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.

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.

Identifying cell class specific losses from serially generated electroretinogram components

Purpose. Processing of information through the cellular layers of the retina occurs in a serial manner. In the electroretinogram (ERG), this complicates interpretation of inner retinal changes as dysfunction may arise from "upstream" neurons or may indicate a direct loss to that neural generator. We propose an approach that addresses this issue by defining ERG gain relationships.

Methods. Regression analyses between two serial ERG parameters in a control cohort of rats are used to define gain relationships. These gains are then applied to two models of retinal disease.

Results. The PIIIamp to PIIamp gain is unity whereas the PIIamp to pSTRamp and PIIamp to nSTRamp gains are greater than unity, indicating "amplification" (P <0.05). Timing relationships show amplification between PIIIit to PIIit and compression for PIIit to pSTRit and PIIit to nSTRit, (P <0.05). Application of these gains to ?-3-deficiency indicates that all timing changes are downstream of photoreceptor changes, but a direct pSTR amplitude loss occurs (P <0.05). Application to diabetes indicates widespread inner retinal dysfunction which cannot be attributed to outer retinal changes (P <0.05).

Conclusions. This simple approach aids in the interpretation of inner retinal ERG changes by taking into account gain characteristics found between successive ERG components of normal animals.

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.

Multichannel interference in high-order-harmonic generation from Ne+ driven by an ultrashort intense laser pulse

We apply the time-dependent R-matrix method to investigate harmonic generation from Ne+ at a wavelength of 390 nm and intensities up to 1015 W cm−2. The 1s22s22p4 (3Pe,1De, and 1Se) states of Ne2+ are included as residual-ion states to assess the influence of interference between photoionization channels associated with these thresholds. The harmonic spectrum is well approximated by calculations in which only the 3Pe and 1De thresholds are taken into account, but no satisfactory spectrum is obtained when a single threshold is taken into account. Within the harmonic plateau, extending to about 100 eV, individual harmonics can be suppressed at particular intensities when all Ne2+ thresholds are taken into account. The suppression is not observed when only a single threshold is accounted for. Since the suppression is dependent on intensity, it may be difficult to observe experimentally.

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.

Distillable entanglement and area laws in spin and harmonic-oscillator systems

We address the presence of nondistillable (bound) entanglement in natural many-body systems. In particular, we consider standard harmonic and spin-1/2 chains, at thermal equilibrium and characterized by few interaction parameters. The existence of bound entanglement is addressed by calculating explicitly the negativity of entanglement for different partitions. This allows us to individuate a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We discuss how the appearance of bound entanglement can be linked to entanglement-area laws, typical of these systems. Various types of interactions are explored, showing that the presence of bound entanglement is an intrinsic feature of these systems. In the harmonic case, we analytically prove that thermal bound entanglement persists for systems composed by an arbitrary number of particles. Our results strongly suggest the existence of bound entangled states in the macroscopic limit also for spin-1/2 systems.