Near-integrable dynamics of the Fermi-Pasta-Ulam-Tsingou problem.

It is well known that the classic Fermi-Pasta-Ulam-Tsingou (FPUT) study of a chain of nonlinear oscillators is closely related to a number of completely integrable systems, including the Toda lattice. Here, we present a method that captures the departure of nonintegrable FPUT dynamics from those of a nearby integrable Toda lattice. Using initial long-wave data, we find that the former depart rather sharply from the latter near the predicted shock time of an asymptotic partial differential equation approximation, at which point energy cascades into higher lattice modes.

Subcycle spatiotemporal compression of infrared pulses in semiconductors.

Using a full-field propagator model, we report on the emergence of highly localized, subcycle solitonic structures for few-cycle long-wave-infrared (LWIR) pulses propagating through optical semiconductor materials with efficient quadratic nonlinearities and broad anomalous transmission windows. We briefly discuss the theoretical basis for the observed spatiotemporal carrier-wave dynamics and compare it to simulations of a weakly perturbed pulse's propagation through two currently grown, low-loss IR semiconductor crystals.

Optical Carrier-Wave Subcycle Structures Associated with Supercritical Collapse of Long-Wavelength Intense Pulses Propagating in Weakly Anomalously Dispersive Media.

We predict the emergence of attosecond-duration structures on an optical carrier wave when intense, long-wavelength pulses propagate through bulk media with weak anomalous dispersion. Under certain conditions, these structures can undergo a new type of carrier-resolved supercritical collapse, forming infinite spatiotemporal gradients in the field. The mathematical conditions for the onset of this singularity are briefly overviewed, and we demonstrate with a full 3D+time (3+1) simulation that such structures persist under realistic conditions for a 10 micron laser pulse propagating in air.