Nonlinear Wavepacket Dynamics in Proximity to a Stationary Inflection Point

A stationary inflection point (SIP) in the Bloch dispersion relation of a periodic waveguide is an exceptional point degeneracy where three Bloch eigenmodes coalesce forming the so-called frozen mode with a divergent amplitude and vanishing group velocity of its propagating component. We have developed a theoretical framework to study the time evolution of wavepackets centered at an SIP. Analysis of the evolution of statistical moments distribution of linear pulses shows a strong deviation from the conventional ballistic wavepacket dynamics in dispersive media. The presence of nonlinear interactions dramatically changes the situation, resulting in a mostly ballistic propagation of nonlinear wavepackets with the speed and even the direction of propagation essentially dependent on the wavepacket amplitude. Such a behavior is unique to nonlinear wavepackets centered at an SIP.Comment: 9 pages, 5 figure

Adiabatic monoparametric autonomous motors enabled by self-induced nonconservative forces

Archetypal motors produce work when two slowly varying degrees of freedom (DOF) move around a closed loop of finite area in the parameter space. Here, instead, we propose a simple autonomous {\it monoparametric} optomechanical engine that utilizes nonlinearities to turn a constant energy current into a nonconservative mechanical force. The latter self-sustains the periodic motion of a mechanical DOF whose frequency is orders of magnitude smaller than the photonic DOF. We have identified conditions under which the maximum extracted mechanical power is invariant and show a new type of self-induced robustness of the power production against imperfections and driving noise.Comment: Main text: 8 pages, 4 figures. Includes supplement: 8 pages, 5 figure

Optical Kinetic Theory of Nonlinear Multi-mode Photonic Networks

Recent experimental developments in multimode nonlinear photonic circuits (MMNPC), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a non-equilibrium transport theory for these systems, when they are in contact with thermal reservoirs, is still {\it terra incognita}. Here, by combining Landauer and kinematics formalisms we develop a one-parameter scaling theory that describes the transport in one-dimensional MMNPCs from a ballistic to a diffusive regime. We also derive a photonic version of the Wiedemann -Franz law that connects the thermal and power conductivities. Our work paves the way toward a fundamental understanding of the transport properties of MMNPC and may be useful for the design of all-optical cooling protocols.Comment: 6 pages, 3 figures && Supplementary Material (6 pages, no figures

Ballistic Energy Transport in Oligomers

ConspectusThe development of nanocomposite materials with desired heat management properties, including nanowires, layered semiconductor structures, and self-assembled monolayer (SAM) junctions, attracts broad interest. Such materials often involve polymeric/oligomeric components and can feature high or low thermal conductivity, depending on their design. For example, in SAM junctions made of alkane chains sandwiched between metal layers, the thermal conductivity can be very low, whereas the fibers of ordered polyethylene chains feature high thermal conductivity, exceeding that of many pure metals. The thermal conductivity of nanostructured materials is determined by the energy transport between and within each component of the material, which all need to be understood for optimizing the properties. For example, in the SAM junctions, the energy transport across the metal-chain interface as well as the transport through the chains both determine the overall heat conductivity, however, to separate these contributions is difficult. Recently developed relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy is capable of studying energy transport in individual molecules in the time domain. The transport in a molecule is initiated by exciting an IR-active group (a tag); the method records the influence of the excess energy on another mode in the molecule (a reporter). The energy transport time can be measured for different reporters, and the transport speed through the molecule is evaluated. Various molecules were interrogated by RA 2DIR: in molecules without repeating units (disordered), the transport mechanism was expected and found to be diffusive. The transport via an oligomer backbone can potentially be ballistic, as the chain offers delocalized vibrational states. Indeed, the transport regime via three tested types of oligomers, alkanes, polyethyleneglycols, and perfluoroalkanes was found to be ballistic, whereas the transport within the end groups was diffusive. Interestingly, the transport speeds via these chains were different. Moreover, the transport speed was found to be dependent on the vibrational mode initiating the transport. For the difference in the transport speeds to be explained, the chain bands involved in the wavepacket formation were analyzed, and specific optical bands of the chain were identified as the energy transporters. For example, the transport initiated in alkanes by the stretching mode of the azido end group (2100 cm^–1) occurs predominantly via the CH₂ twisting and wagging chain bands, but the transport initiated by the C=O stretching modes of the carboxylic acid or succinimide ester end groups occurs via C–C stretching and CH₂ rocking bands of the alkane chain. Direct formation of the wavepacket within the CH₂ twisting and wagging chain bands occurs when the transport is initiated by the NN stretching mode (1270 cm-1) of the azido end-group. The transport via optical chain bands in oligomers involves rather large vibrational quanta (700–1400 cm^–1), resulting in efficient energy delivery to substantial distances. Achieved quantitative description of various energy transport steps in oligomers, including the specific contributions of different chain bands, can result in a better understanding of the transport steps in nanocomposite materials, including SAM junctions, and lead towards designing systems for molecular electronics with a controllable energy transport speed

Energy Transport in PEG Oligomers: Contributions of Different Optical Bands

The transport of high-frequency vibrational energy in linear oligomer chains can be fast and efficient if specific conditions which permit ballistic transport are satisfied. These conditions include high delocalization and slow dephasing rate of chain states. We present new experimental results probing the energy transport in linear polyethylene glycol (PEG) oligomers of 0, 4, 8, and 12 PEG units terminated with IR-active end groups, N₃ and succinimide ester. The energy transport was initiated by vibrational excitation of one of the end groups and the energy arrival to another end group was detected using dual-frequency, two-dimensional infrared spectroscopy. In addition to end-group to end-group energy transport dynamics, the end-group-to-chain-state and chain-state-to-chain-state waiting-time dynamics are reported. The results show that despite rather short lifetimes for several IR-active chain states, the end-to-end energy transport occurs with a constant and rather high speed of 5.5 Å/ps, regardless of which end group initiated the transport (N₃ or asymmetric CO stretching mode of the succinimide), which contrasts previous reports for similarly terminated alkane chains where the transport was dependent on the way it was initiated. To understand the transport mechanism, the PEG chain dispersion relations were computed, indicating that while many chain bands can contribute to the transport, most of them have short lifetimes (≤1 ps) that cannot support a ballistic regime to distances exceeding that of PEG8. However, the states of a single rocking band, at about 800–850 cm^–1, feature longer lifetimes, permitting ballistic transport via this band for 50 Å at room temperature. Theoretical modeling, based on solving the quantum Liouville equation for a density matrix for a linear chain, was performed. The modeling indicates that under directed diffusion conditions, a switch between ballistic and diffusive transport regimes can occur without abrupt changes of the transport speed. The approaches developed in this study are applicable to other chain types, in particular, those involving heteroatoms in the backbone