Phased and Boltzmann-weighted rotational averages

Andrews, Davıd L.; Harlow, M.J.

doi:10.1103/physreva.29.2796

Cited by 56 publications

(55 citation statements)

References 18 publications

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“…(13) and (14) the subscript f~ is used to denote an orientational average; a distributional average taken over the positions of the molecular centres will be denoted by a subscript R. The form of these polynomial weighted averages may be gleaned from Ref. [9] and are given in Table 1 for tensors up to rank 4. These averages may now be used to evaluate the necessary ensemble averages, the process being illustrated by considering SHG from oriented molecules.…”

Section: S=ti Ingil Imentioning

confidence: 99%

“…As indicated in Ref. [9] the form of the derivation is easily extended to cover averages weighted by a Boltzmann factor and may be used, for example, to derive an expression for steady state electric field induced second harmonic generation (EFISHG). In this paper we consider how use may be made, under appropriate conditions, of rotational averages weighted by Legendre polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…The weighting of orientational averages by phase factors of the form exp(ih-~,), where h and ~, are laboratory and molecule-fixed vectors respectively, is important for consideration of pairwise interactions of molecules with radiation, and has been treated in some detail [9]. As indicated in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Second harmonic generation in partially ordered media and at interfaces: analysis of dynamical and orientational factors

Andrews¹,

Hands²

1996

Chemical Physics

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A new method of modelling molecular orientational dynamics is presented and illustrated by application to optical second harmonic generation (SHG). The method highlights the intricate dependence of the harmonic signal on the form and evolution of the molecular orientational distribution, and reference is made to some examples taken from the recent literature. Specifically, the cases considered relate to SHG in (a) poled polymers, (b) molecules oriented within molecular sieves and (c) molecules in films or adsorbed on surfaces. The technique invokes rotational averages weighted by static or time-dependent distribution functions expressed in terms of Legendre polynomials. Rotational diffusion is used to model the decay of second harmonic intensity associated with a growth or recovery of bulk isotropy, the results allowing several discrete contributions associated with different time constants to be characterised. For polarisation studies using surfaces and films, it is shown that caution is required in how the results are interpreted to reflect molecular orientation, approximations in commonly employed theory readily producing spurious results.

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Section: S=ti Ingil Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second harmonic generation in partially ordered media and at interfaces: analysis of dynamical and orientational factors

Andrews¹,

Hands²

1996

Chemical Physics

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“…It is not straightforward to tackle the associated rotational average; considerable complexity arises in the term that bears a phaseweighted second rank tensor engagement between components of the wave-vector and the electrodynamic properties of the pair. However, an exact analytical procedure has been established for such calculations; 31 the results necessary for the present calculation are drawn from the general analysis and cast in terms of spherical Bessel functions j n . Specifically, we have…”

Section: One-photon Emission From a Pair With Localized Excitationmentioning

confidence: 99%

Optical emission of a molecular nanoantenna pair

Rice

Andrews

2012

The Journal of Chemical Physics

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The optical emission from a pair of nanoantennas is investigated within the theoretical framework of quantum electrodynamics. The analysis of fluorescent emission from a pair of molecular antenna species in close proximity is prompted by experimental work on oriented semiconductor polymer nanostructures. Each physically different possibility for separation-dependent features in photon emission by any such pair is explored in detail, leading to the identification of three distinct mechanisms: emission from a pair-delocalized exciton state, emission that engages electrodynamic coupling through quantum interference, and correlated photon emission from the two components of the pair. Although each mechanism produces a damped oscillatory dependence on the pair separation, each of the corresponding results exhibits an analytically different form. Significant differences in the associated spatial frequencies enable an apparent ambiguity in the interpretation of experiments to be resolved. Other major differences are found in the requisite conditions, the associated selection rules, and the variation with angular disposition of the emitters, together offering grounds for experimental discrimination between the coupling mechanisms. The analysis paves the way for investigations of pair-wise coupling effects in the emission from nanoantenna arrays.

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“…By weighting the averages in equation (20) with the Boltzmann term exp(poO * E / k T ) to allow for the anisotropic distribution, the following expression for the harmonic power is obtained: (21) is traditionally approximated by expanding the exponential and retaining only the linear terms (see for example Chemla andBonneville 1978, Kielich 1979). However, it has recently been shown that an exact result in terms of spherical Bessel functions can be obtained by referring all molecular parameters to a molecule-fixed Cartesian frame (denoted by Greek indices) and averaging over the direction cosines between axes in the laboratory-fixed and molecule-fixed frames (Andrews and Harlow 1984). Thus if li, denotes the direction cosine between the i axis in the laboratory frame and the A axis in the molecular frame, the expression becomes which can be expressed as where…”

Section: Boltzmann-weighted Orientational Averagesmentioning

confidence: 99%

Orientational effects in electric-field-induced second-harmonic generation

Andrews

Sherborne

1986

J. Phys. B: At. Mol. Phys.

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Abstract. The theory of electric-field-induced second-harmonic generation is developed within the framework of quantum electrodynamics. Using a recently developed exact averaging procedure to account for the anisotropy introduced to a dipolar molecular fluid by the static electric field, the polarisation dependence of the process is investigated. A number of experimental arrangements are suggested which allow a discrimination to be made between the two mechanisms involved: the third-order optical route facilitated by the field-induced anisotropy, and the fourth-order electro-optical route. This allows measurement of the corresponding non-linear optical and e!ectro-optical tensor parameters. The full temperature and field-strength dependences are presented in detail, and it is shown that in two particular polarisation cases, that of helicity conversion, and where the static field and pump polarisation are perpendicular to the polarisation of the harmonic, the usual approximation for the orientational average is incomplete and produces misleading results.

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Phased and Boltzmann-weighted rotational averages

Cited by 56 publications

References 18 publications

Second harmonic generation in partially ordered media and at interfaces: analysis of dynamical and orientational factors

Second harmonic generation in partially ordered media and at interfaces: analysis of dynamical and orientational factors

Optical emission of a molecular nanoantenna pair

Orientational effects in electric-field-induced second-harmonic generation

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