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*Present address, Ecole Nationale Supérieure de Cachan, Laboratoire de Photonique Quantique et Moleculaire, 61 avenue du Prés. Wilson, 94235 Cachan, France.
S. Brasselet and J. Zyss, "Multipolar molecules and multipolar fields: probing and controlling the tensorial nature of nonlinear molecular media," J. Opt. Soc. Am. B 15, 257-288 (1998)
A general class of multipolar molecules is introduced in the context of quadratic nonlinear optics by way of extension of the more specific cases of dipolar and octupolar molecules. An adequate irreducible tensor formalism permits us to define rotationally invariant molecular features that couple to corresponding field tensor components, thereby enabling us to account for a variety of coherent and noncoherent processes such as harmonic light (hyper-Rayleigh) scattering, coherent second-harmonic generation in electrically poled media, and the recently proposed optical poling scheme. Experiments in both harmonic light scattering in solution (for some multipolar molecules) and optical poling (in Disperse Red 1–methyl methacrylate thin films) are analyzed in light of this model. A general tensorial permutation lemma of broad validity allows nonlinear light–matter interactions to be condensed in a statistical medium in compact rotationally invariant expressions: The main tensorial symmetry features for both molecular susceptibility and read–write field polarization tensors that jointly drive these interactions are clearly revealed.
S. F. Hubbard, R. G. Petschek, K. D. Singer, N. D’Sidocky, C. Hudson, L. C. Chien, C. C. Henderson, and P. A. Cahill J. Opt. Soc. Am. B 15(1) 289-301 (1998)
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Experimental Results for HLS Depolarization Ratio Molecular Averaged Hyperpolarizability and Cartesian Molecular Anisotropy for Various Types of Molecule
a
DR1 ( symmetry); DNDAB and DADC ( symmetries); NPP, POM, and NPAN (quasi-1D symmetries); Crystal Violet (CRVI; symmetry). β values are The in-plane anisotropy value is inferred from and are evaluated from and Static theoretical values were obtained from intermediate neglect of differential overlap–finite-field calculations40,41 (experimental values are in boldface; theoretical values, in lightface). The experimental fundamental wavelength is specified below the molecular acronym.
Table 2
Cartesian Cubic Tensorial Basis Elements in Terms of the
Reduced Spherical Tensorial Basis Elements
Spherical Basis Elements
Cartesian Basis Element
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 3
Cartesian Cubic Tensorial Basis Elements in Terms of the Reduced Spherical Tensorial Basis Elements
Spherical Basis Elements
Cartesian Basis Element
0
0
0
0
0
0
0
0
0
0
0
Table 4
Cartesian Quadratic Tensorial Basis Elements in Terms of the
Reduced Spherical Tensorial Basis Elements
Spherical Basis Elements
Cartesian Basis Element
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 5
Experimental Results for Molecular Anisotropy ρ Inferred from Macroscopic Depolarization Ratio for the Same Molecules as in Table 1a
Molecular Quantity
Molecule (Incident Wavelength)
NPP (1.064 μm)
POM (1.064 μm)
NPAN (1.064 μm)
DNDAB (1.064 μm)
DADC (1.34 μm)
CRVI (1.34 μm)
DR1 (1.34 μm)
0.47
0.37
0.59
0.26
0.25
0.09
0.73
0.8
0.93
0.80
0.97
0.97
0.99
0.68
ρ
1.9
2.5
1.37
3.7
3.96
10.2
0.93
The spherical molecular quantities and are inferred from and following the calculations of Section 3.
Table 6
Spherical Components and Norms of the Writing Field Tensors for Various Polarization Configurations and Linear Polarizations
Writing Field Component
Linear Polarization (Cartesian Component)
()
0
0
0
Table 7
Spherical Components and Norms of the Writing Field Tensors for Various Polarization Configurations for Circular and Elliptical
a
Writing Field Component
Writing Field Polarization
0
0
0
0
0
0
0
0
0
0
0
0
0
The ellipticity parameter is tan δ.
Table 8
Spherical Components and Norms of the Writing Field Tensors for Elliptical Polarizations for and a
Writing Field Component
The respective ellipticities of and are of and the parameters and denote a possible phase shift of those polarizations.
Tables (8)
Table 1
Experimental Results for HLS Depolarization Ratio Molecular Averaged Hyperpolarizability and Cartesian Molecular Anisotropy for Various Types of Molecule
a
DR1 ( symmetry); DNDAB and DADC ( symmetries); NPP, POM, and NPAN (quasi-1D symmetries); Crystal Violet (CRVI; symmetry). β values are The in-plane anisotropy value is inferred from and are evaluated from and Static theoretical values were obtained from intermediate neglect of differential overlap–finite-field calculations40,41 (experimental values are in boldface; theoretical values, in lightface). The experimental fundamental wavelength is specified below the molecular acronym.
Table 2
Cartesian Cubic Tensorial Basis Elements in Terms of the
Reduced Spherical Tensorial Basis Elements
Spherical Basis Elements
Cartesian Basis Element
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 3
Cartesian Cubic Tensorial Basis Elements in Terms of the Reduced Spherical Tensorial Basis Elements
Spherical Basis Elements
Cartesian Basis Element
0
0
0
0
0
0
0
0
0
0
0
Table 4
Cartesian Quadratic Tensorial Basis Elements in Terms of the
Reduced Spherical Tensorial Basis Elements
Spherical Basis Elements
Cartesian Basis Element
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 5
Experimental Results for Molecular Anisotropy ρ Inferred from Macroscopic Depolarization Ratio for the Same Molecules as in Table 1a
Molecular Quantity
Molecule (Incident Wavelength)
NPP (1.064 μm)
POM (1.064 μm)
NPAN (1.064 μm)
DNDAB (1.064 μm)
DADC (1.34 μm)
CRVI (1.34 μm)
DR1 (1.34 μm)
0.47
0.37
0.59
0.26
0.25
0.09
0.73
0.8
0.93
0.80
0.97
0.97
0.99
0.68
ρ
1.9
2.5
1.37
3.7
3.96
10.2
0.93
The spherical molecular quantities and are inferred from and following the calculations of Section 3.
Table 6
Spherical Components and Norms of the Writing Field Tensors for Various Polarization Configurations and Linear Polarizations
Writing Field Component
Linear Polarization (Cartesian Component)
()
0
0
0
Table 7
Spherical Components and Norms of the Writing Field Tensors for Various Polarization Configurations for Circular and Elliptical
a
Writing Field Component
Writing Field Polarization
0
0
0
0
0
0
0
0
0
0
0
0
0
The ellipticity parameter is tan δ.
Table 8
Spherical Components and Norms of the Writing Field Tensors for Elliptical Polarizations for and a
Writing Field Component
The respective ellipticities of and are of and the parameters and denote a possible phase shift of those polarizations.