Third harmonic field determination

Figure 10 shows a typical measured homodyne waveform and the corresponding numerical fit (solid lines). The measured THz waveform exhibits both the fundamental ECDL difference frequency (Fig. 10(a)) and higher harmonics - predominantly the third harmonic (Fig. 10(b)). Multiple harmonic generation in THz photo-mixers has been previously reported [103], By fitting the observed waveform to a sum of harmonic sinusoidal functions, the amplitude and phase of the THz electric field can be determined separately for the fundamental and third harmonic. The solid line shows a numerical fit to the data. The fundamental extracted frequency, 0.535 THz, compares well to the expected frequency based on the frequency difference of the two ECDL. The extracted E field amplitudes and phases are 3.37 x 10 4 and 2.17 radians for 0.535 THz (Fig. 10(a)) and 5.61 x 10-5 and 3.94 radians for the 1.605 THz third harmonic, respectively (Fig. 10(b)). 

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] ... 

On the assumption of total symmetry of the tensor of third-order nonlinear polarizability c(— co coi, cog, cog), its non-zero and independent elements are the same as those of Table 12. Direct theoretical calculations of c = c(0 0,0,0) have been performed for the atoms of inert gases and some simple molecules. Values of the tensor elements = c(— cu cu, 0,0) have been determined for numerous molecules from static Kerr effect studies and values of c = c(— cd ot>,coi — col) from measurements of optical birefringence induced by laser li t. Measurements of second-harmonic generation by gases in the presence of a static electric field yield the tensor elements c " = c( — 2co co, to, 0), which can also be obtained from second-harmonic scattering in centro-symmetric liquids. The elements of the tensor c = c(— 3co co, co, co)... 

This quantity is the source of the second harmonic and is determined from its intensity and the macroscopic optical parameters. If the intensity of the optical input is also measured and the static field strength known then the susceptibility in the equation can be calculated. In practice the intensity of the SHG is measured relative to a known standard that for solution work has usually been quartz, occasionally lithium iodate. In the gas phase a calculated value for an inert gas has been used. The macroscopic third order susceptibility has to be related to the response functions for the active molecule in the solution. 

The first common method for molecular first hyperpolarizability determination is the electric field-induced second harmonic generation (EFISH) technique in solution [6-10]. This technique can be applied only to dipolar molecules. Under an applied external electric field, molecules in solution orient approximately in the direction of the field giving rise to second harmonic generation. The measured third-order nonlinear optical susceptibility is given by the following expression ... 

---