Nonlinear metasurfaces have become prominent tools for controlling and engineering light at the nanoscale. Usually, polarization of total generated third harmonic is studied. However, diffraction orders may present different polarizations. Here, we design an high quality factor silicon metasurface generation perform back focal plane imaging orders, which a rich variety states. Our results demon...

Semiclassical spectra beyond the Gutzwiller and Berry-Tabor approximation for chaotic and regular systems, respectively, are obtained by harmonic inversion of the \ expansion of the periodic orbit signal. The method is illustrated for the circle billiard, where the semiclassical error is reduced by one to several orders of magnitude with respect to the lowest order approximation used previously...

Elastic waves in materials with cylindrical orthotropy are considered, this being a plausible model for waves in wood. For time-harmonic motions, the problem is reduced to some coupled ordinary differential equations. Methods for solving these equations are discussed. These include the method of Frobenius (power-series exapansions) and the use of Neumann series (expansions in series of Bessel f...

Abstract. In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of h̄ can be constructed for them without referring to the actual coordinate space wavefunctions from which the Wigner functions are typically calculated. We find such a picture by a careful analysis around th...

The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transitions in molecules and crystals, in order to derive general properties of harmonic generation to all orders. In particular, we obtain Kramers-Krönig relations and sum rules referred to all momenta of the susceptibility, and Miller’s ...

Second harmonic generation (SHG) is a nonlinear optical response arising exclusively from broken inversion symmetry in the electric-dipole limit. Recently, SHG has attracted widespread interest as versatile and noninvasive tool for characterization of crystal emerging ferroic or topological orders quantum materials. However, conventional far-field optics unable to probe local at deep subwavelen...

We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the phase error can also be eliminated two orders higher than that of the integrator. The use of fourth order forward time step integrators can result in sixth order...

A technique is proposed to generate ultrashort coherent soft x-ray radiation in storage rings using angular-modulated electron beams. In the scheme a laser operating in the TEM01 mode is first used to modulate the angular distribution of the electron beam in an undulator. After passing through a special beam line with nonzero transfer matrix element R54, the angular modulation is converted to d...

The time and place that Brownian motion on a Riemannian manifold first exits a normal ball of radius e is considered and a general procedure is given for computing asymptotic expansions, as e decreases to zero, for joint moments of the first exit time and place random variables. It is proven that asymptotic versions of exit time and place distribution properties that hold on harmonic spaces are...

We show that the lack of inversion symmetry in monolayer MoS2 allows strong optical second harmonic generation. The second harmonic of an 810-nm pulse is generated in a mechanically exfoliated monolayer, with a nonlinear susceptibility on the order of 10−7 m/V. The susceptibility reduces by a factor of seven in trilayers, and by about two orders of magnitude in even layers. A proof-of-principle...