Nonlinear optics theoretical formalism

ANALYSIS OF NONLINEAR OPTICAL ACTIVITY 3.1 Theoretical Formalism... 

Recently, it was theoretically shown, on the basis of standard density-matrix formalism of nonlinear optics, that chiral isotropic media can possess an electrooptic response [174]. Such materials would be inherently stable and could therefore be extremely useful for the development of electro-optic devices. Contrary to usual electro-optic materials, index (absorption) modulation in such media is due to the imaginary (real) part of the electro-optic susceptibility. The response relies on the damping of the material response. 

A diagrammatic approach that can unify the theory underlying these many spectroscopies is presented. The most complete theoretical treatment is achieved by applying statistical quantum mechanics in the form of the time evolution of the light/matter density operator. (It is recommended that anyone interested in advanced study of this topic should familiarize themselves with density operator formalism [8, 9,10, JT and 12]. Most books on nonlinear optics [13. 14. 15. 16 and 17] and nonlinear optical spectroscopy [18. 19] treat this in much detail.) Once the density operator is known at any time and position within a material, its matrix in the eigenstate basis set of the constituents (usually molecules) can be determined. The ensemble averaged electrical polarization, P, is then obtained— the centrepiece of all spectroscopies based on the electric component of the EM field. 

Puig-Molina et a/.141 compared the theoretical and experimental electron density in the nonlinear optical material 2-amino-5-nitropyridinium dihydrogen phosphate, 2A5NPDP. The experimental p was determined from X-ray diffraction data interpreted in terms of the Hansen Coppens pseudoatom formalism. The BCP properties of the total experimental electron density agree fairly well with Hartree-Fock calculations for the isolated ions. The analysis of the... 

D. Li, T. J. Marks, M. A. Ratner, Nonlinear optical phenomena in conjugated organic chromophores. theoretical investigations via a Ji-electron formalism. J. Phys. Chem. 1992, 96, 4325. 

---