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  • 1
    Electronic Resource
    Electronic Resource
    Longwave properties of the orientation averaged Mueller scattering matrix for particles of arbitrary shape. II. Molecular parameters and Perrin symmetry (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 4726-4740 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In Part I of this paper, we started from a dipole array model of elastic light scattering, and found the longwave asymptotic formulas for all 16 elements of the orientation averaged Mueller scattering matrix. However, the Perrin symmetry of the scattering matrix was not obvious from the formulas obtained in Part I. In this paper, Part II, we carry the analysis further, finding the molecular parameter identities which result in the Perrin symmetries. The formulas we present provide a very practical method for model calculations in the longwave limit. After evaluation of ten sums over pairs of the dipolar subunits of the model, the orientation averaged Mueller scattering matrix, as a function of scattering angle, is given by simple trigonometric polynomials. For models containing several hundred subunits the computation is easily carried through by a desktop computer. We verify the asymptotic formulas by numerical comparison with our analytic orientation averaging program PMAT2. We use a helical model with spherical subunits, in which the first Born approximation gives excellent results for the dipole elements (symmetry DSE). In this same model the first, second, and third Born approximations are utterly worthless for calculating the helicity-retardation elements M13 and M23 and their transposes, but fourth Born gives nearly the exact result. These observables therefore use four bounces to feel out the helicity of the array, and may be more sensitive to structural variations than the traditional circular difference observable M14, which responds after only two bounces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460584
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  • 2
    Electronic Resource
    Electronic Resource
    Erratum: Nondipole light scattering by partially oriented ensembles. III. The Müller pattern for achiral macromolecules [J. Chem. Phys. 91, 4435 (1989)] (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 3995-3996 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458618
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  • 3
    Electronic Resource
    Electronic Resource
    Nondipole light scattering by partially oriented ensembles. II. Analytic algorithm (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 6956-6964 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider the elastic single scattering of light from an ensemble of identical particles with nonrandom orientational distribution. The particle is modeled as an arbitrary rigid array of N dipole polarizabilities, and the polarizabilities within each particle interact through the retarded dipole–dipole tensor. We consider the scattering ensemble to be an "optical element'' in the Müller formalism; thus its polarized scattering properties, both dipole and nondipole, are specified completely by a four-by-four Müller matrix M(ψ), where ψ is the scattering angle. In a previous work on orientationally random ensembles, the slow convergence of the nondipole elements suggested that they might be particularly sensitive to small orienting forces. This was confirmed by numerical calculations, which, however, also demonstrated the need for a faster analytic averaging algorithm. In this paper we extend the uniform distribution analytic algorithm to cases in which the orientation of the particles is specified by a general nonuniform distribution. We then specialize the general formula to the case of axially nonrandom orientation, such as might be caused by an external static electric field E operating on a permanent electric dipole of the model particle. We present an explicit algorithm for M(ψ,E) for this special case, together with an estimate of its computability. For models with just a few subunits, it should be computable by a desktop machine with four megabytes of memory. For more realistic models using 1000 subunits, the job can easily rise into the supercomputer range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456271
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  • 4
    Electronic Resource
    Electronic Resource
    Polarized light scattering from large quantum systems with zero initial and final angular momentum (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 7394-7401 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider the scattering of light from a molecule or a cluster. The scattering may be elastic or inelastic, but we limit ourselves to the special case of transitions from initial states having total angular momentum number J=0 to final states also having J=0. In practice, this covers elastic scattering from clusters as the rotational temperature drops toward absolute zero. This hypothesis allows us to do the orientation average at the amplitude level, a method fundamentally incorrect in the general case. Without approximation, we are able to deduce the pattern of the observable Mueller matrix M of the scattering. We find a new symmetry that reflects the spherical nature of the J=0 states: M11+M33=M22+M44. This result includes all multipole orders of the scattered light, and is therefore valid for clusters large compared to wavelength, as well as for small clusters. In an Appendix, we discuss a new generating function for orientation averages, which allows one to make exact tensor averages weighted by two plane waves (for scattering, one incoming and one outgoing).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462442
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  • 5
    Electronic Resource
    Electronic Resource
    The Mueller matrix for elastic scattering in static magnetic field (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 8086-8094 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a central multipole calculation of the effect of a static magnetic field on nonresonant elastic scattering by an isotropic solution of molecules that are small compared to wavelength. Results are presented as perturbations to the observable Mueller scattering matrix. It is particularly interesting that perturbations appear in the six retardation elements of the matrix because these are otherwise exactly zero. The perturbation formulas for the whole matrix yield a number of relations that are empirically testable without prior knowledge of central multipole tensors α˜, G˜, and A˜ or their magnetic field derivatives.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462360
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  • 6
    Electronic Resource
    Electronic Resource
    Nondipole light scattering by partially oriented ensembles. I. Numerical calculations and symmetries (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 4783-4794 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider the elastic scattering of light by an ensemble of scatterers with radius of gyration greater than about one-tenth of a wave; e.g., visible light scattered by an aqueous suspension of viruses or bacteria. We model the scattering molecule as an asymmetric rigid array of interacting point polarizabilities, and we include, as the source of anisotropy in the scattering ensemble, a permanent dipole moment on the molecule and a uniform electric field E° in the scattering cell. We calculate the entire Müller matrix M(θ, E(open circle)x, E(open circle)y, E(open circle)z), for scattering angles θ from 0° to 360° and for E(open circle)x, E(open circle)y, E(open circle)z nonzero one at a time, where z is the incidence axis, y is perpendicular to the scattering plane, and x is perpendicular to y and z. Our first major finding is that the nondipole elements of M are enormously more sensitive to partial orientation than are the dipole elements. The second major finding is a set of new symmetries governing the scattering matrix for the case of axially anisotropic scattering clouds. The Perrin reciprocity symmetries for isotropic clouds may be symbolized by M(θ)=PM(θ), where P stands for matrix transpose plus negation of third row and column (with double negation of element 3,3). Using this operator our new axial symmetries may be expressed as PM(+θ, 0, E(open circle)y, 0)=M(+θ, 0, −E(open circle)y,0)=M(−θ, 0, E(open circle)y, 0). The second symmetry may be generalized to fields in any direction as M(+θ,−E(open circle)x, −E(open circle)y, E(open circle)z)= M(−θ, E(open circle)x, E(open circle)y, E(open circle)z). We also show in Appendix A how the nonlocal polarizabilities used in the theory may be calculated by the inversion only of symmetric matrices, with a significant saving in calculation time when the number of subunits is large.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456573
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  • 7
    Electronic Resource
    Electronic Resource
    Longwave properties of the orientation averaged Mueller scattering matrix for particles of arbitrary shape. I. Dependence on wavelength and scattering angle (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 5605-5615 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Starting from a dipole array theory of elastic light scattering by particles of arbitrary shape and composition, we develop long-wave asymptotic formulas for all sixteen elements of the Mueller scattering matrix, valid after orientation averaging. The six dipole elements have long been known to be asymptotically proportional to k4 where k is the wave vector length of the light. However, the remaining ten nondipole elements experience intricate cancellations within the averaging operation that cause the asymptotic behavior to go like k5, k8, or k9; or at certain angles, like k6. For example, we show that (M34)=Ck9 sin2(θ), where C is a constant dependent on particle properties, and θ is the scattering angle. We find analogous simple angular basis functions for all 16 of the formulas and we show that they agree with numerical results from the exact algorithm. We contrast dipole array theory with central multipole expansion theory, which fails to account correctly for six of the Mueller elements, no matter how many multipoles are used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459631
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  • 8
    Electronic Resource
    Electronic Resource
    Nondipole light scattering by partially oriented ensembles. III. The Müller pattern for achiral macromolecules (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4435-4439 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Müller matrix representing elastic scattering of light by an isotropic suspension of particles has long been known to contain eight vanishing elements among its total of sixteen elements, provided that the particles have no handedness. We generalize the proof of this property to the case of anisotropic suspensions of particles, so that it may apply to symmetric biostructures such as viruses, undergoing electrophoresis. The matrix for the partially oriented case generally contains four crucial pieces of structural information missing from the randomly oriented case. In particular, the circular intensity difference scattering (CIDS) element M14 may be nonzero for an oriented ensemble of particles that have no helicity at all.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456779
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  • 9
    Electronic Resource
    Electronic Resource
    Two-Photon Molecular Electronic Spectroscopy (1980)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Physical Chemistry 31 (1980), S. 559-577 
    Details
    ISSN: 0066-426X
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.pc.31.100180.003015
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  • 10
    Electronic Resource
    Electronic Resource
    Comparison of numerical and analytical orientation average methods in polymer light scattering (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4986-4994 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have calculated the Perrin matrix for elastic light scattering by two distinct numerical methods, and we present here a critical comparison. Both methods assume the dipole array model with retarded dipole–dipole interaction between subunits. However, the average over all orientations of the model is carried out differently in the two methods. The conceptually simplest method (and the easiest to program) is rotation by Cartesian matrix (CM) algebra with three-dimensional numerical integration over Euler angles. The second method is based on rotations by Wigner matrix (WM) algebra with analytic integration, and requires an infinite sum in one index which must be truncated. The two methods agree when they are pushed far enough. Both methods require substantial calculation, but the analytic method is shown to be far superior in its convergence properties. Comparing calculations of the whole Perrin matrix of scattering curves (16 curves, 21 scattering angles) in which all curves are computed to 1% accuracy, the CPU times for the numerical integration over Euler angles is about 500 times slower.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452813
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