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.

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.

Strong second harmonic generation in SiC, ZnO, GaN two-dimensional hexagonal crystals from first-principles many-body calculations

The second harmonic generation (SHG) intensity spectrum of SiC, ZnO, GaN two-dimensional hexagonal crystals is calculated by using a real-time first-principles approach based on Green's function theory [Attaccalite et al., Phys. Rev. B: Condens. Matter Mater. Phys. 2013 88, 235113]. This approach allows one to go beyond the independent particle description used in standard first-principles nonlinear optics calculations by including quasiparticle corrections (by means of the GW approximation), crystal local field effects and excitonic effects. Our results show that the SHG spectra obtained using the latter approach differ significantly from their independent particle counterparts. In particular they show strong excitonic resonances at which the SHG intensity is about two times stronger than within the independent particle approximation. All the systems studied (whose stabilities have been predicted theoretically) are transparent and at the same time exhibit a remarkable SHG intensity in the range of frequencies at which Ti:sapphire and Nd:YAG lasers operate; thus they can be of interest for nanoscale nonlinear frequency conversion devices. Specifically the SHG intensity at 800 nm (1.55 eV) ranges from about 40-80 pm V(-1) in ZnO and GaN to 0.6 nm V(-1) in SiC. The latter value in particular is 1 order of magnitude larger than values in standard nonlinear crystals.

Relativistic plasma surfaces as an efficient second harmonic generator

We report on the characterization of the specular reflection of 50 fs laser pulses in the intensity range 10(17)-10(21)Wcm(-2) obliquely incident with p-polarization onto solid density plasmas. These measurements show that the absorbed energy fraction remains approximately constant and that second harmonic generation (SHG) achieves efficiencies of 22 +/- 8% for intensities approaching 10(21)Wcm(-2). A simple model based on the relativistic oscillating mirror concept reproduces the observed intensity scaling, indicating that this is the dominant process involved for these conditions. This method may prove to be superior to SHG by sum frequency mixing in crystals as it is free from dispersion and retains high spatial coherence at high intensity.

High contrast plasma mirror: spatial filtering and second harmonic generation at 10(19)Wcm(-2)

Recently, the use of plasma optics to improve temporal pulse contrast has had a remarkable impact on the field of high- power laser-solid density interaction physics. Opening an avenue to previously unachievable plasma density gradients in the high intensity focus, this advance has enabled researchers to investigate new regimes of harmonic generation and ion acceleration. Until now, however, plasma optics for fundamental laser reflection have been used in the sub-relativistic intensity regime (10(15) - 10(16)Wcm(-2)) showing high reflectivity (similar to 70%) and good focusability. Therefore, the question remains as to whether plasma optics can be used for such applications in the relativistic intensity regime (> 10(18)Wcm(-2)). Previous studies of plasma mirrors (PMs) indicate that, for 40 fs laser pulses, the reflectivity fluctuates by an order of magnitude and that focusability of the beam is lost as the intensity is increased above 5 x 10(16)Wcm(-2). However, these experiments were performed using laser pulses with a contrast ratio of similar to 10(7) to generate the reflecting surface. Here, we present results for PM operation using high contrast laser pulses resulting in a new regime of operation - the high contrast plasma mirror (HCPM). In this regime, pulses with contrast ratio > 10(10) are used to form the PM surface at > 10(19)Wcm(-2), displaying excellent spatial filtering, reflected near- field beam profile of the fundamental beam and reflectivities of 60 +/- 5%. Efficient second harmonic generation is also observed with exceptional beam quality suggesting that this may be a route to achieving the highest focusable harmonic intensities. Plasma optics therefore offer the opportunity to manipulate ultra-intense laser beams both spatially and temporally. They also allow for ultrafast frequency up-shifting without detrimental effects due to group velocity dispersion (GVD) or reduced focusability which frequently occur when nonlinear crystals are used for frequency conversion.

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.

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.

2ND-HARMONIC LIGHT GENERATION IN THE INTERACTION OF LASER-BEAMS WITH UNDERCRITICAL PLASMAS

The process of second harmonic generation (SHG) in undercritical plasmas is studied. It is shown that filamentation and self-focusing of the laser beam in the plasma can break the plasma density symmetry and lead to SHG by free electrons. In turn, second harmonic emission may be used to investigate the plasma parameters and to diagnose the process of laser beam filamentation itself.

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. 

On-line monitoring of laser modification of titanium dioxide using optical surface second harmonic

TiO₂ photocatalysis is a promising technology for the destruction of organic pollutants in both waste and potable waters with the mineralisation of a wide range of compounds having been reported. TiO ₂ has many advantages over other semiconductors, it is highly photoreactive, cheap, non-toxic, chemically and biologically inert, and photostable. The photocatalytic activity of TiO₂ has been shown to depend upon many criteria including the ratio of anatase/rutile crystal phase, particle size and oxidation state. This paper reports the use of optical surface second harmonic generation (SSHG) to monitor modifications in TiO ₂ powder induced following laser treatment. SSHG is a non-contact, non-destructive technique, which is highly sensitive to both surface chemical and physical changes. Results show that three different SSH intensities were observable as the TiO₂ samples were irradiated with the laser light. These regions were related to changes in chemical characteristics and particle size of the TiO₂ powder

The application of surface second harmonic sensor to probe laser induced modification of titanium dioxide

The effects of high power pulsed laser light on a TiO2 photocatalyst have been investigated using a surface second harmonic generation (SSHG) sensor. When TiO2 is irradiated with a laser at 355mm a visible change in colour from white to dark blue crystals was observed. X-ray diffraction studies indicate that the crystal structure of the TiO2 developed a more rutile form following laser exposure.

Ectopic bone formation in rapidly fabricated acellular injectable dense collagen-Bioglass hybrid scaffolds via gel aspiration-ejection

Gel aspiration-ejection (GAE) has recently been introduced as an effective technique for the rapid production of injectable dense collagen (IDC) gel scaffolds with tunable collagen fibrillar densities (CFDs) and microstructures. Herein, a GAE system was applied for the advanced production and delivery of IDC and IDC-Bioglass® (IDC-BG) hybrid gel scaffolds for potential bone tissue engineering applications. The efficacy of GAE in generating mineralizable IDC-BG gels (from an initial 75-25 collagen-BG ratio) produced through needle gauge numbers 8G (3.4 mm diameter and 6 wt% CFD) and 14G (1.6 mm diameter and 14 wt% CFD) was investigated. Second harmonic generation (SHG) imaging of as-made gels revealed an increase in collagen fibril alignment with needle gauge number. In vitro mineralization of IDC-BG gels was confirmed where carbonated hydroxyapatite was detected as early as day 1 in simulated body fluid, which progressively increased up to day 14. In vivo mineralization of, and host response to, acellular IDC and IDC-BG gel scaffolds were further investigated following subcutaneous injection in adult rats. Mineralization, neovascularization and cell infiltration into the scaffolds was enhanced by the addition of BG and at day 21 post injection, there was evidence of remodelling of granulation tissue into woven bone-like tissue in IDC-BG. SHG imaging of explanted scaffolds indicated collagen fibril remodelling through cell infiltration and mineralization over time. In sum, the results suggest that IDC-BG hybrid gels have osteoinductive properties and potentially offer a novel therapeutic approach for procedures requiring the injectable delivery of a malleable and dynamic bone graft that mineralizes under physiological conditions

Generation and control of ultrafast pulse trains for quasi-phase-matching high-harmonic generation

Two techniques are demonstrated to produce ultrashort pulse trains capable of quasi-phase-matching high-harmonic generation. The first technique makes use of an array of birefringent crystals and is shown to generate high-contrast pulse trains with constant pulse spacing. The second technique employs a grating-pair stretcher, a multiple-order wave plate, and a linear polarizer. Trains of up to 100 pulses are demonstrated with this technique, with almost constant inter-pulse separation. It is shown that arbitrary pulse separation can be achieved by introducing the appropriate dispersion. This principle is demonstrated by using an acousto-optic programmable dispersive filter to introduce third-and fourth-order dispersions leading to a linear and quadratic variation of the separation of pulses through the train. Chirped-pulse trains of this type may be used to quasi-phase-match high-harmonic generation in situations where the coherence length varies through the medium. (C) 2010 Optical Society of America