A. R. Zakharian

Tunable high-power high-brightness linearly polarized vertical-external-cavity surface-emitting lasers

We report on the development and the demonstration of tunable high-power high-brightness linearly polarized vertical-external-cavity surface-emitting lasers (VECSELs). A V-shaped cavity, in which the antireflection-coated VECSEL chip (active mirror) is located at the fold, and a birefringent filter are employed to achieve a large wavelength tuning range. Multiwatt cw linearly polarized TEM00 output with a 20nm tuning range and narrow linewidth is demonstrated at room temperature.

The von Neumann paradox in weak shock reflection

We present a numerical solution of the Euler equations of gas dynamics for a weak-shock Mach reflection in a half-space. In our numerical solutions, the incident, reflected, and Mach shocks meet at a triple point, and there is a supersonic patch behind the triple point, as proposed by Guderley. A theoretical analysis supports the existence of an expansion fan at the triple point, in addition to the three shocks. This solution is in complete agreement with the numerical solution of the unsteady transonic small-disturbance equations obtained by Hunter & Brio (2000), which provides an asymptotic description of a weak-shock Mach reflection. The supersonic patch is extremely small, and this work is the first time it has been resolved in a numerical solution of the Euler equations. The numerical solution uses six levels of grid refinement around the triple point. A delicate combination of numerical techniques is required to minimize both the effects of numerical diffusion and the generation of numerical oscillations at grid interfaces and shocks.

Generalization of the FDTD algorithm for simulations of hydrodynamic nonlinear Drude model

In this paper we present a numerical method for solving a three-dimensional cold-plasma system that describes electron gas dynamics driven by an external electromagnetic wave excitation. The nonlinear Drude dispersion model is derived from the cold-plasma fluid equations and is coupled to the Maxwells field equations. The Finite-Difference Time-Domain (FDTD) method is applied for solving the Maxwells equations in conjunction with the time-split semi-implicit numerical method for the nonlinear dispersion and a physics based treatment of the discontinuity of the electric field component normal to the dielectric-metal interface. The application of the proposed algorithm is illustrated by modeling light pulse propagation and second-harmonic generation (SHG) in metallic metamaterials (MMs), showing good agreement between computed and published experimental results.

Wave interactions in magnetohydrodynamics, and cosmic-ray-modified shocks

Multiple-scales perturbation methods are used to study wave interactions in magnetohydrodynamics (MHD), in one Cartesian space dimension, with application to cosmic-ray-modified shocks. In particular, the problem of the propagation and interaction of short wavelength MHD waves, in a large-scale background flow, modified by cosmic rays is studied. The wave interaction equations consist of seven coupled evolution equations for the backward and forward Alfven waves, the backward and forward fast and slow magnetoacoustic waves and the entropy wave. In the linear wave regime, the waves are coupled by wave mixing due to gradients in the background flow, cosmic-ray squeezing instability effects, and damping due to the diffusing cosmic rays. In the most general case, the evolution equations also contain nonlinear wave interaction terms due to Burgers self wave steepening for the magnetoacoustic modes, resonant three wave interactions, and mean wave field interaction terms. The form of the wave interaction equations in the ideal MHD case is also discussed. Numerical simulations of the fully nonlinear cosmic ray MHD model equations are compared with spectral code solutions of the linear wave interaction equations for the case of perpendicular, cosmic-ray-modified shocks. The solutions are used to illustrate how the different wave modes can be generated by wave mixing, and the modification of the cosmic ray squeezing instability due to wave interactions. It is shown that the Alfven waves are coupled to the magnetoacoustic and entropy waves due to linear wave mixing, only in background flows with non-zero field aligned electric current and/or vorticity (i.e. if B · ∇ × B ≠0 and/or B · ∇ × u ≠0, where B and u are the magnetic field induction and fluid velocity respectively).

Nonlinear and three-wave resonant interactions in magnetohydrodynamics

Hamiltonian and variational formulations of equations describing weakly nonlinear magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension are discussed. For wave propagation in uniform media, the wave interactions of interest consist of (a) three-wave resonant interactions in which highfrequency waves may evolve on long space and time scales if the wave phases satisfy the resonance conditions: (b) Burgers self-wave steepening for the magnetoacoustic waves, and (c) mean wave field effects, in which a particular wave interacts with the mean wave field of the other waves. The equations describe four types of resonant triads: slow-fast magnetoacoustic wave interaction, Alfven-entropy wave interaction, Alfven-magnetoacoustic wave interaction, and magnetoacoustic-entropy wave interaction. The formalism is restricted to coherent wave interactions. The equations are used to investigate the Alfven-wave decay instability in which a large-amplitude forward propagating Alfven wave decays owing to three-wave resonant interaction with a backward-propagating Alfven wave and a forward-propagating slow magnetoacoustic wave. Exact solutions of the equations for Alfven-entropy wave interactions are also discussed.

Enhanced light-matter interaction in semiconductor heterostructures embedded in one-dimensional photonic crystals

The optical properties of semiconductor quantum wells embedded in one-dimensional photonic crystal structures are analyzed by a self-consistent solution of Maxwells equations and a microscopic many-body theory of the material excitations. For a field mode spectrally below the photonic band edge it is shown that the optical absorption and gain are enhanced, exceeding by more than 1 order of magnitude the values of a homogeneous medium. For the photonic crystal structure inside a microcavity the gain increases superlinearly with the number of wells and for more than five wells exceeds the gain of a corresponding vertical-cavity surface-emitting laser.

Stability of a cosmic ray modified tangential discontinuity

We consider the dispersion relation for waves in a cosmic ray modified plasma for the case when the background flow consists of a cosmic ray pressure balance structure, in which pg+pc=const. where pc and pg denote the cosmic ray and thermal gas pressures respectively. The stability analysis shows that waves at an arbitrary point in the flow may be driven unstable if the cosmic ray pressure gradient is sufficiently large to overcome wave damping due to cosmic ray diffusion. Following S. Chalov’s work (1) we analyze the instability of a cosmic ray modified tangential discontinuity. Chalov considered the case where pc=const. throughout the structure, whereas in our analysis both pc and pg vary in the direction perpendicular to the surface separating two flow regions. Predictions of the linear theory are compared to numerical simulations. Applications to the stability of the heliopause are discussed.

Parametric instabilities and wave coupling in Alfvén simple waves

A wave coupling formalism for magnetohydrodynamic (MHD) waves in a non-uniform background flow is used to study parametric instabilities of the large-amplitude, circularly polarized, simple plane Alfven wave in one Cartesian space dimension. The large-amplitude Alfven wave (the pump wave) is regarded as the background flow, and the seven small-amplitude MHD waves (the backward and forward fast and slow magnetoacoustic waves, the backward and forward Alfven waves, and the entropy wave) interact with the pump wave via wave coupling coefficients that depend on the gradients and time dependence of the background flow. The dispersion equation for the waves D ( k ,ω) = 0 obtained from the wave coupling equations reduces to that obtained by previous authors. The general solution of the initial value problem for the waves is obtained by Fourier and Laplace transforms. The dispersion function D ( k ,ω) is a fifth-order polynomial in both the wavenumber k and the frequency ω. The regions of instability and the neutral stability curves are determined. Instabilities that arise from solving the dispersion equation D ( k ,ω) = 0, both in the form ω = ω( k ), where k is real, and in the form k = k (ω), where ω is real, are investigated. The instabilities depend parametrically on the pump wave amplitude and on the plasma beta. The wave interaction equations are also studied from the perspective of a single master wave equation, with multiple wave modes, and with a source term due to the entropy wave. The wave hierarchies for short- and long-wavelength waves of the master wave equation are used to discuss wave stability. Expanding the dispersion equation for the different long-wavelength eigenmodes about k = 0 yields either the linearized Korteweg–deVries equation or the Schrodinger equation as the generic wave equation at long-wavelengths. The corresponding short-wavelength wave equations are also obtained. Initial value problems for the wave interaction equations are investigated. An inspection of the double-root solutions of the dispersion equation for k , satisfying the equations D ( k ,ω) = 0 and ∂ D ( k ,ω) = ∂ k = 0 and pinch point analysis shows that the solutions of the wave interaction equations for hump or pulse-like initial data develop an absolute instability. Fourier solutions and asymptotic analysis are used to study the absolute instability.

Wave mixing of magnetohydrodynamic waves

A formalism for magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension is developed using multiple scales perturbation methods. In particular, wave mixing equations describing the mutual interaction of Alfven, magnetoacoustic, and entropy waves due to large scale gradients in the background flow are obtained. The waves are assumed to propagate along the x-axis of a rectangular, Cartesian coordinate system OXYZ, and the background flow depends on x and time t. Equations are obtained for both the strictly hyperbolic case, where all the wave speeds are distinct, and also for the degenerate eigenvalue cases k∥B and k⊥B, where k is the wave vector, and B is the background magnetic field induction. The Alfven waves are modified by their interaction with the magnetoacoustic and entropy waves due to wave mixing, only if the background flow has non-zero field aligned vorticity (B⋅∇×u≠0) and/or non-zero field aligned electric current (B⋅∇×B≠0). The relation of these equations to the well known...

Hamiltonian aspects of three-wave resonant interactions in gas dynamics

Equations describing three-wave resonant interactions in adiabatic gas dynamics in one Cartesian space dimension derived by Majda and Rosales are expressed in terms of Lagrangian and Hamiltonian variational principles. The equations consist of two coupled integro-differential Burgers equations for the backward and forward sound waves that are coupled by integral terms that describe the resonant reflection of a sound wave off an entropy wave disturbance to produce a reverse sound wave. Similarity solutions and conservation laws for the equations are derived using symmetry group methods for the special case where the entropy disturbance consists of a periodic saw-tooth profile. The solutions are used to illustrate the interplay between the nonlinearity represented by the Burgers self-wave interaction terms and wave dispersion represented by the three-wave resonant interaction terms. Hamiltonian equations in Fourier (p,t) space are also obtained where p is the Fourier space variable corresponding to the fast phase variable of the waves. The latter equations are transformed to normal form in order to isolate the normal modes of the system.