Molecular Tensor Analysis of Third-Harmonic Scattering in Liquids
05 Jan 2018-Journal of Physical Chemistry A (American Chemical Society)-Vol. 122, Iss: 2, pp 563-573
TL;DR: This work presents a rigorous quantum electrodynamical analysis of the scattering process, involving a partially index-symmetric construction of the fourth-rank γ tensor-dispensing with the Kleinman symmetry condition.
Abstract: Third-harmonic scattering is a nonlinear optical process that involves the molecular second-hyperpolarizability, γ. This work presents a rigorous quantum electrodynamical analysis of the scattering process, involving a partially index-symmetric construction of the fourth-rank γ tensor—dispensing with the Kleinman symmetry condition. To account for stochastic molecular rotation in fluids, methods of isotropic averaging must be employed to relate the molecular properties to accessible experimental quantities such as depolarization ratio. A complete eighth-rank tensor rotational average yields results for observable third-harmonic scattering rates, cast as a function of the natural-invariant γ components, and the polarization geometry of the experiment. Decomposing the tensor γ into irreducible weights allows specific predictions to be made for each molecular point group, allowing greater discrimination between the results for different molecular symmetries.
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TL;DR: The authors use second harmonic scattering and Fourier-plane imaging to dynamically monitor size, shape and concentration of ZIF-8 in situ during the growth process, highlighting the potential of dynamic angle-resolved harmonic light scattering to probe crystal growth processes, assembly–disassembly of biological systems, adsorption, transport through membranes and myriad other applications.
Abstract: Recent developments in nonlinear optical light scattering techniques have opened a window into morphological and structural characteristics for a variety of supramolecular systems. However, for the study of dynamic processes, the current way of measuring is often too slow. Here we present an alternative measurement scheme suitable for following dynamic processes. Fast acquisition times are achieved through Fourier imaging, allowing simultaneous detection at multiple scattering angles for different polarization combinations. This allows us to follow the crystal growth of the metal organic framework ZIF-8 in solution. The angle dependence of the signal provides insight into the growth mechanism by probing the evolution of size, shape and concentration, while polarization analysis yields structural information in terms of point group symmetry. Our findings highlight the potential of dynamic angle-resolved harmonic light scattering to probe crystal growth processes, assembly–disassembly of biological systems, adsorption, transport through membranes and myriad other applications.
26 citations
TL;DR: In this paper , the third-harmonic Mie scattering optical activity from suspensions of CdTe nanostructured helices is observed, opening ways for chiroptical characterization of semiconductor and other chiral non-metallic particles in volumes potentially of the order of 10-17 m3.
Abstract: Chiroptical spectroscopies provide structural analyses of molecules and nanoparticles but they require sample volumes that are incompatible with generating large chemical libraries. New optical tools are needed to characterize chirality for the ultrasmall (<1 µl) volumes required in the high-throughput synthetic and analytical stations for chiral compounds. Here we show experimentally a novel photonic effect that enables such capabilities—third-harmonic Mie scattering optical activity—observed from suspensions of CdTe nanostructured helices in volumes <<1 µl. Third-harmonic Mie scattering was recorded on illuminating CdTe helices with 1,065, 1,095 and 1,125 nm laser beams and the intensity was around ten-times higher in the forward direction than sideways. The third-harmonic ellipticity was as high as 3° and we attribute this effect to the interference of chiral and achiral effective nonlinear susceptibility tensor components. Third-harmonic Mie scattering on semiconductor helices opens a path for rapid high-throughput chiroptical characterization of sample volumes as small as 10−5 µl. Third-harmonic Mie scattering optical activity from suspensions of semiconductor (CdTe) nanostructured helices is observed, opening ways for chiroptical characterization of semiconductor and other chiral non-metallic particles in volumes potentially of the order of 10–17 m3.
19 citations
TL;DR: In the wide realm of applications of quantum electrodynamics, a non-covariant formulation of theory is particularly well suited to describing the interactions of light with molecular matter, and a variety of symmetry principles are drawn out with reference to applications.
Abstract: In the wide realm of applications of quantum electrodynamics, a non-covariant formulation of theory is particularly well suited to describing the interactions of light with molecular matter The robust framework upon which this formulation is built, fully accounting for the intrinsically quantum nature of both light and the molecular states, enables powerful symmetry principles to be applied With their origins in the fundamental transformation properties of the electromagnetic field, the application of these principles can readily resolve issues concerning the validity of mechanisms, as well as facilitate the identification of conditions for widely ranging forms of linear and nonlinear optics Considerations of temporal, structural, and tensorial symmetry offer significant additional advantages in correctly registering chiral forms of interaction More generally, the implementation of symmetry principles can considerably simplify analysis by reducing the number of independent quantities necessary to relate to experimental results to a minimum In this account, a variety of such principles are drawn out with reference to applications, including recent advances Connections are established with parity, duality, angular momentum, continuity equations, conservation laws, chirality, and spectroscopic selection rules Particular attention is paid to the optical interactions of molecules as they are commonly studied, in fluids and randomly organised media
18 citations
Cites background from "Molecular Tensor Analysis of Third-..."
...Recent work on third harmonic scattering has again shown that emphatic differences arise, according to whether or not full index symmetry is assumed [119]....
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TL;DR: In this article, the third-harmonic (hyper) Rayleigh scattering optical activity (THRS OA) was observed from Ag nanohelices randomly dispersed in water.
Abstract: In 3D isotropic liquids, optical third-harmonic generation is forbidden, with circularly polarized light (CPL). Yet the associated nonlinear susceptibility directly influences the optical properties at the fundamental frequency by intensity dependence (Kerr effect). Here, the hidden third-harmonic optical properties upon CPL illumination are revealed by demonstrating a new effect, in hyper-Rayleigh scattering. This effect is succinctly enunciated: the intensity of light scattered at the third-harmonic frequency of the CPL incident light depends on the chirality of the scatterers. It is referred to as third-harmonic (hyper) Rayleigh scattering optical activity (THRS OA) and was observed from Ag nanohelices randomly dispersed in water. The first analytical theory model for the new effect in nanohelices is also provided, highlighting the role of localized transition dipoles along the helical length. THRS OA is remarkably user-friendly. It offers access to intricate optical properties (hyperpolarizabilities) that have so far been more easily accessible by computation and that are essential for the understanding of light−matter interactions. The new effect could find applications in hyper-sensitive characterization of the chirality in molecules and in nanostructures; this chirality plays a fundamental role in the function of bio/nano-machinery, with promising applications in next generation technologies.
17 citations
13 Nov 2019
TL;DR: In this paper, the authors used second-and third-harmonic scattering techniques to elucidate the mechanism and kinetics of the aggregation process and the role of external stimuli in the supramolecular organization.
Abstract: Solubilized poly(3-alkylthiophene)s are known to self-assemble into well-ordered supramolecular aggregates upon lowering the solvent quality. This supramolecular organization largely determines the optical and electronic properties of these polymers. However, despite numerous studies the exact mechanism and kinetics of the aggregation process and the role of external stimuli are still poorly understood. Classical characterization techniques such as electronic spectroscopy, dynamic light scattering, and diffraction-based techniques have not been able to provide a full understanding. Here we use second-harmonic scattering (SHS) and third-harmonic scattering (THS) techniques to investigate this supramolecular aggregation mechanism. Our results indicate that the actual supramolecular aggregation is preceded by the formation of structured polymer-solvent clusters consistent with a nonclassical crystallization pathway. The optoelectronic and photophysical properties of conjugated polymers are strongly influenced by the formation of supramolecular aggregates. Here the authors use second- and third-harmonic scattering techniques to elucidate the mechanism and kinetics of the aggregation process and the role of external stimuli in the supramolecular organization.
15 citations
References
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TL;DR: In this paper, hyper-rayleigh scattering in solution is used for the determination of the hyperpolarizability of nonlinear optical molecules, which is an advantage over the electric-field-induced second-harmonic generation technique.
Abstract: Hyper-Rayleigh scattering in solution is used for the determination of the hyperpolarizability of nonlinear optical molecules. Obtaining the first hyperpolarizability \ensuremath{\beta} without having to independently determine the dipole moment \ensuremath{\mu} and the second hyperpolarizability \ensuremath{\gamma} is an advantage over the electric-field-induced second-harmonic generation technique. Values of the first hyperpolarizability \ensuremath{\beta} of 23\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}30}$ esu for para-nitroaniline, 105\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}30}$ esu for 4-methoxy-4'-nitrostilbene, and 95\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}30}$ esu for 4-hydroxy-4'-nitrostilbene dissolved in chloroform have been obtained. The equivalent-internal-field model is shown to hold for small saturated molecules.
640 citations
TL;DR: In this paper, it is shown that for molecules of low symmetry, elliptically polarized light must be used in order to determine five independent quadratic forms in the 18 symmetric components (βijk+βikj).
Abstract: Double‐quantum light scattering by a system of molecules is discussed in this paper. Expressions have been obtained for the scattered light intensity considering both the coherent and incoherent contributions. In that coherent contributions are also considered in this treatment, it goes beyond the scope of previous studies. It is shown that, for molecules of low symmetry, elliptically polarized light must be used in order to determine five independent quadratic forms in the 18 symmetric components (βijk+βikj). According to the present results, the apparent discrepancy between the observed value of ⅓ for the depolarization ratio for CCl4 and the value to be expected from theory may be due to the fact that the coherent contribution had been neglected in previous theoretical considerations. In general, orientational correlation is essential if there is to be appreciable contribution from coherent scattering. For macromolecules, this constitutes a major difference between single‐ and double‐quantum scattering...
369 citations
TL;DR: In this paper, a systematic method for deriving the required tensor averages is presented, and results up to the seventh rank are explicitly shown where appropriate both reducible and irreducible expressions are given and their equivalence.
Abstract: In theories which describe the response of freely rotating molecules to externally imposed stimuli it is frequently necessary to average rotationally a product of direction cosines relating space‐fixed and molecular coordinate frames. In this paper a systematic method for deriving the required tensor averages is presented, and results up to the seventh rank are explicitly shown. Where appropriate both reducible and irreducible expressions are given and their equivalence is demonstrated. Finally, some useful identities relating rotational averages of different ranks are noted.
281 citations
TL;DR: In this article, a method for determining the third-order nonlinear susceptibility of liquids using third harmonic generation (THG) is presented, which relies on use of a cell with wedged windows and a wedged liquid chamber which when placed in a vacuum chamber and translated across the optical path generates complex THG intensity fringes.
Abstract: A method for determining the third‐order nonlinear susceptibility of liquids using third harmonic generation (THG) is presented. A review of molecular polarizability and discussion of the relationship to susceptibilities are presented. All materials, including air and windows of the liquid cell, can make substantial contributions to the total THG intensity; this technique accordingly accounts for their effects. The method relies on use of a cell with wedged windows and a wedged liquid chamber which when placed in a vacuum chamber and translated across the optical path generates complex THG intensity fringes. By analysis of the latter, the liquid susceptibility is extracted. Several simple neat liquids are used to demonstrate the method.
149 citations
TL;DR: In this paper, two methods are used to develop non-ivergent, compact, sum-over-states formulas for dynamic hyperpolarizabilities up to fifth order. But the formulas do not explicitly take into account secular divergences in a simple and clear way.
Abstract: Two methods are used to develop nondivergent, compact, sum‐over‐states formulas for dynamic hyperpolarizabilities up to fifth order. Expressions for both atoms and molecules are given; those at fourth and fifth order for the first time. The fifth‐order formula is related to such nonlinear optical phenomena as stimulated hyper‐Raman scattering and the self‐induced intensity‐dependent refractive index. Questions of time‐reversal invariance are also discussed. Importantly, the derivations explicitly take into account secular divergences in a simple and clear way.
131 citations