Dependent Second Harmonic Generation Research Articles

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects are important, all the effective third order nonlinear response coefficients show a strong field dependence.

Optical characterisation of plasmonic nanostructures on planar substrates using second-harmonic generation.

Off-normal, polarization dependent second-harmonic generation (SHG) measurements were performed ex situ on plasmonic nanostructures grown by self-assembly on nanopatterned templates. These exploratory studies of Ag nanoparticle (NP) arrays show that the sensitivity of SHG to the local fields, which are modified by the NP size, shape and distribution, makes it a promising fixed wavelength characterization technique that avoids the complexity of spectroscopic SHG. The off-normal geometry provides access to the out-of-plane SH response, which is typically an order-of-magnitude larger than the in-surface-plane response measured using normal incidence, for example in SHG microscopy. By choosing the plane of incidence orthogonal to the NP array direction, it was shown that the p-polarized SH response, as a function of input polarization, is very sensitive to NP morphology, with a change of 20% in the aspect ratio of the NPs producing a variation of a factor of 30 in the easily measureable ratio of the p-polarized SH field strength for s- and p-polarized input. The results show that such a fixed geometry could be used for the in situ characterization of anisotropic nanostructure morphology during growth by self-assembly, which could be particularly useful in situations where rotating the sample may be neither desirable nor easily accomplished.

Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam.

We extend the subtractive imaging method to label-free second harmonic generation (SHG) microscopy to enhance the spatial resolution and contrast. This method is based on the intensity difference between two images obtained with circularly polarized Gaussian and doughnut-shaped beams, respectively. By characterizing the intensity and polarization distributions of the two focused beams, we verify the feasibility of the subtractive imaging method in polarization dependent SHG microscopy. The resolution and contrast enhancement in different biological samples is demonstrated. This work will open a new avenue for the applications of SHG microscopy in biomedical research.

Molecular Organization of Crystalline β-Carotene in Carrots Determined with Polarization-Dependent Second and Third Harmonic Generation Microscopy

Polarization-in, polarization-out (PIPO) second harmonic generation (SHG) and third harmonic generation (THG) microscopy was used to study the crystalline organization of β-carotene molecules within individual aggregates contained in the chromoplasts of orange carrots in vivo. Multimodal PIPO SHG and PIPO THG studies of the aggregates revealed one dominant SHG and THG dipole signifying that β-carotene molecules are oriented along a single axis. Three-dimensional visualization of the orientation of β-carotene molecules with respect to the aggregate axis was also performed with both microscopy modalities and revealed organization of the aggregates as ribbon-like structures consisting of twists and folds. Therefore, PIPO SHG and PIPO THG microscopy provides information on the crystalline organization and the orientation of ordered biological structures in vivo where multimodal polarization dependent SHG and THG investigations are particularly advantageous as both noncentrosymmetric and centrosymmetric crystalline organizations can be probed.

Experimental and simulation study of the wavelength dependent second harmonic generation of collagen in scattering tissues

We report on the wavelength dependence of second harmonic generation (SHG) of collagen in scattering tissues over the wavelength range of 800-1200 nm. The study incorporates inclusion of the molecular hyperpolarizability β of collagen and optical scattering, both of which are wavelength dependent. Using 3D SHG imaging and Monte Carlo simulations, we find the wavelength dependence of β is not well described by a two-state model based on known absorption bands. We further find that longer wavelength excitation is inefficient as the reduction in scattering is overcome by the decreased β far from resonance and the optimal excitation is within the 800-900 nm range. The impact is larger for backward collected SHG.

Second Harmonic Generation from Artificially Stacked Transition Metal Dichalcogenide Twisted Bilayers

Optical second harmonic generation (SHG) is known as a sensitive probe to the crystalline symmetry of few-layer transition metal dichalcogenides (TMDs). Layer-number dependent and polarization resolved SHG have been observed for the special case of Bernal stacked few-layer TMDs, but it remains largely unexplored for structures deviated from this ideal stacking order. Here we report on the SHG from homo- and heterostructural TMD bilayers formed by artificial stacking with an arbitrary stacking angle. The SHG from the twisted bilayers is a coherent superposition of the SH fields from the individual layers, with a phase difference depending on the stacking angle. Such an interference effect is insensitive to the constituent layered materials and thus applicable to hetero-stacked bilayers. A proof-of-concept demonstration of using the SHG to probe the domain boundary and crystal polarity of mirror twins formed in chemically grown TMDs is also presented. We show here that the SHG is an efficient, sensitive, and nondestructive characterization for the stacking orientation, crystal polarity, and domain boundary of van der Waals heterostructures made of noncentrosymmetric layered materials.

Deep-Ultraviolet Nonlinear Optical Crystals: Ba3P3O10X (X = Cl, Br)

Deep-ultraviolet nonlinear optical (deep-UV NLO) crystals are of worldwide interest for the generation of coherent light with wavelength below 200 nm by the direct second-harmonic generation (SHG) output from solid-state lasers. The unprecedented deep-UV NLO phosphates representing their own structure types, Ba3P3O10Cl (BPOC), Ba3P3O10Br (BPOB), have been discovered, which display moderate powder SHG intensities in type I phase matchable behaviors with a short UV cutoff edge of 180 nm (measured by a single crystal, one of the shortest values among phosphates to date). Insightfully, the geometry and polarization of the C1-P3O10(5-) building unit are affected by the crystal packing. DFT calculations and cutoff energy dependent SHG coefficient analyses reveal that the SHG origin is from the cooperation of asymmetric C1-P3O10(5-) anion, Ba(2+) cation, and Cl(-)/Br(-) anion.

All Optical Determination of Microscopic and Macroscopic Structure of Chiral, Polar Microcrystals from Achiral, Nonpolar Molecules

Organic microcrystals obtained from an octupolar molecule are studied by polarized nonlinear optical microscopy. While two-photon fluorescence microscopy is employed to verify the monocrystallinity of the analyzed domains, second-harmonic generation microscopy allowed determination of the point group symmetry of the crystallites. This combined analysis revealed that the achiral, octupolar molecules form chiral and polar conglomerate structures; the former are confirmed by circular dichroism spectroscopy. We additionally present a convenient and straightforward image analysis protocol, based on polarization dependent second-harmonic generation microscopy. This allows assessing the local organization and homogeneity of crystalline structures, which is highly relevant for technological applications, with high resolution and sensitivity.

Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths

We study second and third harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths in bulk and cavity environments. Second harmonic generation is due to a combination of spatial symmetry breaking, the magnetic portion of the Lorentz force, and quadrupolar contributions from inner core electrons. The material is assumed to have a nonzero, third-order nonlinearity that gives rise to most of the third harmonic signal. Using the parameters of bulk silicon we predict that cavity environments modify the dependence of second harmonic generation on incident angle, while improving third harmonic conversion efficiency by several orders of magnitude relative to bulk silicon. This occurs despite the fact that the harmonic signals may be tuned to a wavelength range where the dielectric function of the material is negative: A phase-locking mechanism binds the generated signals to the pump and inhibits their absorption. These results point the way to alternative uses and flexibility of materials such as silicon as nonlinear media in the visible and UV ranges.

Click chemistry-based synthesis of azo polymers for second-order nonlinear optics

Four linear polymers containing pendant azo moiety were synthesized through click chemistry for second-order nonlinear optical study. The polymers were found soluble in most of the polar organic solvents such as tetrahydrofuran (THF), chloroform, and dimethyl formamide (DMF). The polymers showed thermal stability up to 300 °C and glass transition temperatures (Tg) in the range of 120–140 °C. The molecular weights (Mw) of these polymers (measured by gel permeation chromatography) were in the range 37,900–55,000 g/mol. The polymers were found to form optically transparent films by solution casting from THF solution. Order parameters were calculated from UV–vis absorption spectra. The morphology changes in the films after poling were characterized by atomic force microscopy. The angular dependence, temperature dependence, and time dependence of second harmonic generation (SHG) intensity were obtained by using 1064 nm Nd:YAG laser. The SHG intensity remained unchanged up to 95 °C. At room temperature, it remained stable up to 8 days after initial drop of about 14%. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012

Ion-implantation induced nano distortion layer and its influence on nonlinear optical properties of ZnO single crystals

Second harmonic generation (SHG) and X-ray diffraction rocking curves of high-quality ZnO single crystals implanted by different ions (He, Cu, and Zn) were investigated. Interestingly, it was found that both He- and Zn-implanted samples show a convinced increment in SHG efficiency while the Cu-implanted one does not. X-ray diffraction rocking curves of the samples show satellite structures, and the simulations firmly reveal the formation of quasi-interfaces inside He- and Zn-implanted crystals. These quasi-interfaces lead to SHG improvement in the two samples. Polarization dependence of SHG of the samples on the excitation light also evidences this conclusion.

Tuning the mapping of second-harmonic generation in silver nanoshells

The distribution patterns of the second-harmonic generation (SHG) enhancement factor in the incident plane of silver nanoshell at resonance frequencies have been studied by using electrostatic approximation. The mapping feature of SHG corresponding to double frequency local field enhancement is different from that of fundamental case. At longer wavelength (SHG enhancement resulting from local field at double frequency), large SHG enhancements are only observed outside the shell. However, hot spots also take place inside the silver shell at shorter wavelength (SHG enhancement resulting from local field at fundamental frequency). The effect of outer surrounding media on the SHG corresponding to local field at fundamental frequency is also very different from that of double frequency. It has been found that the azimuth angle dependent SHG at shorter wavelength split into two maximums when the surrounding dielectric constant is increased, which is absent for SHG at longer wavelength.

Determination of Collagen Nanostructure from Second-Order Susceptibility Tensor Analysis

A model is proposed to describe the polarization dependence of second harmonic generation (SHG) from type I collagen fibrils. The model is based on sum-frequency vibrational spectrum experiments that attribute the molecular origins of collagen second-order susceptibility to the peptide groups in the backbone of the collagen α-helix and the methylene groups in the pyrrolidine rings. Applying our model to a polarization SHG (P-SHG) experiment leads to a predicted collagen I peptide pitch-angle of 45.82° ± 0.46° and methylene pitch-angle of 94.80° ± 0.97°. Compared to a previous model that accounts for only the peptide contribution, our results are more consistent with the x-ray diffraction determination of collagen-like peptide. Application of our model to type II collagen from rat trachea cartilage leads to similar results. The peptide pitch-angle of 45.72° ± 1.17° is similar to that of type I collagen, but a different methylene pitch-angle of 97.87° ± 1.79° was found. Our work demonstrates that far-field P-SHG measurements can be used to extract molecular structural information of collagen fibers.

Second-Harmonic Generation Imaging of Membrane Potential with Retinal Analogues

Second-harmonic generation (SHG) by membrane-incorporated probes is a nonlinear optical signal that is voltage-sensitive and the basis of a sensitive method for imaging membrane potential. The voltage dependence of SHG by four different probes, three retinoids (all-trans retinal), and two new retinal analogs, 3-methyl-7-(4′-dimethylamino-phenyl)-2,4,6-heptatrienal (AR-3) and 3,7-dimethyl-9-(4′-dimethylamino-phenyl)-2,4,6,8-nonatetraenal (AR-4), and a styryl dye (FM4-64), were compared in HEK-293 cells. Results were analyzed by fitting data with an expression based on an electrooptic mechanism for SHG, which depends on the complex-valued first- and second-order nonlinear electric susceptibilities (χ2 and χ3) of the probe. This gave values for the voltage sensitivity at the cell's resting potential, the voltage where the SHG is minimal, and the amplitude of the signal at that voltage for each of the four compounds. These measures show that χ2 and χ3 are complex numbers for all compounds except all-trans retinal, consistent with the proximities of excitation and/or emission wavelengths to molecular resonances. Estimates of probe orientation and location in the membrane electric field show that, for the far-from-resonance case, the shot noise-limited signal/noise ratio depends on the location of the probe in the membrane, and on χ3 but not on χ2.

On the resonant SHG response of ultra-thin alkali (K, Rb)-covered Si(1 1 1)-7 × 7

Room temperature adsorption of K either on Si(111)-7×7 or on dielectric SiO2-covered Si(111) followed by second-harmonic generation (SHG) observation clearly identified a characteristic resonance enhancement typical to Si(111)-7×7. The polarization selected SHG as a function of coverage obtained at different photon energies between 1.17-eV and 1.55-eV show a similar variation of the SH intensity both for K and Rb adsorption on Si(111)-7×7. For submonolayer coverage, wavelength dependent SHG peak observed around 0.4 monolayer (ML) was followed by an SHG peak around 0.9 ML that was less dependent on the wavelength. Previous proposals for an interpretation of the former peak have been questioned. Instead, the former peak has been suggested as being a resonant enhancement due to the transition between alkali atomic-derived electronic states, while the origin of the latter peak remains unidentified. Multiple SHGs of different origins are identified through a phase measurement of SH fields.

Electronic structure, linear, and nonlinear optical responses in magnetoelectric multiferroic material BiFeO3

BiFeO(3) has attracted great interest for its multiferroic property. The spontaneous electric polarization, multiferroism, and static magnetoelectric coupling have been widely studied both experimentally and theoretically. Here, in this paper, we report on the effects of magnetic ordering, spin fluctuation, and external magnetic field on the linear dielectric function and second-harmonic generation (SHG) in multiferroic BiFeO(3). First, our generalized gradient approximation plus Hubbard U calculations reproduce very well experimental data of linear dielectric function. In the mean time, it is revealed that SHG susceptibilities differ dramatically between antiferromagnetic configuration and ferromagnetic one, which is due to the enhanced contrast in the double-photon resonance absorption. Further Monte Carlo simulation of the coupling between electric order and spin-pair correlation function is presented for the spin fluctuation dependence of SHG. The significant nonlinear optical magnetoelectric effect around the Neel temperature provides novel route to enhancing magnetoelectric coupling in multiferroic materials.

In vivo, pixel-resolution mapping of thick filaments' orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy

The polarization dependence of second harmonic generation (SHG) microscopy is used to uncover structural information in different muscle cells in a living Caenorhabditis elegans (C. elegans) nematode. This is done by using a generalized biophysical model in which element ratios for the associated second-order nonlinear tensor and angular orientations for thick filaments are retrieved using a pixel-by-pixel fitting algorithm. As a result, multiple arbitrary orientations of thick filaments, at the pixel-resolution level, are revealed in the same image. The validity of our method is first corroborated in well-organized thick filaments such as the nonfibrilar body wall muscles. Next, a region of the nonstriated muscular cells of the pharynx is analyzed by showing different regions with homogenous orientations of thick filament as well as their radial distribution. As a result, different sets of the nonstriated muscle cell groups in the pharynx of this nematode were exposed. This methodology is presented as a filtering mechanism to uncover biological information unreachable by common intensity SHG microscopy. Finally, a method to experimentally retrieve the distribution of the effective orientation of active SHG molecules is proposed and tested.

Second harmonic generation by periodically-structured metal surfaces

We present an approach to calculating second harmonic generation from periodically-structured metal surfaces. It requires the numerical solution of Maxwell's equations at both the first and second harmonic, but the electronic response to these fields is treated by a parametrization scheme developed earlier. Several model systems are considered, including metal patches of various shapes or holes in a metal film. Detailed calculations using the finite-difference time-domain method lead to predictions of the frequency dependence of second harmonic generation for different diffracted beams and polarizations. There is more spectral structure than what is evident in the linear reflection or transmission.

Efficient second harmonic generation in ZnO nanorod arrays with broadband ultrashort pulses

Broadband frequency-doubling properties of c-axis oriented zinc oxide (ZnO) nanorod arrays grown by low-temperature chemical bath method on glass substrate were studied. The maximum effective nonlinearity was found to be about 7.5 times higher than that of a type-I beta-barium borate crystal for a pump intensity of 5.5×1010 W/cm2. The angular dependence of second harmonic generation (SHG) was determined experimentally. The measured spectral profile of SHG was found to be in good agreement with theoretical simulations.

Dependence of second-harmonic generation in ferroelectric liquid crystals with a defect on the optical gap

Second-harmonic generation (SHG) in ferroelectric liquid crystal with a twist defect is studied by de Vries' solution. It is shown that the width of the photonic band gap for the SH wave is an important factor to determine the saturation length. SHG is effectively enhanced by using narrow photonic band gaps.