Session C12: Intrinsic Localized Modes: Recent Developments and Future Perspectives

From Discrete Breathers to Many Body Localization and Flatbands

Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves.   

Recent advances in the physics of localized states

We will review several examples of the existence and generation of localized states in optics and metamaterials including weakly coupled optical waveguides and arrays of nonlinear ``meta-atoms'' in metamaterials. We will also mention some recent studies on an interplay of nonlinearity-induced energy localization and edge states in discrete systems appeared in the systems with nontrivial topology   

Shepherding intrinsic localized modes in micro-mechanical arrays

The energy profiles of intrinsic localized modes (ILMs) in periodic physical lattices with nonlinear forces resemble those of localized vibrational modes at defects in a harmonic lattice but, like solitons, they can propagate; however, in contrast with solitons they loose energy as they move through the lattice - the more localized the excitation the faster the energy loss. One of our experimental studies with micro-mechanical arrays involves steady state locking of ILMs, and their interactions with impurities. By measuring the linear response spectra of a driven array containing an ILM both the dynamics of bifurcation transitions and the hopping of vibrational energy have been connected to the transition properties of soft modes. Recently the search for a completely mobile ILM has focused attention on minimizing the resonance interaction that occurs between the localized excitation and small amplitude plane wave modes. Via simulations we demonstrate that when more than one type of nonlinear force is present their Fourier components can often be designed to cancel against each other in the k-space region of the plane wave dispersion curve, removing the resonance. The end result is super-transmission for an ILM in a discrete physical lattice. Such an engineered, intrinsic, low loss channel may prove to be a useful property for other physical systems treated within a tight binding approximation. In collaboration with M. Sato.   

Localized Modes in Granular Chains

Granular crystals are tightly-packed lattices (or more disordered arrangements) of solid particles that deform elastically when they contact each other. In the presence of precompression, they can exhibit breather solutions in the form of intrinsic localized modes and defect modes. I'll give an introduction to granular crystals and will then examine breathers in one-dimensional granular crystals (i.e., granular chains) in both models and experiments. I will give examples using both diatomic configurations and homogeneous configurations with defect particles. I will also consider disordered granular chains and discuss recent work on nonlinear Anderson localization and related phenomena in such systems.   

Intrinsic Localized Modes in Optical Photonic Lattices and Arrays

Discretizing light behavior requires optical elements that can confine optical energy at distinct sites. One possible scenario in implementing such arrangements is to store energy within low loss high Q-microcavities and then allow photon exchange between such components in time. This scheme requires high-contrast dielectric elements that became available with the advent of photonic crystal technologies. Another possible avenue where such light discretization can be directly observed and studied is that based on evanescently coupled waveguide arrays. As indicated in several studies, discrete systems open up whole new directions in terms of modifying light transport properties. One such example is that of discrete solitons. By nature, discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one- and two-dimensional nonlinear waveguide arrays. In recent years such photonic lattices have been implemented or induced in a variety of material systems, including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness can lead to new families of optical solitons that have no counterpart whatsoever in continuous systems. Interestingly, these results paved the way for observations in other physical systems obeying similar evolution equations like Bose-Einstein condensates. New developments in laser writing ultrashort femtosecond laser pulses, now allow the realization of all-optical switching networks in fully 3D environments using nonlinear discrete optics. Using this approach all-optical routing can be achieved using blocking operations. The spatio-temporal evolution of optical pulses in both normally and anomalously dispersive arrays can lead to novel schemes for mode-locking and pulse compression. A strong signature of discrete X-wave formation was also demonstrated in such structures. In the last few years, Anderson localization was unequivocally observed in array systems where the transition from ballistic transport to diffusive, and the cross-over to Anderson localization was studied as a function of disorder and nonlinearity. In recent studies synthetic lattices exhibiting parity-time (PT) symmetry were also considered. The interplay of gain and loss in this latter family of structures leads to counterintuitive characteristics and behavior such as non-reciprocal propagation and power oscillations. The realization of discrete array systems at su-bwavelenth scales is another important direction that is nowadays intensively pursued. References 1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817- 823 (2003). 2. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev and Y. Silberberg, Phys. Reports 463, 1-126 (2008). 3. M Wimmer, A Regensburger, MA Miri, C. Bersch, D.N Christodoulides, and U. Peschel, "Observation of optical solitons in PT-symmetric lattices" Nature Communications 6, 7782 (2015).