Stability Boundaries in Laterally-Coupled Pairs of Semiconductor Lasers

The dynamic behaviour of coupled pairs of semiconductor lasers is studied using normal-mode theory, applied to one-dimensional (slab) and two-dimensional (circular cylindrical) real index confined structures. It is shown that regions of stable behaviour depend not only on pumping rate and laser separation, but also on the degree of guidance in the structures. Comparison of results between normal-mode and coupled-mode theories for these structures leads to the tentative conclusion that the accuracy of the latter is determined by the strength of self-overlap and cross-overlap of the symmetric and antisymmetric normal modes in the two lasers.

Characteristic Acoustic Impedance for Reliable Environmental Characterization

The characteristic acoustic impedance is a favorable observation variable for geoacoustic inversion (GI) owing to its higher sensitivity than that of pressure or particle velocity. However, no theoretical explanations have been provided for it. As an attempt to understand the underlying physical mechanism, interpretations based on the normal mode theory are conducted in this study. Moreover, synthetic Bayesian geoacoustic inversion with two recording scenarios of a vertical line array and single receiver are also performed, both of which proved that the impedance can provide improved estimation.

Nonlinear dynamics induced by linear wave interactions in multilayered flows

Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two-dimensional (2D), inviscid, multilayered fluid system. The strength of our formalism is that one does not have to specify the physics of the waves in advance. Wave interactions may lead to instabilities, which may or may not be of the familiar ‘normal-mode’ type. Contrary to intuition, the underlying dynamical system describing linear wave interactions is found to be nonlinear. Specifically, a saw-tooth jet profile with three interfaces possessing kinematic and geometric symmetry is explored. Fixed points of the system for different ranges of a Froude number like control parameter $\unicode[STIX]{x1D6FE}$ are derived, and their stability evaluated. Depending upon the initial condition and $\unicode[STIX]{x1D6FE}$, the dynamical system may reveal transient growth, weakly positive Lyapunov exponents, as well as different nonlinear phenomena such as the formation of periodic and pseudo-periodic orbits. All these occur for those ranges of $\unicode[STIX]{x1D6FE}$ where normal-mode theory predicts neutral stability. Such rich nonlinear phenomena are not observed in a 2D dynamical system resulting from the two-wave problem, which reveals only stable and unstable nodes.

Experiments on standing waves in a rectangular tank with a corrugated bed

An experimental investigation of resonant standing water waves in a rectangular tank with a corrugated bottom is reported. The study was stimulated by the theory of Howard & Yu (J. Fluid Mech., vol. 593, 2007, pp. 209–234) predicting the existence of normal modes that can be significantly affected by Bragg reflection/scattering. As a result, the amplitude of the standing waves (normal modes) varies exponentially along the entire length of the tank, or from the centre out in each direction, depending on the phase of the corrugations at the tank endwalls. Experiments were conducted in a 5 m tank fitted with a sinusoidal bottom with one adjustable endwall. Waves were excited by small-amplitude sinusoidal horizontal movement of the tank using an electrical motor drive system. Simultaneous time-series data of standing oscillations were recorded at well-separated positions along the tank to measure the growth in amplitude. Waveforms over a section of the tank were filmed through the transparent acrylic walls. Except for very shallow depths and near the tank endwalls, the experimental measurements of resonant frequencies, mean wavelengths, free-surface waveforms and amplitude growth are found in essential agreement with the Bragg resonant normal mode theory.