Second harmonic generation field response

Various combinations of these frequencies give rise to different NLO phenomena for instance, at second order, (0 0, 0), 0 -w, a>, 0), (0 a>, -a>), and P —2co CO, ) define the static, dc-Pockels, optical rectification, and second harmonic generation (SHG) responses, respectively. According to Eq. (8.1), the first hyperpolarizabilities can be formally expressed as the second-order derivatives of the dipole moment with respect to electric fields, or, alternatively, as the third-order derivatives of the total energy E. 

In addition to the fourth-order response field Tfourth, the probe light generates two SH fields of the same frequency 211, the pump-free SH field Eq(2 Q), and the pump-induced non-modulated SH field non(td> 211). The ground-state population is reduced by the pump irradiation and the SH field is thereby weakened. The latter term non(td, 211) is a virtual electric field to represent the weakened SH field. Time-resolved second harmonic generation (TRSHG) has been applied to observe E on (td, 211) with a picosecond time resolution [20-25]. The fourth-order field interferes with the two SH fields to be detected in a heterodyned form. 

The dielectric tensor describes the linear response of a material to an electric field. In many experiments, and particularly in optical rheometry, anisotropy in is the object of measurement. This anisotropy is manifested as birefringence and dichroism, two quantities that will be discussed in detail in Chapter 2. The nonlinear terms are responsible for such effects as second harmonic generation, electro-optic activity, and frequency tripling. These phenomena occur when certain criteria are met in the material properties, and at high values of field strength. 

Second harmonic generation (SHG), attenuated total reflection (ATR) and Stark (electroabsorption) spectroscopy were employed to find PAP. The response of the interaction between an electric field (E ) and a material can be described by Equation (10.14). 

In 1996, Munn extended the microscopic theory of bulk second-harmonic generation from molecular crystals to encompass magnetic dipole and electric quadrupole effects [96] and included all contributions up to second order in the electric field or bilinear in the electric field and the electric field gradient or the magnetic field. This was accomplished by replacing the usual polarization of Refs. 72 and 84 by an effective polarization as well as by defining an effective quadrupole moment. Consequently, the self-consistently evaluated local electric field and electric field gradient were expressed in terms of various molecular response coefficients and lattice multipole tensor sums (up to octupole). In this... 

In order to select a particular experimental technique to measure x , it is very important to keep in mind which parameter of the third-order nonlinear response has to be characterized. For example, if one wants to determine the time-response due to molecular reorientation, one cannot choose Third-Harmonic Generation or Electric-Field-Induced Second-Harmonic Generation, since none of these techniques provide time-response information. Depending on the parameter of interest, a specific technique must be chosen. The following physical mechanisms can contribute to the third-order nonlinear response [54] ... 

The Hartree-Fock method for periodic systems nowadays represents a routine approach coded in several ab initio computer packages. We may analyze the total energy, its dependence on molecular conformation, the density of states, the atomic charges, etc. Also, calculations of first-order responses to the electric field (poljmiers are of interest for optoelectronics) have been successful in the past. However, nonlinear problems (like the second harmonic generation see Chapter 12) stiU represent a challenge. 

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