Related papers: Homotopy analysis method applied to second-order f…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of…
Empirical researchers are usually interested in investigating the impacts of baseline covariates have when uncovering sample heterogeneity and separating samples into more homogeneous groups. However, a considerable number of studies in the…
We propose and experimentally demonstrate a scheme allowing to reach noncollinear phase-matching of high harmonic generation in solids, which may potentially lead to an enhancement of the generation efficiency. The principle is based on…
In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…
High harmonic generation (HHG) is an extremely nonlinear effect, where a medium is driven by a strong laser field, generating coherent broadband radiation with photon energies ranging up to the X-ray and pulse durations reaching attosecond…
Nonlinear optics has been a very dynamic field of research with spectacular phenomena discovered mainly after the invention of lasers. The combination of high intensity fields with resonant systems has further enhanced the nonlinearity with…
In the present work, we use the homotopy perturbation method (HPM) to solve the Newell- Whitehead-Segel non-linear differential equations. Four case study problems of Newell-Whitehead- Segel are solved by the HPM and the exact solutions are…
Theory of the optical parametric amplification at high-frequency pumping in crystals with a regular space modulation of the sign of nonlinear coupling coefficient of interacting waves is developed. By applying the matrix method, the theory…
For future mmWave mobile communication systems the use of analog/hybrid beamforming is envisioned be a key as- pect. The synthesis of beams is a key technology of enable the best possible operation during beamsearch, data transmission and…
Superconducting quantum systems (artificial atoms) have been recently successfully used to demonstrate on-chip effects of quantum optics with single atoms in the microwave range. In particular, a well-known effect of four-wave mixing could…
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…
We consider the problem of reconstructing inhomogeneities in an isotropic elastic body using time harmonic waves. Here we extend the so called monotonicity method for inclusion detection and show how to determine certain types of…
Optical second harmonic generation is a second-order nonlinear process that combines two photons of a given frequency into a third photon at twice the frequency. Due to the symmetry constraints, it is widely used as a sensitive probe to…
A simple and flexible technique for achieving quasi-phase-matching in integrated photonic waveguides without periodic poling is proposed and experimentally demonstrated, referred to as mode-shape-modulation (MSM). It employs a periodic…
In this paper, we extend the method proposed by Cochelin and Vergez [A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (2009) 243-262] to the case of…
We investigate the case of phase-matched high-harmonic generation in a gas-filled capillary waveguide, comparing in detail theory with experiment. We observe three different regimes of phase matching: one where atomic dispersion balances…
In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the (time-harmonic) Maxwell scattering problem with high contrast. The method is constructed for a setting as in Bouchitt\'e, Bourel and Felbacq (C.R. Math. Acad.…
The discovery of second harmonic generation in 1961 marked the birth of nonlinear optics, unlocking a range of applications from frequency conversion to quantum light generation. Yet, phase matching in bulk nonlinear crystals remains a key…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…