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.

Three-wave Nonlinear Scattering by Quasiperiodic Dielectric Structure

The combinatorial frequency generation by a Fibonacci type quasi-periodic dielectric multilayered structure illuminated by two plane waves has been analysed. The effects of the layer parameters and Fibonacci sequence order on the properties of the combinatorial frequency waves emitted from the stacked nonlinear layers are discussed.

Enhanced harmonic generation from Ar+ aligned with M =1

We investigate harmonic generation (HG) from ground-state Ar+ aligned with M=1 at a laser wavelength of 390 nm and intensity of 4×1014Wcm−2. Using time-dependent R-matrix theory, we find that an initial state with magnetic quantum number M=1 provides a fourfold increase in harmonic yield over M=0. HG arises primarily from channels associated with the 3Pe threshold of Ar2+, in contrast with M=0 for which channels associated with the excited, 1De threshold dominate HG. Multichannel and multielectron interferences lead to a more marked suppression of HG for M=1 than M=0.

ESTIMATION OF PURITY FOR A QUANTUM HARMONIC OSCILLATOR INITIALLY PREPARED IN A DISPLACED THERMAL STATE

We address the estimation of purity for a quantum oscillator initially prepared in a displaced thermal state and probed by a suitably prepared qubit interacting with the oscillator via Jaynes-Cummings Hamiltonian without the rotating-wave approximation. We evaluate the quantum Fisher information (QFI) and show that optimal estimation of purity can be achieved by measuring the population of the qubit after a properly chosen interaction time. We also address the estimation of purity at fixed total energy and show that the corresponding precision is independent of the presence of a coherent amplitude.

Qubit-assisted thermometry of a quantum harmonic oscillator

We use the theory of quantum estimation in two different qubit-boson coupling models to demonstrate that the temperature of a quantum harmonic oscillator can be estimated with high precision by quantum-limited measurements on the qubit. The two models that we address embody situations of current physical interest due to their connection with ongoing experimental efforts on the control of mesoscopic dynamics. We show that population measurements performed over the qubit probe are near optimal for a broad range of temperatures of the harmonic oscillator.

Nonlinear optics from an ab initio approach by means of the dynamical Berry phase: Application to second- and third-harmonic generation in semiconductors

We present an ab initio real-time-based computational approach to study nonlinear optical properties in condensed matter systems that is especially suitable for crystalline solids and periodic nanostructures. The equations of motion and the coupling of the electrons with the external electric field are derived from the Berry-phase formulation of the dynamical polarization [Souza et al., Phys. Rev. B 69, 085106 (2004)]. Many-body effects are introduced by adding single-particle operators to the independent-particle Hamiltonian. We add a Hartree operator to account for crystal local effects and a scissor operator to correct the independent particle band structure for quasiparticle effects. We also discuss the possibility of accurately treating excitonic effects by adding a screened Hartree-Fock self-energy operator. The approach is validated by calculating the second-harmonic generation of SiC and AlAs bulk semiconductors: an excellent agreement is obtained with existing ab initio calculations from response theory in frequency domain [Luppi et al., Phys. Rev. B 82, 235201 (2010)]. We finally show applications to the second-harmonic generation of CdTe and the third-harmonic generation of Si. 

Second harmonic generation in h-BN and MoS2 monolayers: Role of electron-hole interaction

We study second-harmonic generation in h-BN and MoS$_2$ monolayers using a novel \emph{ab initio} approach based on Many-body theory. We show that electron-hole interaction doubles the signal intensity at the excitonic resonances with respect to the contribution from independent electronic transitions. This implies that electron-hole interaction is essential to describe second-harmonic generation in those materials. We argue that this finding is general for nonlinear optical properties in nanostructures and that the present methodology is the key to disclose these effects.

Nonlinearly coupled localized plasmon resonances: Resonant second-harmonic generation

The efficient resonant nonlinear coupling between localized surface plasmon modes is demonstrated in a simple and intuitive way using boundary integral formulation and utilizing second-order optical nonlinearity. The nonlinearity is derived from the hydrodynamic description of electron plasma and originates from the presence of material interfaces in the case of small metal particles. The coupling between fundamental and second-harmonic modes is shown to be symmetry selective and proportional to the spatial overlap between polarization dipole density of the second-harmonic mode and the square of the polarization charge density of the fundamental mode. Particles with high geometrical symmetry will convert a far-field illumination into dark nonradiating second-harmonic modes, such as quadrupoles. Effective second-harmonic susceptibilities are proportional to the surface-to-volume ratio of a particle, emphasizing the nanoscale enhancement of the effect.

Effects of buried high-Z layers on fast electron propagation

By extending a prior model [A. R. Bell, J.R. Davies, S. M. Guerin, Phys. Rev. E 58, 2471 (1998)], the magnetic field generated during the transport of a fast electron beam driven by an ultraintense laser in a solid target is derived analytically and applied to estimate the effect of such field on fast electron propagation through a buried high-Z layer in a lower-Z target. It is found that the effect gets weaker with the increase of the depth of the buried layer, the divergence of the fast electrons, and the laser intensity, indicating that magnetic field effects on the fast electron divergence as measured from K-a X-ray emission may need to be considered for moderate laser intensities. On the basis of the calculations, some considerations are made on how one can mitigate the effect of the magnetic field generated at the interface.