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Finite length effects on first hyperpolarizability tensor for chiral carbon nanotubes with application to second harmonic far‐field radiation pattern
Author(s) -
De Dominicis L.,
Fantoni R.
Publication year - 2009
Publication title -
journal of raman spectroscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.748
H-Index - 110
eISSN - 1097-4555
pISSN - 0377-0486
DOI - 10.1002/jrs.2254
Subject(s) - hyperpolarizability , physics , carbon nanotube , mathematical analysis , mathematics , optics , quantum mechanics , molecular physics , materials science , polarizability , molecule , composite material
The general form of the first hyperpolarizability third‐rank tensor β for chiral carbon nanotubes (CNTs) with symmetry Ln p 22 is calculated with group projector technique method. For this purpose, the group natural factorization has been adopted and the associated irreducible representations, parameterized in terms of suitable quantum numbers, then used to construct the group projector operator in the relevant vector space. The followed approach allows to model the finite length effects on the tensor and to study its convergence to the invariant form as a function of CNT topology. As an applicative example, to elucidate the role played by finite length effects, the obtained results are applied to the study of second harmonic (SH) far‐field radiation pattern emitted by a chiral CNT within the linear dielectric homogeneity approximation. The particular case of a tube forming an angle of π/4 with the propagation direction of the linearly polarized exciting laser beam is treated. It is demonstrated that the radiation pattern consists of two main lobes with high directivity along the specular reflected and transmitted directions. According to the model developed and for the cases considered, finite length effects introduce asymmetries in the intensity distribution of the two lobes. Copyright © 2009 John Wiley & Sons, Ltd.