Magnetic dipole, contribution

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... 

The numbers of IR- and Raman-active modes are 4 (4tiJ and 10 (2ag + 8hg), respectively. On the other hand, hyper-Raman-active modes are all of the modes with u symmetry, including the silent modes. Compared with the theoretically calculated result, the expected modes are clearly seen in the spectmm. (The appearance of Raman-active modes is due to magnetic dipole contributions.)... 

Nonlinear Optical Activity and Magnetic Dipole Contributions... 

We see that the electric dipole allowed transitions are, in general, much more intense than the magnetic dipole allowed transitions. In fact, the magnetic dipole contribution to an optical transition of a center dominated by an electric dipole character is usually completely masked by the much more intense J electric dipole transitions. 

In this equation, d2u) represents the angle of the radiated SH light with respect to the surface normal, 7(co) is the pump intensity, and e(2co) is the polarization at the SH frequency. The vectors e(co) and e(2co) are related to the unit polarization vectors e(co) and e(2co) in medium 2 by Fresnel coefficients. The effective surface nonlinear susceptibility incorporates the surface nonlinear susceptibility x( and the bulk magnetic dipole contributions to the nonlinearity. The result simplifies since, for isotropic media, there are only three nonzero independent elements of xf These are x%, X% = X%.> and XsfL where 1 =... 

We can deduce the symmetry of a response tensor by considering the operators that enter the numerator of its quantum mechanical expression. For example, the product of three electric-dipole transition moment operators in Eq. (14) render SFG a parity-odd and time-even process. It follows that a third-order process requires nonlocal magnetic-dipole contributions in order to be parity-odd and that a local fourth-order process is parity-odd within the electric-dipole approximation. Some pseudoscalars that arise at order n are tabulated below. 

For randomly oriented molecules, the averaging leaves only the electric dipole-magnetic dipole contribution and the scalar rotatory strength is given by... 

The additional electric quadrupole and magnetic dipole contributions from the bulk can be separated from the real surface contributions only under special conditions for example, if one modifies the surface layer in the form of an evaporated thin film and if one extracts the bulk contributions by calculating the interface contributions (Koopmans et al. 1993). The bulk contributions are proportional to the field gradient, meaning that a zone of about A/27T 5... 10 nm contributes to the total signal intensity. 

An effective method for the prediction of the magnetic dipole character of a transition is intensity calculation. The intensity of a magnetic dipole transition can be calculated if appropriate wavefunctions are available (see sect. 4). Wavefunctions are obtained from a set a free-ion (and crystal-field) parameters. The parameter sets are derived from the energetic positions of the transitions. If a zero or nearly zero intensity is calculated for the magnetic dipole contribution of a particular transition observed in the spectrum, we can conclude that this transition has mainly an induced electric dipole character. 

The matrix elements calculated in eqs. (24.12-24.14) must be transformed into the intermediate coupling scheme before computation of the magnetic dipole contribution represented by eq. (24.11). 

---