Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Nonlinear transport and localization in single-walled carbon nanotubes

We have measured the electrical transport properties of mats of single-walled carbon nanotubes (SWNT) as a function of applied electric and magnetic fields. We find that at low temperatures the resistance as a function of temperature R(T) follows the Mott variable range hopping (VRH) formula for hopping in three dimensions. Measurement of the electric field dependence of the resistance R(E) allows for the determination of the Bohr radius of a localized state a = 700nm. The magnetoresistance (MR) of SWNT mat samples is large and negative at all temperatures and fields studied. The low field negative MR is proportional to H2, in agreement with variable range hopping in two or three dimensions. 3D VRH indicates good intertube contacts, implying that the localization is due to the disorder experienced by the individual tubes. The 3D localization radius gives a measure of the ID localization length on the individual tubes, which we estimate to be >700 nm. Implications for the electron-phonon mean free path are discussed.

Signal-to-Noise Ratio Analysis for Nonlinear N-ary Phase Filters

The problem of recognising targets in non-overlapping clutter using nonlinear N-ary phase filters is addressed. Using mathematical analysis, expressions were derived for an N-ary phase filter and the intensity variance of an optical correlator output. The N-ary phase filter was shown to consist of an infinite sum of harmonic terms whose periodicity was determined by N. For the intensity variance, it was found that under certain conditions the variance was minimised due to a hitherto undiscovered phase quadrature effect. Comparison showed that optimal real filters produced greater SNR values than the continuous phase versions as a consequence of this effect.

Nonlinear dynamics and solitons in Debye bi-crystals

The nonlinear dynamics of longitudinal dust lattice waves propagating in a dusty plasma bi-crystal is investigated. A “diatomic”-like one-dimensional dust lattice configuration is considered, consisting of two distinct dust grain species with different charges and masses. Two different frequency dispersion modes are obtained in the linear limit, namely, an optical and an acoustic wave dispersion branch. Nonlinear solitary wave solutions are shown to exist in both branches, by considering the continuum limit for lattice excitations in different nonlinear potential regimes. For this purpose, a generalized Boussinesq and an extended Korteweg de Vries equation is derived, for the acoustic mode excitations, and their exact soliton solutions are provided and compared. For the optic mode, a nonlinear Schrödinger-type equation is obtained, which is shown to possess bright- (dark-) type envelope soliton solutions in the long (short, respectively) wavelength range. Optic-type longitudinal wavepackets are shown to be generally unstable in the continuum limit, though this is shown not to be the rule in the general (discrete) case.

Hänsch--Couillaud locking of Mach--Zehnder interferometer for carrier removal from a phase-modulated optical spectrum

We describe and analyse the operation and stabilization of a Mach--Zehnder interferometer, which separates the carrier and the first-order sidebands of a phase-modulated laser field, and which is locked using the H\"ansch--Couillaud method. In addition to the necessary attenuation, our interferometer introduces, via total internal reflection, a significant polarization-dependent phase delay. We employ a general treatment to describe an interferometer with an object which affects the field along one path, and we examine how this phase delay affects the error signal. We discuss the requirements necessary to ensure the lock point remains unchanged when phase modulation is introduced, and we demonstrate and characterize this locking experimentally. Finally, we suggest an extension to this locking strategy using heterodyne detection.

Real-time approach to the optical properties of solids and nanostructures: Time-dependent Bethe-Salpeter equation

Many-body effects are known to play a crucial role in the electronic and optical properties of solids and nanostructures. Nevertheless, the majority of theoretical and numerical approaches able to capture the influence of Coulomb correlations are restricted to the linear response regime. In this work, we introduce an approach based on a real-time solution of the electronic dynamics. The proposed approach reduces to the well-known Bethe-Salpeter equation in the linear limit regime and it makes it possible, at the same time, to investigate correlation effects in nonlinear phenomena. We show the flexibility and numerical stability of the proposed approach by calculating the dielectric constants and the effect of a strong pulse excitation in bulk h-BN.

Nanoscale Origins of Nonlinear Behavior in Ferroic Thin Films

The nonlinear response of a ferroic to an applied field has been studied through the phenomenological Rayleigh Law for over a hundred years. Yet, despite this, the fundamental physical mechanisms at the nanoscale that lead to macroscopic Rayleigh behavior have remained largely elusive, and experimental evidence at small length scales is limited. Here, it is shown using a combination of scanning probe techniques and phase field modeling, that nanoscale piezoelectric response in prototypical Pb(Zr,Ti)O3 films appears to follow a distinctly non-Rayleigh regime. Through statistical analysis, it is found that an averaging of local responses can lead directly to Rayleigh-like behavior of the strain on a macroscale. Phase-field modeling confirms the twist of the ferroelastic interface is key in enhancing piezoelectric response. The studies shed light on the nanoscale origins of nonlinear behavior in disordered ferroics.

Probing Ferroelectrics Using Optical Second Harmonic Generation

Nonlinear optics is an essential component of modern laser systems and optoelectronic devices. It has also emerged as an important tool in probing the electronic, vibrational, magnetic, and crystallographic structure of materials ranging from oxides and metals, to polymers and biological samples. This review focuses on the specific technique of optical second harmonic generation (SHG), and its application in probing ferroelectric complex oxide crystals and thin films. As the dominant SHG interaction mechanism exists only in materials that lack inversion symmetry, SHG is a sensitive probe of broken inversion symmetry, and thus also of bulk polar phenomena in materials. By performing in-situ SHG polarimetry experiments in different experimental conditions such as sample orientation, applied electric field, and temperature, one can probe ferroelectric hysteresis loops and phase transitions. Careful modeling of the polarimetry data allows for the determination of the point group symmetry of the crystal. In epitaxial thin films with a two-dimensional arrangement of well-defined domain orientations, one can extract information about intrinsic material properties such as nonlinear coefficients, as well as microstructural information such as the local statistics of the different domain variants being probed. This review presents several detailed examples of ferroelectric systems where such measurements and modeling are performed. The use of SHG microscopic imaging is discussed, and its ability to reveal domain structures and phases not normally visible with linear optics is illustrated.

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.

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

Comprehensive numerical modelling of the performance of a second harmonic generation stage coupled with a low-gain optical parametric amplifier

We present a comprehensive model for predicting the full performance of a second harmonic generation-optical parametric amplification system that aims at enhancing the temporal contrast of laser pulses. The model simultaneously takes into account all the main parameters at play in the system such as the group velocity mismatch, the beam divergence, the spectral content, the pump depletion, and the length of the nonlinear crystals. We monitor the influence of the initial parameters of the input pulse and the interdependence of the two related non-linear processes on the performance of the system and show its optimum configuration. The influence of the initial beam divergence on the spectral and the temporal characteristics of the generated pulse is discussed. In addition, we show that using a crystal slightly longer than the optimum length and introducing small delay between the seed and the pump ensures maximum efficiency and compensates for the spectral shift in the optical parametric amplification stage in case of chirped input pulse. As an example, calculations for bandwidth transform limited and chirped pulses of sub-picosecond duration in beta barium borate crystal are presented.