On the multipole expansion in the theory of optical activity

1976 ◽  
Vol 54 (5) ◽  
pp. 471-474 ◽  
Author(s):  
J. Van Kranendonk ◽  
J. E. Sipe
Keyword(s):  
Electromagnetic Field ◽  
Optical Activity ◽  
Canonical Transformation ◽  
Multipole Expansion ◽  
Isotropic Media

The different Hamiltonians for a molecule interacting with the electromagnetic field, which have been used in the literature on the optical activity of isotropic media, are shown to be related by a canonical transformation and hence to be equivalent. Because of its greater simplicity, the use of the multipole Hamiltonian in the theory of optical activity is advocated.

scholarly journals Diffraction of Light by a Two-Dimensional Lattice of Spheres

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Bernard de Dormale ◽  
Vo-Van Truong
Keyword(s):  
Electromagnetic Field ◽  
Optical Properties ◽  
Multipole Expansion ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Theoretical Approaches ◽  
Diffraction Of Light ◽  
Potential Applications ◽  
Computational Procedures ◽  
A New Technique

Two-dimensional arrays of particles are of great interest because of their very characteristic optical properties and numerous potential applications. Although a variety of theoretical approaches are available for the description of their properties, methods that are accurate and convenient for computational procedures are always sought. In this work, a new technique to study the diffraction of a monochromatic electromagnetic field by a two-dimensional lattice of spheres is presented. The method, based on Fourier series, can take into account an arbitrary number of terms in the multipole expansion of the field scattered by each sphere. This method has the advantage of leading to simple formulas that can be readily programmed and used as a powerful tool for nanostructure characterization.

Theory of Nonlinear Optical Activity in Isotropic Media and Liquid Crystals

1982 ◽  
Vol 29 (10) ◽  
pp. 1359-1369 ◽  
Author(s):  
S.A. Akhmanov ◽  
G.A. Lyakhov ◽  
V.A. Makarov ◽  
V.I. Zharikov
Keyword(s):  
Liquid Crystals ◽  
Optical Activity ◽  
Nonlinear Optical ◽  
Isotropic Media

THE MULTIPOLE EXPANSION IN QUANTUM THEORY

1963 ◽  
Vol 41 (1) ◽  
pp. 12-20 ◽  
Author(s):  
J. Fiutak
Keyword(s):  
Electromagnetic Field ◽  
Charged Particles ◽  
Multipole Expansion ◽  
Classical Field ◽  
Arbitrary System ◽  
First Order ◽  
Electric Component ◽  
Quantized Field ◽  
Interaction Term ◽  
Radiation Processes

The Hamiltonian of a system of charged particles interacting with the electromagnetic field is investigated. For an arbitrary system the multipole expansion of the interaction between the system and the field is derived by means of a suitable canonical transformation. The transformed Hamiltonian is obtained from the Hamiltonian of the system by replacing the momenta by the transformed kinetic momenta and by adding to the Hamiltonian a term representing the interaction of the system with the electric component of the field. By expanding this interaction term, as well as the transformed momenta, in powers of the dimension of the system over the wavelength, the multipole expansion of the Hamiltonian is obtained. For a system interacting with a classical field the multipole form of the Hamiltonian is exactly equivalent to the original Hamiltonian. For a quantized field this is not true, and the multipole form of the transformed Hamiltonian is shown to be equivalent to the original Hamiltonian only for first-order radiation processes.

Some remarks on the interpretation of natural and magnetically induced optical activity data

1967 ◽  
Vol 297 (1448) ◽  
pp. 16-26 ◽  
Keyword(s):  
Optical Activity ◽  
Dipole Transition ◽  
Optically Active ◽  
Optical Rotatory Dispersion ◽  
Perturbation Approach ◽  
Activity Data ◽  
Rotational Strength ◽  
Optical Rotatory Dispersion Curve ◽  
Isotropic Media ◽  
Induced Optical Activity

1. Introduction—A classification for optically active chromophores One of the most useful concepts that emerges from the perturbation approach to the theory of natural optical activity is that of the ‘rotational strength’ of a transition (Condon 1937). This signed quantity conveniently and effectively measures how strongly a particular transition contributes to both the dispersive and absorp­tive aspects of the optical activity of a molecule (Moscowitz 1962); it is obtainable experimentally from either the pertinent partial optical rotatory dispersion curve or the partial circular dichroism curve (Djerassi 1960), and it is amenable to theo­retical calculation for homogeneous isotropic media as the following scalar product (Condon 1937; Moscowitz 1962; Djerassi 1960; Rosenfield 1928). R ba = I {( a | μ e | b ). ( b | μ m | a )}. Here ( a | μ e | b ) and ( b | μ m | a ) are the electric and magnetic dipole transition moments, respectively, connecting the ground state a and the excited state b , and I means imaginary part. Accessible as such to both theory and experiment, the rotational strength provides one of the most suitable foundations on which to build quanti­tative correlations between optical activity data and molecular structure.

Dyadic green function for the electromagnetic field in multilayered isotropic media: an operator approach

1985 ◽  
Vol 132 (5) ◽  
pp. 329 ◽  
Author(s):  
T. Sphicopoulos ◽  
V. Teodoridis ◽  
F.E. Gardiol
Keyword(s):  
Electromagnetic Field ◽  
Green Function ◽  
Operator Approach ◽  
Isotropic Media
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