Third-harmonic Generation Experiments Research Articles

LGYSB:Nd─High-Performance Lasing in the Near-Infrared Region.

Three incongruent melting LawNdxGdyYzSc4-w-x-y-z(BO3)4 (LGYSB:Nd) crystals with different Y concentrations (z = 0.15, 0.05, and 0.025) have been grown by the Czochralski method for the first time. The LGYSB:Nd-type crystals exhibit an acentric structure similar to that of the natural mineral huntite CaMg3(CO3)4, with space group R32. The composition of the LGYSB:Nd_3 (z = 0.025) crystal grown from the starting melt composition La0.628Gd0.547Y0.025Nd0.05Sc2.75(BO3)4 was measured by inductively coupled plasma mass spectrometry method, and it was found to be La0.6794Gd0.4105Y0.0178Nd0.0381Sc2.8542(BO3)4. The transversal spatial distribution of the refractive index in the LGYSB:Nd_3 crystal was investigated. Third-order nonlinear optical susceptibility χ(3) of the LGYSB:Nd_3 crystal was determined from third-harmonic generation experiments with ultrashort (fs) laser pulses. The optical transmission spectrum was measured in the range of 200-2000 nm. The absorption cross-section at 808 nm in σ-polarization was determined to be 1.18 × 10-19 cm2 for the LGYSB:Nd_3 crystal. The 10K absorption spectra revealed that the Nd3+ ions occupy only La3+ cationic sites in the LGYSB host matrix. The emission cross-section at 1064 nm in σ-polarization was determined to be σem(σ) = 1.74 × 10-19 cm2 for the LGYSB:Nd_3 crystal. The fluorescence lifetime was found to be τ = 115 μs for all of the LGYSB:Nd crystals. The LGYSB:Nd_3 laser was operated at an emission wavelength of 1062 nm with very high slope efficiencies of ηsa = 0.74 and ηsa = 0.64 in quasi-cw and cw regimes, respectively.

Quench-drive spectroscopy and high-harmonic generation in BCS superconductors

In pump-probe spectroscopies, THz pulses are used to quench a system, which is subsequently probed by either a THz or optical pulse. In contrast, third-harmonic generation experiments employ a single multicycle driving pulse and measure the induced third harmonic. In this work, we analyze a spectroscopy setup where both a quench and a drive are applied and two-dimensional spectra as a function of time and quench-drive delay are recorded. We calculate the time evolution of the nonlinear current generated in the superconductor within an Anderson-pseudospin framework and characterize all experimental signatures using a quasiequilibrium approach. We analyze the superconducting response in Fourier space with respect to both the frequencies corresponding to the real time and the quench-drive delay time. In particular, we show the presence of a transient modulation of higher harmonics, induced by a wave mixing process of the drive with the quench pulse, which probes both quasiparticle and collective excitations of the superconducting condensate.

Current-assisted Raman activation of the Higgs mode in superconductors

The Higgs mode in superconductors is a scalar mode without electric or magnetic dipole moment. Thus, it is commonly believed that its excitation is restricted to a nonlinear two-photon Raman process. However, recent efforts have shown that a linear excitation in the presence of a supercurrent is possible, resulting in a new resonant enhancement at $\Omega=2\Delta$ with the driving light frequency $\Omega$ and the energy of the Higgs mode $2\Delta$. This is in contrast to the usual $2\Omega = 2\Delta$ resonance condition found in nonlinear third-harmonic generation experiments. In this communication, we show that such a linear excitation can still be described as an effective Raman two-photon process, with one photon at $\omega=2\Delta$ and one virtual photon at $\omega=0$ which represents the dc supercurrent. At the same time we demonstrate that a straightforward infrared activation with a single photon excitation is negligible. Moreover, we give a general context to our theory, providing an explanation for how the excitation of the Higgs mode in both THz quench and drive experiments can be understood within a conventional difference-frequency generation or sum-frequency generation process, respectively. In such a picture, the observed new resonance condition $\Omega = 2\Delta$ is just a special case. With the same approach, we further discuss another recent experiment, where we find a suppression of odd order higher harmonics in the presence of a dc supercurrent.

Theory of driven Higgs oscillations and third-harmonic generation in unconventional superconductors

Higgs spectroscopy is a new field in which Higgs modes in nonequilibrium superconductors are analyzed to gain information about the ground state. One experimental setup in which the Higgs mode in s-wave superconductors was observed is periodic driving with THz light, which shows resonances in the third-harmonic generation (THG) signal if twice the driving frequency matches the energy of the Higgs mode. We derive expressions of the driven gap oscillations for arbitrary gap symmetry and calculate the THG response. We demonstrate that the possible Higgs modes for superconductors with non-trivial gap symmetry can lead to additional resonances if twice the driving frequency matches the energy of these Higgs modes and we disentangle the influence of charge density fluctuations (CDF) to the THG signal within our clean-limit analysis. With this we show that THG experiments on unconventional superconductors allow for a detection of their Higgs modes. This paves the way for future studies on realistic systems including additional features to understand the collective excitation spectra of unconventional superconductors.

Tuning NLO Susceptibility in Functionalized DNA

The reversible tunability of the third‐order nonlinear optical susceptibility of a deoxyribonucleic (DNA)‐based thin film, doped with a photochromic molecule, by light is shown. This tunability is demonstrated by optical third‐harmonic generation (THG) experiments at the excitation wavelength of 1064 nm. It is based on the light control of the two photon resonance when shuttling from the merocyanine (MR) to the spiropyran (SP) form and on the changes in the π electron conjugation length. A total decrease of the THG intensity by a factor of 25, that is the NLO susceptibility decreases by a factor of 5, is observed when a complete transformation from the MR to the SP form is achieved. This observation not only applies to THG experiments, the NLO susceptibility tunability is also obvious in other NLO processes that implicate the interaction of 4 photons. Second harmonic generation experiments show the same results, but are less obvious for practical application. The potential applications of the effect in photonics are also discussed.

Assessment of the global and range-separated hybrids for computing the dynamic second-order hyperpolarizability of solution-phase organic molecules

The dynamic second-order hyperpolarizability from the third-harmonic generation experiment, 〈γ〉(−3ω;ω;ω;ω), of 59 solution-phase organic molecules has been theoretically calculated and compared with available experimental data. The DFT/6-311+G(2d,p)//(CAM-)B3LYP/6-31G(2df,p) level of theory with the polarizable continuum model was employed to evaluate the static second-order hyperpolarizability. The theoretical static values were then corrected to dynamic estimates of 〈γ〉(−3ω;ω;ω;ω) by employing a two-level approximation (Chen et al. in J Chem Phys 101(7):5860–5864, 1994). Calculated results showed that for the property of interest, the range-separated hybrids provided more accurate and consistent estimate than the global hybrids and the CAM-B3LYP optimized geometry delivered more accurate estimate than the B3LYP optimized geometry.

355nm laser generation based on Na3La9O3(BO3)8 crystal

Na3La9O3(BO3)8 (NLBO) single crystals with size up to 35 × 20 × 15 mm3 have been grown by the top-seeded solution growth (TSSG) method. The phase-matching (PM) conditions and the effective nonlinear coefficients were fully calculated for third-harmonic generation (THG) at different wavelengths. The THG experiments for NLBO crystals were performed for the first time. A 355 nm UV light output of 1.9 mW was successfully obtained under a picosecond Nd:YAG laser. Through the calculations of effective nonlinear coefficients, we believe that the output power and conversion efficiency will further increase if the high optical quality NLBO samples can be utilized.

High-efficiency third harmonic generation at 355nm based on La_2CaB_10O_19

La2CaB10O19 (LCB) crystals with size up to 55 × 35 × 25 mm3 have been grown by the top-seeded solution growth (TSSG) method. The refractive indices were accurately measured over the full transmission range, and the second-order nonlinear optical coefficients were determined by the Maker fringe technique. The phase-matching(PM) conditions were calculated for third-harmonic generation (THG) at different wavelengths. The THG experiments for type I and type II LCB crystals were performed. For type I LCB, a 355 nm UV light output of 5.0 mW corresponding to the conversion efficiency of 28.3% was generated under a picosecond Nd:YAG laser, and 16 W with the efficiency of 17.5% was generated under a nanosecond 1064 nm pumping source. For type II LCB, 3.5mW THG output with conversion efficiency of 21.1% was obtained under a picosecond Nd:YAG laser, and 7.6 W with the efficiency of 7.9% was generated under a nanosecond 1064 nm pumping source. The results indicated that the LCB crystal is a promising UV nonlinear optical material because of its good THG performance and nonhygroscopicity.

Synthesis and third-order nonlinear optical studies of a novel four-coordinated organoboron derivative and a bidentate ligand: The effect of the N → B coordinative bond

The third-order nonlinear optical characterization of a new boronate ( 2) derived from 4-dimethylaminocinnamaldehyde was performed by third-harmonic generation (THG) at the infrared wavelength of 1550 nm. Compound 2 was prepared from the reaction of diphenylboronic acid and the bidentate ligand ( 1) and characterization was made through UV, IR, 1H, 11B, and 13C NMR and X-ray diffraction. The THG experiments showed that the N → B coordinative bond in 2 enhanced the second molecular hyperpolarizability of the type γ (3)(−3ω, ω, ω, ω) by a factor of three with respect to the value exhibited by the ligand 1. On the other hand, Z-scan studies at 800 nm (femtosecond (fs) pulses) also showed that such coordinative bond increased the nonlinear absorption (two-photon absorption (TPA)) in 2 with respect to 1. These studies demonstrate that the N → B coordinative bond facilitates the polarization of the electronic π-system, a situation that optimizes the third-order NLO response. Results on the excited state absorptions in these compounds are also presented.

Time resolved measurements of melting and solidification in Si using third harmonic generation of light

Time resolved measurements of melting and solidification on (001) Si using third harmonic generation (THG) were performed with subpicosecond time resolution. Following 120fs laser pulses at fluences above the melt threshold, the circularly polarized THG signal decreases by over three orders of magnitude. It regains its original intensity on solidification after ≈2ns. The authors show that the THG signal is sensitive to specimen temperature, decreasing by a factor of ≈5 between 298K and the melting temperature. The work demonstrates that complete thermal and phase histories can be obtained during ultrafast laser heating using single-shot THG experiments.

Influence of the central metal atom on the nonlinear optical properties of MPcs solutions and thin films

Third order nonlinear optical susceptibility ( χ 〈3〉) of metallophthalocyanines (MPcs, where M = Co, Cu, Zn, Mg) thin films and solutions was investigated by standard backward degenerate four wave mixing (DFWM) method at 532 nm. Third harmonic generation (THG) measurement at 1064 nm performed on MPcs thin films is also discussed. MPcs thin films were grown by conventional thermal evaporation in high vacuum and solution were dissolved in tetrahydrofuran (THF), in which the studied materials are soluble. In the case of microscopic nonlinearity, we calculated the second order hyperpolarizability ( γ) for MPcs solutions. We found that the χ 〈3〉 and the γ values are affected by the nature of the central metal atom. We also found that the χ DFWM 〈 3 〉 value is larger than that measured via THG experiment. The variation in χ 〈3〉 values occurs due to the different resonance contributions.

Lineshape of harmonic generation by metallic nanoparticles and metallic photonic crystal slabs

We study the linear- and nonlinear-optical lineshapes of metal nanoparticles (theory) and metallic photonic crystal slabs (experiment and theory). For metal nanoparticle ensembles, we show analytically and numerically that femtosecond second- or third-harmonic-generation (THG) experiments together with linear extinction measurements generally do not allow to determine the homogeneous linewidth. This is in contrast to claims of previous work in which we identify a technical mistake. For metallic photonic crystal slabs, we introduce a simple classical model of two coupled Lorentz oscillators, corresponding to the plasmon and waveguide modes. This model describes very well the key experimental features of linear optics, particularly the Fano-like lineshapes. The derived nonlinear-optical THG spectra are shown to depend on the underlying source of the optical nonlinearity. We present corresponding THG experiments with metallic photonic crystal slabs. In contrast to previous work, we spectrally resolve the interferometric THG signal, and we additionally obtain a higher temporal resolution by using 5 fs laser pulses. In the THG spectra, the distinct spectral components exhibit strongly different behaviors versus time delay. The measured spectra agree well with the model calculations.

Calculation of refractive indices and third-harmonic generation susceptibilities of liquid benzene and water: Comparison of continuum and discrete local-field theories

The refractive indices (linear response) and the nonlinear susceptibility for third harmonic generation (THG) at λ=1064 nm of liquid water and benzene are predicted, using ab initio molecular (hyper)polarizabilities and local-field corrections calculated according to the Lorentz model, the generalized reaction-field model of Onsager, and a discrete local-field theory applied to liquid structures obtained by classical molecular simulation methods. The ratio of the calculated THG susceptibilities for the two liquids is compared with experimental results, in order to avoid ambiguities concerning the factors used to calibrate the THG experiments. All models are able to reproduce the experimental refractive indices of both liquids accurately, but are less successful for the THG susceptibility. The discrete local-field corrections for the THG susceptibility are considerably larger than those of the continuum model in the form of the more accurate extended reaction-field approach.

Synthesis and physical investigation of donor-donor and acceptor-acceptor end-functionalized monodisperse poly(triacetylene) oligomers.

Two series of monodisperse, terminally donor-donor [D-D, D=4-(dimethylamino)phenyl] and acceptor-acceptor [A-A, A=4-nitrophenyl] functionalized poly(triacetylene) (PTA) oligomers ranging from monomer to hexamer were synthesized by oxidative Hay oligomerization under end-capping conditions. The corresponding D-D and A-A end-substituted polymers with an average degree of polymerization (DP) of n approximately 18 and n approximately 12, respectively, were also prepared and served as reference points for the corresponding infinitely long polymers. These terminally functionalized PTA oligomers and polymers are yellow- to orange-colored compounds, displaying excellent solubility in aprotic solvents with melting points above 200 degrees C for the hexamers. For the 4-(dimethylamino)phenyl substituted compounds, a consistent first oxidation potential around +0.42 V versus Fc/Fc+ (ferrocene/ferricinium) was observed, whereas the 4-nitrophenyl functionalized systems underwent a reversible reductive two-electron transfer around -1.40V versus Fc/Fc+. The nature of the end-groups has a dramatic influence on the electronic absorption spectra. Saturation of the linear optical properties in the D-D series occurs at significantly shorter chain-length [effective conjugation length (ECL) of n approximately 4 monomer units] than in the A-A substituted or the previously reported Me3Si- and Et3Si-end-capped PTA oligomer series (ECL: n approximately 10 monomer units). Similar observations with respect to the ECL were made by measurement of the Raman-active v(C triple bound C) stretches. Third-harmonic generation (THG) and degenerate four-wave mixing (DFWM) experiments showed that shorter oligomers of terminally D-D or A-A functionalized PTAs display higher second hyperpolarizabilities gamma than the corresponding R3Si-end-capped series (R=alkyl). Moreover, they disclose a distinct peak of the nonlinearity per monomer unit at intermediate backbone lengths. In THG experiments, the second hyperpolarizabilities for long D/A-functionalized PTA oligomers attained the same saturation values as observed for the corresponding R3Si-end-capped rods. The nonlinearities measured by DFWM of the D-D and A-A substituted PTAs were found to be larger than for the silylated ones, which can be explained by the closeness of the two-photon resonance.

Growth and noncritical phase-matching third-harmonic-generation of Gd xY 1− xCa 4O(BO 3) 3 crystal

A series of solid-solution crystals Gd x Y 1− x Ca 4O(BO 3) 3 (Gd x Y 1− x COB) ( x=0–1) were grown by the Czochralski (CZ) method. The distribution coefficients of Gd 3+ and Y 3+ ions in Gd x Y 1− x COB crystal are 0.952 and 1.069, respectively, which were measured by X-ray fluorescent analysis. So Y 3+ ions are easier to incorporate into Gd x Y 1− x COB crystal lattice than Gd 3+ ions. The composition of crystal from the seed to the bottom is homogeneous. The noncritical phase-matching (NCPM) third-harmonic generation (THG) of Nd : YAG laser (1064 nm) can be realized in Gd 0.37Y 0.63COB crystal along the Y-principal axis. The UV cutoff of Gd 0.37Y 0.63COB is at 320 nm when measured by HITARCHI U-3500 spectrophotometer. For the first time, THG experiments of Gd 0.37Y 0.63COB crystal were performed using Q-switched Nd : YAG laser. The output energy is up to 88.2 mJ at 355 nm when the input energy is 600 mJ for 11 mm long Gd 0.37Y 0.63COB crystal. The THG optical–optical conversion efficiency of Gd 0.37Y 0.63COB crystal is 14.7%.

Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities

Cascaded second-order contributions to third-harmonic generation are analyzed in detail, and are exploited to obtain reliable reference values for third-order nonlinear optical susceptibilities at several wavelengths. We describe the influence of boundary conditions on the measured properties for the case of high nonlinearity crystals such as ${\mathrm{KNbO}}_{3}$ and the organic salt 4-N, N${\ensuremath{-}\mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\ensuremath{-}4}^{\ensuremath{'}}$-${N}^{\ensuremath{'}}$-methylstilbazolium toluene-p-sulfonate (DAST). Wavelength dispersion relations for the electronic third-order susceptibilities derived from third-harmonic generation experiments are discussed. Our reference standards allow a comparison of the third-harmonic generation results with measurements of the Kerr susceptibility determined with degenerate four-wave mixing and the z-scan technique and shows that ${\ensuremath{\chi}}^{(3)}(\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})>~{\ensuremath{\chi}}^{(3)}(\ensuremath{-}3\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})$ in the investigated wavelength range. The investigation of structure-property relationships between the perovskite crystals ${\mathrm{KNbO}}_{3}$ and ${\mathrm{KTaO}}_{3}$ indicates similar bond nonlinearities in these two compounds.

Calculation of macroscopic first- and third-order optical susceptibilities for the benzene crystal

Starting from a set of high-level ab initio frequency-dependent molecular first- and third-order polarizabilities, the macroscopic first-order (linear) and third-order (cubic) susceptibilities of the benzene crystal are calculated. Environmental effects are taken into account using a rigorous local-field theory and are compared with the anisotropic Lorentz field factor approach. The experimentally determined first-order susceptibility of crystalline benzene is accurately reproduced. Dispersion curves for the first-order susceptibility and results for electric-field-induced second-harmonic generation and third-harmonic generation experiments are predicted. Comparison with similar calculations conducted in the course of molecular simulations of liquid benzene shows that the theoretical results for the two phases are of comparable accuracy. Overall, the results show that for the fairly compact nonpolar benzene molecules, environmental effects on the effective molecular response are small.

Second- and third-order nonlinear optical properties of multilayer and composite C 60-based thin films

The nonlinear optical properties of C 60-based composites and multilayered charge-transfer structures with 5,10,15,20-tetraphenyl-21 H,23 H-porphine (TPP) and 5,6,11,12-tetraphenylnaphthacene (rubrene) (TPN) acting as electron donors are studied by transverse optical second- and third-harmonic generation. The results are compared with those obtained on pristine and vacuum-photolyzed C 60 thin films. Second-harmonic generation (SHG) is observed from composite films containing C 60 molecules. A significant enhancement in SHG signal is observed in the multilayered structures. This result is interpreted in terms of a ground state permanent electron transfer from the electron-donating molecules to C 60. The third-harmonic generation experiments show an enhancement of the cubic susceptibility from vacuum-photolyzed C 60 thin films.

Third-order nonlinear optical susceptibilities of the Langmuir–Blodgett films of octa-substituted metallophthalocyanines

The third-order susceptibilities χ(3)(−3ω:ω,ω,ω) of Langmuir–Blodgett films of a series of octasubstituted metallophthalocyanines have been measured by third-harmonic generation experiments at 1.064 and 1.904 μm. For the latter excitation wavelength a marked enhancement of the nonlinearity for the cobalt-containing compound has been found, and χ(3) values are one order of magnitude larger than for the other systems. The effect has been associated to the role of two-photon allowed metal (possibly d−d) transitions in the cobalt derivative.

Effect of the Solid State Structure on the Third-Order Nonlinear Optical Response of Poly(2,5-dialkoxy-p-phenyleneethynylene)s

The third-order nonlinear optical (NLO) properties of a series of poly(2,5-dialkoxy-p-phenyleneethynylene)s (PPEs) have been investigated in solution and in the solid state. In these PPEs, different alkoxy side chains are attached to the rigid-rod polymer main chain, leading to a series of polymers having an identical conjugated backbone but different supramolecular structures in the solid state. The nonresonant third-order NLO susceptibilities χ(3)(−3ω;ω,ω,ω) were measured by third-harmonic generation experiments. χ(3) values of up to 7.5 x 10-20 m2/V2 in solution and 14 × 10-20 m2/V2 in the solid state were determined. In solution, the NLO susceptibilities were found to be proportional to the content of polymer backbone, which depends on the functionalization of the PPEs. The solid state NLO susceptibilities were found to be related to the degree of long-range order in the samples, increasing with increasing order. In samples which adopt only a small extent of long-range order, the rigid-rod conjugated polymer backbones behave if they were “dissolved” in a hydrocarbon solvent, and consequently the nonlinear optical susceptibilities are comparable to those determined for solutions of these polymers. In films in which the polymer chains were found to adopt lamellar type supramolecular structures, the coplanar orientation of the conjugated polymer backbones is assumed to lead to intermolecular electronic interactions which give rise to extended conjugation lengths and hence lead to an increase of the nonlinear optical response.