Wave mixing of hybrid Bogoliubov modes in a Bose-Einstein condensate

Mode-mixing of coherent excitations of a trapped Bose-Einstein condensate is modeled using the Bogoliubov approximation. Calculations are presented for second-harmonic generation between the two lowest-lying even-parity m=0 modes in an oblate spheroidal trap. Hybridization of the modes of the breather (l=0) and surface (l=4) states leads to the formation of a Bogoliubov dark state near phase-matching resonance so that a single mode is coherently populated. Efficient harmonic generation requires a strong coupling rate, sharply-defined and well-separated frequency spectrum, and good phase matching. We find that in all three respects the quantal results are significantly different from hydrodynamic predictions. Typically the second-harmonic conversion rate is half that given by an equivalent hydrodynamic estimate.

Harmonic generation and wave mixing in nonlinear metamaterials and photonic crystals (Invited paper)

The basic concepts and phenomenology of wave mixing and harmonic generation are reviewed in context of the recent advances in the enhanced nonlinear activity in metamaterials and photonic crystals. The effects of dispersion, field confinement and phase synchronism are illustrated by the examples of the on-purpose designed artificial nonlinear structures. (c) 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:469482, 2012.

Wave mixing by periodic nonlinear semiconductor multilayers

The properties of the combinatorial frequency generation and wave scattering by periodic stacks of nonlinear passive semiconductor layers are explored. It is demonstrated that the nonlinearity in passive weakly nonlinear semiconductor medium has the resistive nature associated with the dynamics of carriers. The features of the combinatorial frequency generation and the effects of the pump wave scattering and parameters of the constituent semiconductor layers on the efficiency of the frequency mixing are discussed and illustrated by the examples. © 2013 IEICE.

Time-resolved four-wave-mixing spectroscopy for inner-valence transitions

Noncollinear four-wave-mixing (FWM) techniques at near-infrared (NIR), visible, and ultraviolet frequencies have been widely used to map vibrational and electronic couplings, typically in complex molecules. However, correlations between spatially localized inner-valence transitions among different sites of a molecule in the extreme ultraviolet (XUV) spectral range have not been observed yet. As an experimental step toward this goal, we perform time-resolved FWM spectroscopy with femtosecond NIR and attosecond XUV pulses. The first two pulses (XUV-NIR) coincide in time and act as coherent excitation fields, while the third pulse (NIR) acts as a probe. As a first application, we show how coupling dynamics between odd- and even-parity, inner-valence excited states of neon can be revealed using a two-dimensional spectral representation. Experimentally obtained results are found to be in good agreement with ab initio time-dependent R-matrix calculations providing the full description of multielectron interactions, as well as few-level model simulations. Future applications of this method also include site-specific probing of electronic processes in molecules.

Effects of Geometrical Discontinuities on Distributed Passive Intermodulation in Printed Lines

This paper presents the results of experimental study of passive intermodulation (PIM) generation in microstrip lines with U-shaped and meandered strips, impedance tapers, and strips with the profiled edges. It is shown that the geometrical discontinuities in printed circuits may have a noticeable impact on distributed PIM generation even when their effect is indiscernible in the linear regime measurements. A consistent interpretation of the observed phenomena has been proposed on the basis of the phase synchronism in the four-wave mixing process. The results of this study reveal new features of PIM production important for the design and characterization of low-PIM microstrip circuits. © 2010 IEEE.

Passive Intermodulation Generation on Printed Lines: Near-Field Probing and Observations

The phenomenological mechanisms of passive intermodulation (PIM) in printed lines have been explored by mapping intermodulation products generated by the two-tone traveling waves in microstrip lines. Near-field probing based upon a commercial PIM analyzer has been employed for identification of the PIM sources in printed lines. The results of extensive near-field probing provide the direct experimental evidences of cumulative growth of the intermodulation products in the matched uniform microstrip lines and reveal the fundamental role of the nonlinear scattering by the lumped nonlinear inclusions in the intermodulation production. The distributed nature of the PIM generation in microstrip lines has been conclusively demonstrated and comprehensively described in terms of the four-wave mixing process that proved to be fully consistent with the results of experimental observations of third-order PIM products on the matched and mismatched microstrip lines. © 2006 IEEE.

Nonlinear scattering by anisotropic dielectric periodic structures

The combinatorial frequency generation by the periodic stacks of binary layers of anisotropic nonlinear dielectrics is examined. The products of nonlinear scattering are characterised in terms of the three-wave mixing processes. It is shown that the intensity of the scattered waves of combinatorial frequencies is strongly influenced by the constitutive and geometrical parameters of the anisotropic layers, and the frequency ratio and angles of incidence of pump waves. The enhanced efficiency of the frequency conversion at Wolf-Bragg resonances has been demonstrated for the lossless and lossy-layered structures. © 2012 O. V. Shramkova and A. G. Schuchinsky.

GAUSSIAN PULSE SCATTERING BY NONLINEAR THUE-MORSE QUASIPERIODIC MULTILAYERS

The pulse mixing and scattering by finite nonlinear Thue-Morse quasi-periodic dielectric multilayered structure illuminated by two Gaussian pulses with different centre frequencies and lengths are investigated. The three-wave mixing technique is applied to study the nonlinear processes. The properties of the scattered waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed.

Effect of magnetic bias on Gaussian pulse scattering by stacked nonlinear semiconductor layers

The nonlinear scattering of pulses by periodic stacks of semiconductor layers with magnetic bias has been studied in the self-consistent problem formulation, taking into account mobility of carriers. The three-wave mixing technique has been applied to the analysis of the waveform evolution in the stacks illuminated by two Gaussian pulses with different central frequencies and lengths. The effects of external magnetic bias, and stack physical and geometrical parameters on the properties of the scattered waveforms are discussed. © 2013 IEEE.

Pulsed second harmonic generation by stacks of magnetically biased semiconductor layers

The pulsed second harmonic generation (SHG) by periodic stacks of nonlinear semiconductor layers with external magnetic bias has been studied in the self-consistent problem formulation, taking into account mobility of carriers. The products of nonlinear scattering in the three-wave mixing process are examined. It is demonstrated that the waveform evolution in magnetoactive weakly nonlinear semiconductor periodic structure illuminated by Gaussian pulse is strongly affected by the magnetic bias and collision frequency of the carriers. The effect of nonreciprocity on the SHG efficiency is discussed and illustrated by the examples. © 2013 European Microwave Association.

Combinatorial Frequency Generation in Quasi-Periodic Stacks of Nonlinear Dielectric Layers

Three-wave mixing in quasi-periodic structures (QPSs) composed of nonlinear anisotropic dielectric layers, stacked in Fibonacci and Thue-Morse sequences, has been explored at illumination by a pair of pump waves with dissimilar frequencies and incidence angles. A new formulation of the nonlinear scattering problem has enabled the QPS analysis as a perturbed periodic structure with defects. The obtained solutions have revealed the effects of stack composition and constituent layer parameters, including losses, on the properties of combinatorial frequency generation (CFG). The CFG features illustrated by the simulation results are discussed. It is demonstrated that quasi-periodic stacks can achieve a higher efficiency of CFG than regular periodic multilayers.

Nonreciprocal scattering by stacked nonlinear magneto-active semiconductor layers

The combinatorial frequency generation by the periodic stacks of magnetically biased semiconductor layers has been modelled in a self-consistent problem formulation, taking into account the nonlinear dynamics of carriers. It is shown that magnetic bias not only renders nonreciprocity of the three-wave mixing process but also significantly enhances the nonlinear interactions in the stacks, especially at the frequencies close to the intrinsic magneto-plasma resonances of the constituent layers. The main mechanisms and properties of the combinatorial frequency generation and emission from the stacks are illustrated by the simulation results, and the effects of the individual layer parameters and the structure arrangement on the stack nonlinear and nonreciprocal response are discussed. © 2014 Elsevier B.V. All rights reserved.

Nonreciprocal nonlinear scattering by stacked magnetoactive semiconductor layers

The combinatorial frequency generation by the periodic stacks of magnetically biased semiconductor layers has been modelled in the self-consistent problem formulation, taking into account the nonlinear dynamics of carriers. It has been shown that the nonlinear response of the magnetoactive semiconductor periodic structure is strongly enhanced by magnetic bias and combinations of the layer physical and geometrical parameters. The effects of the pump wave nonreciprocal reflectance and field displacement on the efficiency of three-wave mixing process is illustrated by the simulation results

A developed stage of Alfven wave phase mixing

Alfven wave phase mixing is an extensively studied mechanism for dissipating wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave coupling does not occur. However, weakly nonlinear studies have shown that phase mixing generates magnetoacoustic modes. Numerical results are presented which show the nonlinear generation of magnetosonic waves by Alfven wave phase mixing. The efficiency of the effect is determined by the wave amplitude, the frequency of the Alfven waves and the gradient in the background Alfven speed. Weakly nonlinear theory has shown that the amplitude of the fast magnetosonic wave grows linearly in time. The simulations presented in this paper extend this result to later times and show saturation of the fast magnetosonic component at amplitudes much lower than that of the Alfven wave. For the case when Alfven waves are driven at the boundary, simulating photospheric footpoint motion, a clear modulation of the saturated amplitude is observed. All the results in this paper are for a low amplitude (less than or equal to 0.1), single frequency Alfven wave and a uniform background magnetic field in a two dimensional domain. For this simplified geometry, and with a monochromatic driver, we concluded that the nonlinear generation of fast modes has little effect on classical phase mixing.