Second Harmonic Generation Coefficients Research Articles

Second harmonic generation in polymers containing a new azo chromophore based on phenylnitrobenzoxazole

AbstractThe synthesis of the new chromophores 2‐{4‐[4‐(N,N‐dihydroxyethylamino)‐phenylazo]‐phenyl}‐6‐nitrobenzoxazole (1) and 4‐[4‐(N,N‐dihydroxyethylamino)phenylazo]‐benzoic acid (2) is described. Three homopolymers obtained by the polycondensation of 1 with propyloxy‐terephthalic acid and 1 and 2 with 2,4‐tolylenediisocianate as well as two copolymers obtained by polycondensation of appropriate mixtures of chromophores 1 and 2 with 2,4‐tolylene‐diisocianate were prepared and characterized. All as‐prepared polymers but one (homopolyurethane of 1) were amorphous and exhibited good optical clarity, good thermal stability above the glass transition, and solubility in organic solvents. The second‐order nonlinear optical behavior of the amorphous polymers was investigated on spin‐coated corona‐poled films through second harmonic generation (SHG) experiments at 1064 nm. At this wavelength, resonance‐enhanced values of the SHG coefficient d33 were found in the range between 6 and 34 pm/V where higher values were observed for polymers with a higher molar content of 1. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1468–1475, 2002

Exploiting structure/property relationships in organic non-linear optical materials: developing strategies to realize the potential of TCNQ derivatives

The intrinsic relationship between molecular structure and non-linear optical (NLO) properties is exploited with regard to materials for use in second-harmonic generation (SHG). A bond-length-alternation (BLA) study is performed on all available crystal structures of tetracyanoquinodimethane (TCNQ) derivatives in order to predict better SHG contenders. This builds upon a previous bond-length-alternation study that was carried out on a series of TCNQ derivatives. There, a formalism was derived to calculate the relative level of delocalisation within the central TCNQ fragment and relate this to the molecular hyperpolarizability, β, the measure of the SHG coefficient on the molecular scale. This formalism is based upon the ‘strength–length’ relationship in bonds that has been validated via a charge-density study on one of these TCNQ derivatives using a topological approach. The results of the study are grouped according to the relative levels of delocalisation present in each molecule and compared with known SHG contenders. The promise of TCNQ derivatives for non-linear optics lies partly in their typically high molecular dipole moments, μ. However, large values of μ usually force the molecules to pack centrosymmetrically in a crystalline environment since the dipoles oppose each other in close proximity, and centrosymmetry precludes any SHG effect since this property is a third-rank tensor. A strategy for forming these materials in a solid-state head-to-tail arrangement that is regular but not crystalline is therefore highly desirable. A feasibility study on the adsorption of a TCNQ derivative into zeolite, ZSM-5, shows that this objective may be achievable in this class of materials, thus providing a mechanism for realizing the potential of highly SHG-active materials identified in the bond-length-alternation study.

Second-Order Optical Nonlinearities and Related Numerical Estimates in Bulk Ferroelectrics

Second and third order nonlinear optic coefficients can be calculated from the Landau expansion for paraelectric and ferroelectric phases by means of the Landau-Khalatnikov dynamical equations. The focus here is on second-order phase transitions and an expression for the second-harmonic generation coefficient is given. Numerical estimates for the relevant parameters using data for PbTiO 3 are presented. We then develop the model further for second harmonic generation.

Mechanism for linear and nonlinear optical effects in monoclinic bismuth borate (BiB3O6) crystal

Electronic structure calculations of BiB3O6 crystal from first principles are performed based on a plane-wave pseudopotential method. The linear refractive indices and the static second-harmonic generation (SHG) coefficients are also calculated by the SHG formula improved by our group. The calculated values are in good agreement with the experimental values. A real-space atom-cutting method is adopted to analyze the respective contributions of the cation and anionic groups to the optical response. The results show that the contribution of the (BiO4)5− anionic group to the SHG coefficients is more pronounced than that of the (BO3)3− and (BO4)5− groups.

Temporal Stability of Second-Order Optical Nonlinearity of Polyurethane: Influence of Poling Conditions

Poling-condition dependence of second-order optical nonlinearity of a polyurethane sample has been studied by the second-harmonic generation (SHG) method. Not only the magnitude of an SHG coefficient (d31) but also the temporal stability of d31 depended on the poling conditions. The dependence of the temporal stability was weaker than that of the magnitude. The poling temperature (Tpol) affected the stability more than the poling voltage, the poling time and the preheating time. The Tpol leading to the best temporal stability agreed approximately with that leading to the highest d31. The dependence of the temporal stability is discussed from the viewpoint of molecular dynamics.

Second-harmonic generation of I-III-VI2chalcopyrite semiconductors: Effects of chemical substitutions

We report first-principles calculations of the second-order optical response coefficients in the I-III-${\mathrm{VI}}_{2}$ $(\mathrm{I}=\mathrm{A}\mathrm{g},\mathrm{C}\mathrm{u};$ $\mathrm{I}\mathrm{I}\mathrm{I}=\mathrm{G}\mathrm{a},\mathrm{I}\mathrm{n};$ $\mathrm{V}\mathrm{I}=\mathrm{S},\mathrm{S}\mathrm{e},\mathrm{T}\mathrm{e})$ chalcopyrite semiconductors. The computational approach uses the length-gauge formulation of perturbation theory which explicitly separates pure interband from mixed intraband-interband contributions. The expressions for static and frequency dependent second-harmonic generation coefficients are evaluated from band structures based on the local density approximation but including semiempirical gap corrections. The linear muffin-tin orbital method is used to calculate the required band structures and matrix elements. The results are in good agreement with experiment for the compounds for which data are available and provide predictions in the other cases. The trends show that the dominating factor determining ${\ensuremath{\chi}}^{(2)}$ is the anion rather than the group I or group III cation. The ${\ensuremath{\chi}}^{(2)}$ values clearly fall into separated groups with increasing value going from S to Se to Te. While this correlates approximately inversely with the band gap, several exceptions are notable: (1) Cu compounds have smaller gaps than corresponding Ag compounds and nevertheless have slightly lower ${\ensuremath{\chi}}^{(2)};$ (2) ${\mathrm{AgGaTe}}_{2}$ has a higher gap than ${\mathrm{AgInSe}}_{2}$ but nevertheless has a much higher ${\ensuremath{\chi}}^{(2)}.$ An analysis of the various contributions to the frequency dependent imaginary part of the response functions, $\mathrm{Im}{{\ensuremath{\chi}}^{(2)}(\ensuremath{-}2\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})},$ is presented in an attempt to correlate the ${\ensuremath{\chi}}^{(2)}$ values with band structure features. The main findings of this analysis are that (1) there is a large compensation between intra/inter- and interband contributions frequency by frequency as well as in the static values; (2) the static ${\ensuremath{\chi}}^{(2)}$ value is strongly affected by the sign of the low frequency parts of these separate contributions; (3) these low frequency parts correspond to only a few valence and conduction bands and only to so-called $2\ensuremath{\omega}$ resonances; (4) the general shape of the $\mathrm{Im}{{\ensuremath{\chi}}^{(2)}(\ensuremath{-}2\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})}$ response functions is determined by the band structures alone while the intensity, which ultimately explains the difference between tellurides and selenides, arises from the magnitude of the matrix elements. Starting from ${\mathrm{AgGaSe}}_{2},$ the smaller effect on the ${\ensuremath{\chi}}^{(2)}$ due to In subsitution for Ga than to Te substitution for Se can be explained by the fact that the Ga to In substitution changes the gap only in a small region near the center of the Brillouin zone, while the Se to Te substitution changes the gap throughout the Brillouin zone. This shows that contributions from other parts of the Brillouin zone than the center dominate the behavior. The difference between Cu and Ag based compounds can be explained on the basis of a different degree of compensation of inter- and intra/interband contributions.

Preparation of Pyridinium Iodide-CdI2 Hybrids for Nonlinear Optical Materials

In order to obtain a new type of organic-inorganic hybrid material for nonlinear optics, two pyridinium-CdI2 crystals, i.e., bis(4-cyano-1-methyl-pyridinium) tetraiodocadmate (CNP/CdI4) and bis(4-dimethylamino-1-methylpyridinium) tetraio-docadmeate (DAP/CdI4) were prepared. From X-ray crystal structure analyses, the inorganic parts of both of the crystals are found to be the tetrahedral [CdI4]2- structure. Although the CNP/CdI4 crystals have a centrosymmetric layered structure, the DAP/CdI4 crystals do not have layered structures resulting in non-centrosymmetric space group Cc and second-order nonlinear optical activity. Thus, the second-harmonic generation (SHG) coefficients (d) of the DAP/CdI4 crystal were estimated using the oriented gas model. In spite of the shorter cutoff wavelength of DAP/CdI4 compared with that of the well-known 2-methyl-4-nitroaniline (MNA) crystal, the maximum d value was expected to reach one-third of that of the MNA in the diagonal component.

CALCULATIONS FOR THE LINEAR AND NONLINEAR OPTICAL COEFFICIENTS OF NaNO2 CRYSTAL

Based on a plane-wave pseudopotential method,the electronic structure calculations of NaNO2 from first principles are perforined.The linear refractive indices and the static second-harmonic generation (SHG) coefficients are also calculated by the SHG formula improved by us.The calculated values are in good agreement with the experimental values.A real-space atom-cutting method is adopted to analyze the respective contributions of the cation and anionic groups to optical response.The results show that the contribution of the (NO2)- anionic group to the birefringence and the SHG coefficients is dominated in NaNO2 crystal,which is in agreement with the result obtained by the anionic group model.

Crystallization and optical nonlinearity in GeO2–SiO2 glass poled with ArF excimer-laser irradiation

We report on crystallization and second- and third-order optical nonlinearities of GeO2–SiO2 glass poled with ArF laser irradiation. With laser power and 100 mJ/cm2/pulse, the treatment generates crystallites in the glass, provided that the poling field strength is greater than 0.5×105 V/cm. Its crystal structure is possibly the cristobalite phase of the Ge–Si–O system. A large coefficient of second-harmonic generation (SHG), d33, is induced in the glass with the crystallite generation, and its value is comparable to d22 of LiNbO3. Moreover, the third-order optical susceptibility χ(3) increases by a factor of approximately 15 compared to that of glass without the crystallites. Even after the d33 coefficient decays out, the crystallites and χ(3) are retained. The result suggests that the large SHG in the glass is not induced from inert second-order nonlinearity of the crystallites, but the main origin of the induction is the associated effective second-order nonlinearity with the formation of the space-charge field.

Mechanism for linear and nonlinear optical effects inLiB3O5,CsB3O5,andCsLiB6O10crystals

Electronic structure calculations of ${\mathrm{LiB}}_{3}{\mathrm{O}}_{5},$ ${\mathrm{CsB}}_{3}{\mathrm{O}}_{5},$ and ${\mathrm{CsLiB}}_{6}{\mathrm{O}}_{10}$ crystals from first principles are performed based on a plane-wave pseudopotential method. The static second-harmonic generation (SHG) coefficients are calculated at the independent-particle level with a formalism improved by our group and co-workers [Phys. Rev. B 60, 13 380 (1999)]. A real-space atom-cutting method is adopted to analyze the respective contributions of the cation and anionic groups to optical response. The calculated refractive indices and SHG coefficients are in good agreement with the experimental values. On the basis of these calculations, the influence of the cations on the band gaps and the optical responses is evaluated. The results show that with the increase of their radius their contributions to SHG become slightly more pronounced.

Stress-induced enhancement of second-order nonlinear optical susceptibilities of barium titanate films

A method introducing stress is suggested to enhance optical nonlinearity. Three stress induced samples of BaTiO3 thin film, BaTiO3/SrTiO3 superlattice, and cerium doped BaTiO3/SrTiO3 superlattice were epitaxially grown on SrTiO3 (100) substrates by laser molecular beam epitaxy. The measurement of the dependence of the effective second-harmonic generation (SHG) coefficients on the fundamental polarization angle and incident angle indicates that SHG coefficients d33 of the three samples are greatly enhanced, with the maximum value being one order of magnitude larger than that of the bulk BaTiO3 crystal. Our results clearly show that the introduction of stress is a very powerful means to enhance nonlinear optical susceptibility.

Second-Order Nonlinear Optical Properties of the Hybrid-Film of a Clay and a Chiral Metal Complex

Second-harmonic generation (SHG) properties of the hybrid-films of a clay and [δ-Ru (4,7-diphenyl-1,10-phenanthroline)3](ClO4)2 (δ-Ru(dpp)3), which was found to be stable enough over a very long time, were studied. The ratio of the SHG signal intensity between Z-and Y-Type films of δ-Ru(dpp)3 has been compared. Furthermore, the SHG coefficient d 33 at 1.06 μm is determined as 30 pm/V for the Y-Type hybrid-film of δ-Ru(dpp)3.

Determination of the nonlinear optical coefficients of YCa_4O(BO_3)_3 crystal

The nonlinear optical coefficients of YCa4O(BO3)3 (YCOB) have been calculated for the first time to the authors’ knowledge by use of the revised Gaussian 92 program on the basis of the anionic group theory. The d11,d12,d32, and d33 coefficients of the crystal were determined by the Maker fringes method at λ=1064 nm, and d13, and d31 were also evaluated by measurement of the Maker fringes. The coefficients determined by the Maker fringes are in agreement with the theoretical values. On the basis of the dij coefficients and the Sellmeier equations, the effective second-harmonic generation (SHG) coefficient deff of YCOB as a function of phase-matching angles θ and Φ was determined. It is interesting that the maximum effective SHG coefficient deff of YCOB is not in the principal plane but is located out of the X–Z plane in the positions θ=65.9°,Φ=36.5° and θ=66.3°,Φ=143.5°. It is also worth noting that the largest deff of YCOB in the region of 0°<θ<90°,90°<Φ<180° is larger than that in 0°<θ<90°,0°<Φ<90°. These calculated results have been proved by the effective SHG coefficient measurements of YCOB and conversion-efficiency measurements of frequency-doubling experiments on Nd:YCOB.

Electric-field frequency dependence of Pockels coefficients in 2-amino-5-nitropyridium dihydrogen phosphate organic–inorganic crystals

The electro-optic and dielectric properties of organic–inorganic 2-amino-5-nitropyridium dihydrogen phosphate crystals were measured near room temperature at a wavelength of 632.8 nm and as a function of an electric-field frequency that varied from 1 kHz to 40 MHz. The frequency dispersion of the electro-optic coefficients and their comparison with the second-harmonic generation coefficients showed that the largest part of the electro-optic properties is electronic in origin (whereas the piezo-optic contribution is small). Results reveal a large anisotropy of the ionic and electronic contributions that is related to the contributions of the organic molecule to nonlinear polarizability.

Second-harmonic generation in Ce:BaTiO_3 nanocrystallites grown by pulsed laser deposition

Ce:BaTiO3 nanocrystallites were prepared on fused quartz substrates by pulsed laser deposition. The structural properties of the nanocrystallites were studied by scanning electron microscopy and x-ray diffraction. The refractive indices and absorption edges were obtained from the optical transmission spectra with an approximate formula. The incidence and polarization angle–dependent second-harmonic generation (SHG) were measured. The effective SHG coefficient was reduced by decreasing the deposition temperature. Some possible mechanisms of the correlation between the SHG coefficient and the deposition temperature are discussed.

Improved method of corona poling for highly developed dipolar orientation

New maleimide-based high-Tg polymer with good solubility (PHND) was synthesized for second-order non-linear optics. The PHND polymer was obtained by radical copolymerization of N-(4-hydroxyphenyl)maleimide and 2-norbornene followed by polymer modifying reactions with 4-[N-ethyl-N-(2-hydroxyethyl)amino]-4′-nitroazobenzene (DR-1) as a dye using Mitsunobu reaction process. High quality thin film was obtained from the PHND due to a good solubility in organic solvents. The films were treated by corona poling technique. In order to achieve the highest possible dipolar orientation, an improved method of corona poling and an optimized condition for treating PHND film were proposed. Optical non-linearity of poled films was measured by second harmonic generation (SHG) and electro-optic (EO) measurement. The PHND polymer poled at the optimized condition exhibited large SHG coefficients (d33) more than 600 × 10−9 e.s.u (250 pm/V) at the wavelength of 1.064 µm for fundamental light source. It should be noted that this value is more than twice as much as that obtained under conventional corona poling conditions. Using the poled PHND thin film with large optical non-linearity, EO device was fabricated and successfully achieved high performance. Copyright © 2000 John Wiley & Sons, Ltd.

Highly sensitive frequency-resolved optical gating in 1.55 [micro sign]m region using organic nonlinear optical crystal for second-harmonic generation

With the aim of realising optical pulse characterisation in the optical communication band at 1.5 /spl mu/m, the authors demonstrate a highly sensitive frequency-resolved optical gating (FROG) using an organic crystal: AANP-amnD (2-adamantylamino-5-nitropyridine) for second-harmonic generation (SHG). The proposed SHG FROG system is an alignment-free fibre-coupled system with a small insertion loss. The high SHG coefficient of the crystal and low insertion loss of the system allow the FROG error to be reduced below 1% at a peak power as low as 4 W.

Crystal Growth, Structure, and Properties of New Nonlinear Optical Materials: K2Ln(NO3)5·2H2O (Ln=La, Ce, Pr, Nd, Sm)

Single crystals of K2Ln(NO3)5·2H2O (Ln=La, Ce, Pr, Nd, Sm) (KLnN) were grown by evaporation in aqueous solution under constant temperature conditions. The structure of KPrN was determined from the single-crystal X-ray diffraction data. The KPrN crystallizes in the orthorhombic space group Fdd2 with parameters a=21.411(3) Å, b=11.2210(10) Å, c=12.208(2) Å, Z=6, V=2933.0(7) Å3, R=0.0240, Rw=0.0603. The powder second harmonic generation (SHG) intensities of KLnN (Ln=La, Ce, Pr, Nd, Sm) are also studied. The results demonstrate that their SHG intensities are 4–9 times larger than that of KDP, in which the KPrN shows the highest SHG coefficient.

Mechanism for linear and nonlinear optical effects inβ−BaB2O4crystals

Electronic structure calculations of $\ensuremath{\beta}\ensuremath{-}{\mathrm{BaB}}_{2}{\mathrm{O}}_{4}$ from first principles are performed based on a plane-wave pseudopotential method, and the linear optical properties are then obtained. The static second-harmonic generation (SHG) coefficients are calculated at the independent-particle level with a formalism originally given by Aversa and Sipe [Phys. Rev. B 52, 14 636 (1995)] and later rearranged by Rashkeev et al. [Phys. Rev. B 57, 3905 (1998)] to explicitly show Kleinman's symmetry. The formalism is improved to be more efficient in reducing the $k$ points necessary for convergence. A real-space atom-cutting method is suggested to analyze the respective contributions of various transitions among ions and ion groups to optical response. The contribution of the cation Ba to SHG effects is found to be not important but non-negligible, while its contribution to birefringence is negligible.

First-principles calculation of the second-harmonic-generation coefficients of borate crystals

We report the calculation of the second-harmonic-generation (SHG) coefficients of ${\mathrm{LiB}}_{3}{\mathrm{O}}_{5}$ (LBO), ${\mathrm{CsB}}_{3}{\mathrm{O}}_{5}$ (CBO), and ${\mathrm{BaB}}_{2}{\mathrm{O}}_{4}$ (BBO) using the linearized augmented plane-wave band method in the local-density approximation with a scissors operator that includes the renormalization of the momentum operator. The analysis that is based on the spectral and spatial decomposition of the calculated results reveals that, for the large component of SHG coefficients, the dominant source of the optical nonlinearities for these borate crystals is the nonlinear response of the high-lying $2p$ electrons of oxygen atoms, while the cations play a minor role even in the heavier Cs and Ba cases, though they dominate the conduction-band minimum. But for the small SHG component, the role of the cation became important, particularly when the isolated anionic group has little contribution due to the restriction of the symmetry. In the case of LBO and CBO, due to the linkage of anionic groups, the contributions of off-ring O atoms are almost the same as those of in-ring O atoms. Yet for BBO where there is no such linkage, the off-ring O atom plays a much more important role than the in-ring O atom does. We also find that the contribution of the virtual-hole process cannot be ignored as is usually done in the semiconductors case.