Harmonic field

Both components will radiate, giving rise to second-harmonic radiation polarized in the zx plane. Hence, the polarization of the second-harmonic field is the same as that of the fundamental field. 

The presence of chirality introduces an additional component in the y direction. This component will rotate the polarization of die second-harmonic field with respect to the polarization of the incident radiation. The amount of optical rotation will depend on the relative magnitude of the chiral and achiral susceptibility components. Furthermore, Py changes sign between the enantiomers... 

Figure 9.8 Second-harmonic generation from thin film (or surface). Fundamental beam at frequency > i p or. v polarized) is incident on film at angle 0. The p- and. s-polarized second-harmonic fields (frequency 2 co) are generated in reflection and transmission. 

The second-harmonic field generated in the sample can be calculated by 20... 

From an experimental point of view, it is more practical to consider the second-harmonic intensity instead of the second-harmonic fields. For simplicity, the intensity is expressed as the square of the amplitude of the electric... 

The vector Fc is a complex representation of the real field F. If all our operations on time-harmonic fields are linear (e.g., addition, differentiation, integration), it is more convenient to work with the complex representation. The reason this may be done is as follows. Let be any linear operator we can operate on the field (2.10) by operating on the complex representation (2.11) and then take the real part of the result ... 

Note that there is a degree of arbitrariness associated with the complex representation of a real field F could just as easily have been written F - Re(F, where F = C exp(/to/) and the asterisk denotes the complex conjugate. Thus, there are two possible choices for the time-dependent factor in u complex representation of a time-harmonic field exp(/co/) and exp( — iat). It mukcs no difference which choice is made the quantities of physical interest arc ttlwuys real. But once a sign convention has been chosen it must be used conniMcntly in all analysis. We shall take the time-dependent factor to be exp(-/u>/) this is the convention found in standard books on optics (Born Mini Wolf, 1965) and electromagnetic theory (Stratton, 1941 Jackson, 1975) as... 

To obtain the frequency-dependent susceptibility x(<°), we need the polarization in response to a time-harmonic field E0e ... 

Besides its appearance in the FFMF equation in plasma physics, as well as associated with time-harmonic fields in chiral media, the chiral Beltrami vector field reveals itself in theoretical models for classical transverse electromagnetic (TEM) waves. Specifically, the existence of a general class of TEM waves has been advanced in which the electric and magnetic field vectors are parallel [59]. Interestingly, it was found that for one representation of this wave type, the magnetic vector potential (A) satisfies a Beltrami equation ... 

Figure 4. Illustration of the dependence of the amplitude of the harmonic field E(2co) on its phase relationship with the polarization response P(3co).

It was indicated numerous times that the SHG intensity is dependent on both the magnitude of x<2) tensor elements as well as the phase relationships between fundamental and harmonic fields in the crystal. Under certain circumstances, it is possible to achieve phase matched propagation of the fundamental and harmonic beams. Under these conditions, power is continually transferred from the fundamental to harmonic beam over a path length, which is only limited by the ability... 

Kajzar and Messier have analyzed the THG from their cell described above. A brief overview of their analysis is given here. The cell is comprised of two thick wedge windows and a thin liquid wedge compartment. Since the windows are thick, they are considered to be infinite nonlinear media. Since the liquid chamber is thin, the laser field is treated as a plane wave in that region. The third harmonic field at the output of the cell is the resultant of the fields generated in the three media... 

To treat an absorbing medium with a complex it is necessary to resort to eq. 17 including appropriate transmission factors accounting for absorption of the fundamental and/or third harmonic fields (31). In this case the third harmonic intensity is (again suppressing transmission coefficients, t)... 

MM2 [189] uses cubic anharmonic potential to represent the bond stretching, up to sixth power expansion for the valence angle bending, and harmonic field for the out-of-plane deformations. The stretch-bending cross term is included. 

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