Second-order Nonlinear Response Research Articles

Nonlinear optical response from single spheres coated by a nonlinear monolayer

We detected the second-order nonlinear response from single isolated spheres comprised from a centrosymmetric material but covered by a layer of a material with strong second-order nonlinear properties and isolated from an ensemble by the optical trapping technique. We show that when large size parameter spheres are used, the measured second-harmonic efficiency deviates strongly from the prediction of the nonlinear Rayleigh scattering theory. Our results are in very good agreement with the predictions from the exact nonlinear Mie scattering theory.

Control of multiphoton excited emission and phase retardation in Kleinman-disallowed hyper-Rayleigh scattering measurements

We describe improvements to the Kleinman-disallowed hyper-Rayleigh scattering (HRS) measurement technique, which can be used to measure all of the rotationally invariant figures of merit for the first molecular nonlinear optical hyperpolarizability tensor βijk. As multiphoton excited fluorescence continues to be an accuracy-limiting factor in any HRS experiment, we have implemented time-resolved single photon counting in HRS using a Ti:sapphire laser. We show, however, that spectral analysis is necessary to ensure that the fluorescence and second harmonic are emitted on different time scales in order to allow temporal separation and thus improved accuracy. We also demonstrate how an electrically controlled liquid-crystal phase retarder can be used to vary the polarization state of the probe light in order to determine the second-order nonlinear response tensor. It was found that results agree with those obtained using a rotating quarter-wave plate to control the polarization state and demonstrate improved precision and reproducibility.

Second-order nonlinear response in mono- and di-substituted triazine derivatives: A combined experimental and theoretical analysis

Abstract Several mono- and di-substituted triazine derivatives are synthesized. Their molecular first hyperpolarizability ( β ) and absorption properties are determined. The observed trends in the β values obtained from the experiments as well as from the theory are in good agreement. In moving from mono- to di-substituted triazine derivatives the absorption maximum ( λ max ) shows a negligible shift, but the β values are enhanced. In most of the cases the dipole moment decreases with increasing substitution. With these advantages new trends for the molecular design of s -triazine compounds for second-order NLO applications are proposed.

Second harmonic generation in boracites

The M3B7O13X (M=Mg, Ni, Cd; X=Cl, Br, I) boracites were synthesized and characterized by x-ray diffraction and second harmonic generation. Their nonlinear optical susceptibility was estimated using the Phillips-Van Vechten-Levine model. The results demonstrate that the nature of the halogen has an insignificant effect on the second-order nonlinear response of the boracites.

Single-Beam and Enhanced Two-Beam Second-Harmonic Generation from Silicon Nanocrystals by Use of Spatially Inhomogeneous Femtosecond Pulses

Optical second-harmonic generation (SHG) is used as a noninvasive probe of the interfaces of Si nanocrystals (NCs) embedded uniformly in an SiO2 matrix. Measurements of the generated SH mode verify that the second-harmonic polarization has a nonlocal dipole form proportional to (E x Delta inverted) E that depends on inhomogeneities in the incident field E, as proposed in recent models based on a locally noncentrosymmetric dipolar response averaged over the spherical NC interfaces. A two-beam SHG geometry is found to enhance this polarization greatly compared to single-beam SHG, yielding strong signals useful for scanning, spectroscopy, and real-time monitoring. This configuration provides a general strategy for enhancing the second-order nonlinear response of centrosymmetric samples, as demonstrated here for both Si nanocomposites and their glass substrates.

Frequency up-conversion of s-triazine derivatives via two photon absorption and second-harmonic generation

A three-branched octupolar compound, 2,4,6-tris[2-(4-N,N-diethylamino)phenylethenyl]-1,3,5-s-triazine (compound III), as well as its one- and two-branched analogues (compounds I and II respectively) have been synthesized. The structures of I and II have been determined by X-ray diffraction. The linear and nonlinear spectra of these compounds regularly vary: (1) the spectral positions (λmax values) of the linear absorption, the single-photon excited fluorescence (SPEF) and the two-photon excited fluorescence (TPEF) show regular red-shifts when the branch number increases from 1 to 3; (2) the spectral intensities, including the linear absorbance emax and the two-photon absorption cross-section σ, the SPEF and the TPEF intensities are all increased significantly when going from I to III. The values of emax/MW and σ/MW (of compounds I, II and III) vary with the ratios of 1.0 : 1.3 : 1.7 and 1.0 : 1.4 : 1.3, respectively. All the photophysical data indicate that by incorporating more branches into the triazine ring, the linear and nonlinear optical responses have been significantly enhanced, and that the spectral behaviour of II is closer to that of III, while more different from that of I. The single-branched compound I crystallizes in the noncentrosymmetric polar space group Cc. Its crystalline powder sample shows remarkable macro second-order nonlinear response with a SHG intensity of 46.8 times that of urea under a fundamental picosecond Nd : YAG laser beam (1064 nm). An important factor of such a large SHG intensity is that all the molecular dipoles take the same-oriented packing style that makes the crystal maximally polarized, fulfilling the optimization in the sense of crystal engineering.

Effects of fluorine atoms on the optical nonlinear response of stilbene derivatives

The effect of fluorine atoms on the second-order optical nonlinear response of 4-nitro-4′-methoxy- trans-stilbene and polyene derivatives containing up to three double bonds ( n=1, 2, 3) has been investigated within a semiempirical context (PM3 Hamiltonian). Experimental data reported in literature indicate a β vec(SHG) value of 34, 47 and 76 (×10 −30 esu) for n=1, 2, 3, respectively, at 0.65 eV in CHCl 3 solutions. Our calculations show that fluorinating the nitrophenyl group the β vec(SHG) is doubled. Further increase in the second-order nonlinear response can be obtained fluorinating the CC bond linkers between the aromatic moieties. Besides, the effect of different donor–acceptor pairs has been studied and the results interpreted in the two-state model context. Some results concerning the third-harmonic generation (THG), γ (THG), are presented, and a possible interpretation proposed.

Color opponent retinal ganglion cells in the tammar wallaby retina.

In behavioral tests, tammar wallabies (Macropus eugenii) are dichromats. We investigated the neural basis for this color discrimination by making patch clamp recordings from retinal ganglion cells in an in vitro preparation. Pseudo-random noise stimuli were used to probe the spectral and temporal properties of the receptive fields. Color opponent ganglion cells were excited by medium wavelength-sensitive cones and inhibited by short wavelength-sensitive cones, and were classified as M-on/S-off cells. The S-off response was delayed by 15 ms relative to the M-on response, but, otherwise, the time course of the two responses was very similar. Second-order nonlinear response components, estimated by nonlinear systems analysis, served to accentuate the color opponency. Possible synaptic mechanisms underlying the cone opponent inputs are discussed.

Ultrafast frequency-selective optical switching based on thin self-assembled organic chromophoric films with a large second-order nonlinear response

Thin films consisting of self-assembled chromophoric superlattices exhibit very large second-order nonlinear responses [χ(2)]. Using such films, a “static” diffraction grating is created by the interference of two coherent infrared beams from a pulsed yttritium–aluminum–garnet laser. This grating is used to switch the second-harmonic and third-harmonic “signal” beams (generated from the fundamental “pump” beam or mixed within the chromophoric superlattice) into different channels (directions). Ultrafast switching response as a function of the time overlap of the pumping beams is demonstrated. It is suggested that such devices can be used to spatially and temporally separate signal trains consisting of pulses having different frequencies and arrival times.

Crystal Structure and SHG Characterization of γ-BiSeO3Cl

γ-BiSeO3Cl crystals were grown and characterized by x-ray microanalysis and second harmonic generation. The structure of γ-BiSeO3Cl was determined by single-crystal x-ray diffraction: sp. gr. Pna21, a = 11.707(4) A, b = 7.047(5) A, c = 5.315(1) A, Z = 4, R1 = 0.564, wR2 = 0.1272. The structures and second-order nonlinear responses of α- and γ-BiSeO3Cl are discussed in comparison with those of MTeO3X (M = Bi, rare earth; X = Cl, Br, I) oxyhalides.

Application of classical models of chirality to surface second harmonic generation

Two classical models (Kuhn and Kauzmann) are extended to calculate the second-order nonlinear response of an isotropic layer of chiral molecules. Calculation of the various nonlinear susceptibilities (electric dipolar, magnetic dipolar, and electric quadrupolar) is performed and applied to the derivation of the second harmonic field radiated by the molecules. It is shown that the two models give strikingly different results about the origin of the chiral response in such experiments. Previously published results are analyzed in view of this calculation which allows to understand the different interpretations proposed. This calculation emphasizes the interest of surface second harmonic generation to access information about the microscopic origin of optical activity in chiral molecules.

Surface Second Harmonic Generation from Asymmetric Multilayer Assemblies: Gaining Insight into Layer-Dependent Order

We report on the use of surface second harmonic generation (SHG) measurements to probe microscopic organization in asymmetrically bound aliphatic multilayer assemblies. The use of layers that are bound asymmetrically using metal ion coordination chemistry allows the orientation of the individual layer constituents to be controlled, and the asymmetric coordination makes the assemblies χ(2)-active. We find that, for the systems we report here, the surface second-order nonlinear response increases in proportion to the square of the number of layers initially and then saturates and decreases with additional adlayers. Optical null ellipsometry and FTIR data point to regular growth in terms of thickness and chromophore density, and the surface SHG data point to increasing disorder with the adsorption of additional layers. The FTIR data suggest a subtle decrease in overall order of these chains with increasing number of layers, but this trend is not as pronounced as that seen in the surface SHG data. We interpret these data in the context of an increase in the distribution of nonlinear chromophore orientations with layer growth and not a change in the average orientation angle.

Second-order classical nonlinear response theory

Second-order classical nonlinear response theory

A simple, novel method for the preparation of polymer-tetherable, zwitterionic merocyanine NLO-chromophores

A suite of polymer-ready nonlinear optical merocyanines has been synthesised and characterised. The tethering functionality—a vicinal dihydroxypropyl residue—is introduced onto the donor nitrogen of the chromophore precursor without the need for protection/deprotection steps, thereby giving ready access to potentially high Tg condensation polymer systems. An X-ray crystal structure determination on a representative chromophore 5 confirms the largely zwitterionic nature of these systems and experimental measurements of second-order nonlinear response [β(0)], by hyper-Raleigh scattering, indicate that a pyridylidene donor–quinomethide acceptor combination gives rise to the largest nonlinearity.

Measurements of second-order susceptibility at λ=1.5 μm in CdTe-based ternary alloys for efficient wavelength conversion

We have characterized the second-order optical nonlinear response of II-VI semiconductor ternary compounds Cd0.8Zn0.2Te and Cd0.78Mn0.22Te at λ=1.5 μm. A spectrally resolved phase-mismatch second-harmonic generation (SHG) technique has been used on bulk single crystals, exploiting 10−13 s optical pulses and multichannel detection. The nonlinear d coefficient has been measured and chromatic dispersion parameters have been validated. By normalizing SHG results in view of applications to all-optical wavelength conversion, the tested compounds prove to be interesting alternatives to more renowned AlxGa1−xAs.

Wide spectral range nonlinear optical crystals of one-dimensional coordination solids [Et4N][Cd(SCN)3] and [Et4N][Cd(SeCN)3] and the general design criteria for [R4N][Cd(XCN)3] (Where R = Alkyl and X = S, Se, Te) as NLO crystals.

We report herein two new nonlinear optical (NLO) crystals, [Et4N][Cd(XCN)3], where X = S (1) and Se (2), that are transparent from 220 to 3300 nm, covering the entire near-ultraviolet, the visible, and the near-infrared spectral regions and giving rise to a very wide and continuous optical window, which is useful for many frequency conversion applications. Both 1 and 2 exhibit highly efficient second harmonic generation (SHG) as measured via the Kurtz-Perry method. The corresponding [Me4N]+ salts, [Me4N][Cd(XCN)3 where X = S (3) and Se (4), show no SHG effects. All four structures adopt noncentrosymmetric space groups (Cmc2(1) for 1 and 2 and Pna2(1) for 3 and presumably 4) and are based on one-dimensional anionic [Cd(XCN)3-] infinity zigzag chains. However, a detailed analysis of the structures of [R4N][Cd(XCN)3], where R = Et, Me and X = S, Se revealed that the difference in the second-order nonlinear responses of the Et4N+ salts (1 and 2) and the Me4N+ salts (3 and 4) is attributable to the relative alignment of the [Cd(XCN)3-] infinity zigzag chains, being parallel in the crystals of 1 and 2 but antiparallel in the crystals of 3 and 4. Also reported, for the first time, are the synthesis and crystal structure of [Et4N][Cd(SeCN)3] (2). Compound 2 crystallizes in an orthorhombic unit cell of Cmc21 space group symmetry with lattice parameters of 9.938(1) A, 16.868(2) A, 11.054(1) A, and Z = 4. Other issues related to the molecular and crystal engineering of this class of NLO materials are also discussed.

Quasi-Phase-Matching in Chiral Materials

The second-order nonlinear optical coefficients associated with chirality differ in sign for the two mirror-image forms (enantiomers) of a chiral material. Structures comprised of alternating stacks of the enantiomers can therefore be used for quasi-phase-matched frequency conversion, as we demonstrate here by second-harmonic generation from Langmuir-Blodgett films of a helicenebisquinone. Such structures could lead to new types of frequency converters in which both the second-order nonlinear response and quasi-phase-matching arise from the chirality of a material rather than its polar order.

Supramolecular Nonlinearity of Chromophore-Functionalized Poly-L-Tyrosine

Nonlinear optical chromophores can be organized as orientationally correlated side groups of polypeptides with a rigid backbone. In such an organization, each chromophore contributes coherently to the second-order nonlinear response of the polymer structure. The synthesis of poly-L-tyrosine, functionalized with the NLO-phores 4-nitroaniline, 2,4-dinitroaniline, 2-cyano-4-nitroaniline and 4-nitro-4′-nitroazobenzene, which is organized in α-helix conformation are presented. Solvatochromic measurements show that the hyperpolarizability of the supramolecular structure is a module factor of 18.7 higher than that of the model chromophore and that conformational organization leads to a strong enhancement of the molecular hyperpolarizability β.

Multifocal ERG changes in glaucoma.

The multifocal electroretinogram (MERG) can assess regional retinal responses using analysis which gives both first-order and second-order nonlinear responses from multiple retinal regions. The retinal responses from both types of analysis showed amplitude reduction in glaucoma, suggesting that the outer and inner retinal layers are affected. These findings are in accord with the damage which has been reported in advanced glaucoma. The macular response showed a larger amplitude reduction in b-waves (first-order response) and N2P (second-order response) than did peripheral retinal responses. This indicates that loss of macular response is an important sign in glaucoma.

Multifocal ERG changes in glaucoma

The multifocal electroretinogram (MERG) can assess regional retinal responses using analysis which gives both first-order and second-order nonlinear responses from multiple retinal regions. The retinal responses from both types of analysis showed amplitude reduction in glaucoma, suggesting that the outer and inner retinal layers are affected. These findings are in accord with the damage which has been reported in advanced glaucoma. The macular response showed a larger amplitude reduction in b-waves (first-order response) and N2P (second-order response) than did peripheral retinal responses. This indicates that loss of macular response is an important sign in glaucoma.