Self-accelerating self-trapped optical beams

We present self-accelerating self-trapped beams in nonlinear optical media, exhibiting self-focusing and self-defocusing Kerr and saturable nonlinearities, as well as a quadratic response. In Kerr and saturable media such beams are stable under self-defocusing and weak self-focusing, whereas for strong self-focusing the beams off-shoot solitons while their main lobe continues to accelerate. Self-accelerating self-trapped wave packets are universal, and can also be found in matter waves, plasma, etc.     

Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.     

Radiation damage to alkyl chain monolayers on semiconductor substrates investigated by electron spectroscopy

Monolayers of alkyl chains, attached through direct Si-C bonds to Si(111), via phosphonates to GaAs(100) surfaces, or deposited as alkyl-silane monolayers on SiO2, are investigated by ultraviolet and inverse photoemission spectroscopy and X-ray absorption spectroscopy. Exposure to ultraviolet radiation from a He discharge lamp, or to a beam of energetic electrons, leads to significant damage, presumably associated with radiation- or electron-induced H-abstraction leading to carbon-carbon double-bond formation in the alkyl monolayer. The damage results in an overall distortion of the valence spectrum, in the appearance of (occupied) states above the highest occupied molecular orbital of the alkyl molecule, and in a characteristic (unoccupied state) pi resonance at the edge of the carbon absorption peak. These distortions present a serious challenge for the interpretation of the electronic structure of the monolayer system. We show that extrapolation to zero damage at short exposure times eliminates extrinsic features and allows a meaningful extraction of the density of state of the pristine monolayer from spectroscopy measurements.     

Single polymer chains as specific transducers of molecular recognition in scanning probe microscopy

A new approach for the specific detection and mapping of single molecule recognition is presented, based on the nonlinear elastic behavior of a single polymer chain. The process of molecular recognition between a ligand and a receptor is inherently accompanied by a decrease in the translational and rotational degrees of freedom of the two molecules. We show that a polymeric tether linked to the ligand can effectively transduce the configurational constraint imposed by molecular recognition into a measurable force, which is dominated by the entropic elasticity of the polymer. This force is specifically characterized by a strong nonlinearity when the extension of the polymer approaches its contour length. Thus, a polymer chain tethering the ligand to an oscillating cantilevered tip gives rise to a highly anharmonic motion upon ligand-receptor binding. Higher-harmonics atomic force microscopy allows us to detect this phenomenon in real time as a specific signature for the probing and mapping of single-molecule recognition.     

Velocities, Stresses and Vector Bundle Valued Chains

A mathematical framework for the fundamental objects of continuum mechanics is presented. In the geometric setting of general differentiable manifolds, velocity fields over bodies, modeled as sections of a vector bundle W, are generalized using notions of homological integration theory such as flat chains and cochains. The class of bodies includes fractal sets whose irregular boundaries may have infinite measures. Stresses, initially modeled as smooth differential forms valued in the dual of the jet bundle of W, are generalized to cochains represented by L ^??-sections whose weak divergences are also L ^??. The divergence of a stress field, defined in an earlier work, is generalized to apply to stress cochains. The co-divergence of a velocity field is a weak form of the jet extension mapping and it is the counterpart of the boundary operator for real valued flat chains.     

Cross-phase-modulation nonlinearities and holographic solitons in periodically poled photovoltaic photorefractives

We show that the nonlinearity in periodically poled photovoltaic photorefractives can be solely of the cross-phase-modulation type. The effects of self-phase modulation and asymmetric energy exchange, which exist in homogeneously poled photovoltaic photorefractives, can be considerably suppressed by the periodic poling. Finally, we demonstrate numerically that periodically poled photovoltaic photorefractives can support Thirring-type ("holographic") solitons, which to our knowledge have never been observed.     

Experimental observation of self-accelerating beams in quadratic nonlinear media

We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadratic media, which are also the first nonlinear self-accelerating beams in any symmetric nonlinearity. Notably, we show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another, but the coupled harmonics exhibit joint acceleration within the nonlinear medium. Finally, we demonstrate the impact of self-healing effects on the jointly accelerating first and second harmonics.     

A Correction of an Inconsistency in my Paper “Cauchy's Theorem on Manifolds”

The Cauchy postulates are required for the formulation and proof of Cauchy's theorem for the existence of stress. The generalized postulates and theorem in the geometric setting of differentiable manifolds was considered in a previous paper. This note presents an inconsistency in one of the proposed postulates, the boundedness postulate, and corrects it by specifying a weaker requirement.