Experimental progress in the nonlinear behavior of semiconductors

During the past five years spontaneous oscillations and chaotic behavior have been observed in the electronic transport of many semiconductors. Whereas the temperature range of some experiments extends up to room temperature, the majority of the measurements have been performed at liquid helium temperatures. We summarize these experimental developments and discuss their impact on the field of nonlinear dynamics which is rapidly progressing at present.     

Optical Performance and Nonlinear Scattering of Soluble Polystyrene Grafted Multi-Walled Carbon Nanotubes

Three soluble polystyrene grafted multi-walled carbon nanotube （MWNT） samples are synthesized, and their optical performance and nonlinear scattering properties are investigated by z-scan method using nanosecond pulses of 532 nm from a frequency-doubled Q-switched Nd： YLF laser. Analysis of the experimental results shows that other than nonlinear scattering, nonlinear absorption plays a major role in optical limiting performance of these stable and well-dispersed suspensions. These new synthesized materials which can be better dispersed in common organic solvents than MWNT itself can be considered as potential sources for further optical applications.     

Optical Limiting Properties of Two Soluble Polymer/Multi-Walled Carbon Nanotube Composites

Two soluble polymer grafted multi-walled carbon nanotubes （MWNTs）, including poly（N-vinylcarbazole）-MWNTs and poly（methyl methacrylate）-MWNTs, are synthesized. Their nonlinear optical properties and opticaJ limiting （OL） performances are investigated by z-scan method with 527nm nanosecond laser pulses. These grafted MWNTs dissolved in chloroform show much better optical limiting performance than those of MWNTs and C60 in toluene solution. Nonlinear absorption and nonlinear scattering mechanism are taken into consideration for explaining the observed results. The comparison of the experimental results shows that nonlinear absorption is the dominant mechanism for OL performance of these new samples.     

Nonlinear thickness dependence of two-photon absorptance in Al2O3 films

Linear and nonlinear absorptance in Al₂O₃ films of different optical thicknesses are investigated using an ArF laser calorimeter. While the linear absorptance at 193 nm shows the expected linear increase, nonlinear absorptance increases quadratically with increasing film thickness. Thus, it cannot be described by a constant nonlinear absorption coefficient β. The experimental findings are explained by a simple phenomenological approach using excited states with a finite interaction length longer than the actual film thickness. a new material constant Γ is introduced, which describes the nonlinear absorptance behavior correctly. Received: 19 May 2000 / Accepted: 22 May 2000 / Published online: 13 July 2000     

Hysteresis in response of nonlinear bistable interface to continuously varying acoustic loading

In many experimental situations it is an equation of the forced relaxator and not of the forced oscillator that describes a variation in the acoustic field of the interface width (i.e. of a characteristic distance between the surfaces composing the interface). The developed theory predicts that some types of the nonlinear relaxators (depending on the structure of the nonlinear interaction force between the surfaces) exhibit hysteresis in their response to continuous acoustic loading of first increasing and then decreasing amplitude. Nonlinear (unharmonic) variation of the interface width starts at threshold amplitude of the incident sinusoidal acoustic wave, which is higher than threshold amplitude for returning to sinusoidal motion. This dynamic hysteresis (and accompanying it bistability) are possible, in particular, if the dependence of the effective interaction force on the interface width admits two quasi-equilibrium positions of the interface (bistable interface) or if the force itself is hysteretic (hysteretic interface). These theoretical predictions are relevant to some recent experimental observations on the interaction of powerful ultrasonic fields with cracks.     

A Simple Model for Nonlinear Confocal Ultrasonic Beams

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov （KZK） equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.     

From Autonomous Coherence Resonance to Periodically Driven Stochastic Resonance

In periodically driven nonlinear stochastic systems, noise may play a role of enhancing the output periodic signal （termed as stochastic resonance or SR）. While in autonomous excitable systems, noise may play a role of increasing coherent motion （termed as coherence resonance or CR）. So far the topics of SR and CR have been investigated separately as two major fields of studying the active roles of noise in nonlinear systems. We find that these two topics are closely related to each other. Specifically, SR occurs in such periodically driven systems that the corresponding autonomous systems show CR. The SR with sensitive frequency dependence can be observed when the corresponding autonomous system shows CR with finite characteristic frequency. Moreover, ‘resonant noise＇ and ‘resonant frequency＇ of SR coincide with those of CR.     

Observation of indirect parallel pumping of magneto-elastic modes in layered YIG/GGG structures

In this work we report new experimental results on nonlinear excitation of magnetoelastic (ME) modes in layered YIG/GGG waveguide structures at GHz frequencies, obtained by a guided-wave light scattering technique. It is shown that the fundamental spin-dipole wave (SDW) mode induces a secondary microwave field at double frequency that can efficiently excite shear elastic modes of the structure. The distinctive feature of a mechanism for ME coupling proposed is that it is free from the selection rules and provides continuous excitation of elastic modes within a wide frequency range by means of the standard microstripe line excitation system.     

Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate

The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching fiat plate is solved by using the Adomian decomposition method （ADM）. The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.