnetic waves in linear dispersive media, materials where the permittivity depends on the frequency of the wave. We formulate Maxwell's equations as a second order wave equation with an additional time-history term which is associated with the macroscopic electronic response of the material to the external electric field. This formulation allows us to address material interfaces with complex curvilinear geometries, thereby avoiding the drawbacks of the well-known staggered Yee numerical discretization. We use the physical interface conditions and boundary conditions for Maxwell's equations to develop numerical compatibility conditions which preserve the accuracy and stability of the scheme at the interfaces and boundaries. High accuracy simulation of transient waves at dispersive material interfaces is of particular interest in the fields of plasmonic metamaterials and nano-photonics, with various applications in imaging and sensing.**Nonlinearity, PT symmetry, twist, and disorder in Discrete Nonlinear Schrödinger Equation**

Claudia Castro-Castro (Southern Methodist University)

The study of optical fiber arrays has drawn a great deal of attention in the field of nonlinear physics during the past few years since they provide spatially inhomogeneous structures for guiding light signals. We analyze the management and control of light transfer in nonlinear multi-core fibers. We utilize mathematical modeling and numerical simulations to specifically show how nonlinearity, coupling, geometric twist, and balanced gain/loss relate to existence and stability of nonlinear optical modes modeled by the Discrete Nonlinear Schrödinger Equation (DNLS). In addition, we explore the effects of the inherent variability on the fiber core diameter (disorder) by building a statistical understanding of the formation of low or high amplitude (localized/breather) states, and the long-time asymptotics of DNLS with low-amplitude initial conditions.**The Inverse Problem for Maxwell's Equations on a Bounded Lipschitz Domain with Lipschitz Parameters**

Monika Pichler (Northeastern University)

Let D be a bounded Lipschitz domain in R^3. We consider the time-harmonic Maxwell's equations in D with Lipschitz continuous parameters. It is well known that in this case, for every suitable tangential boundary datum, there exists a unique pair of vector functions E and H that solve Maxwell's equations in D and satisfy the boundary condition. The aim of this project is to show unique solvability of the inverse boundary value problem, which aims to recover the parameters of the equations in D, given their values on the boundary of the domain as well as all possible tangential boundary values of solutions to the equations.**Pentamode Gradient Index Lens for Underwater Sound**

Andrew Norris (Rutgers, The State University of New Jersey)

We describe an inhomogeneous acoustic metamaterial lens based on spatial variation of refractive index for broadband focusing of underwater sound. The index gradient follows a modified hyperbolic secant profile designed to reduce aberration and suppress side lobes. The gradient index (GRIN) lens is comprised of transversely isotropic hexagonal microstructures with tunable quasistatic bulk modulus and mass density. In addition, the unit cells are impedance- matched to water and have in-plane shear modulus negligible compared to the e ffective bulk modulus. The lens is essentially an inhomogeneous pentamode structure. The pentamode property is borne out by band diagrams showing the expected one-wave property with almost onstant wave speed mateched to that of water in the frequency range of interest. The GRIN lens is fabricated by cutting hexagonal centimeter scale hollow microstructures in aluminum plates, which are then stacked and sealed from the exterior water. Broadband focusing e ffects are observed within the homogenization regime of the lattice in both finite element simulations and underwater measurements (20-40 kHz). This design approach has potential applications in medical ultrasound imaging and underwater acoustic communications.**Dynamic Materials as Spatial-Temporal Entities: Physical Effects and Mathematical Specifics**

Konstantin Lurie (Worcester Polytechnic Institute)**Universal Spin-momentum Locking of Light**

Todd Van Mechelen (Purdue University)