Pockels coefficient, electrooptic

Figures 32a and 33 show the evaluation of the electrooptic Pockels coefficient 1-33 of our polymeric films during typical PEP cycles at room temperature. These curves were obtained as explained before by continuously recording the lock-in signal modulated at Q near the largest incidence TM mode which gives the direct measurement of An. When the measuring ac ( 3) and poling dc (Eg) electric fields are applied simultaneously to the polymer film, the An (z is equivalent to 3) variation is given by (Eq. 29) ...

Figure 33. Evolution of the Pockels coefficient of a DRl-polyimide film from ATR electrooptic modulation. The sudden jump up and down of the signal when the dc field is switched on and off originates from the third-order nonlinearity...

Assuming a factor of 2-2.5 for the resonance-enhancement factor in the electrooptic Pockels measurements (this range for the enhancement factor has been reported by many authors who measured the dispersion of the electrooptic Pockels coefficient in dc field poled PMMA-DRl) [88,89], and assuming similar NLO molecular densities for both the DRl-polyimide and PMMA-DRl polymers, one can see that the polar order achieved by PEP cycle in the DRl-polyimide high polymer is comparable to the one obtained in a flexible main chain DRl-PMMA copolymer. 

Comments on NLO and Electrooptic Coefficients. Typically, the Pockels effect is observed at relatively low frequencies (up to gigahertz) so that slower nonlinear polarization mechanisms, such as vibrational polarizations, can effectively contribute to the "r" coefficients. The tensor used traditionally by theorists to characterize the second-order nonlinear optical response is xijk Experimentalists use the coefficient dijk to describe second-order NLO effects. Usually the two are simply related by equation 31 (16) ... 

As shown in previous sections of this chapter, when an external perturbation is applied to the polymer film (such as irradiation), the ATR guided modes shift their angular positions and the reflectivity is modulated (Fig. 31b). These angular shifts are very small in the case of electrooptic experiments they correspond to refractive index variations of the order of 10 . One has then to modulate the measuring electric field at a low frequency Q( = cos fit) and to detect the modulated signal with lock-in amplifiers. The lock-in signals detected at the modulation frequency and its second harmonic give, respectively, the linear (or Pockels) and the quadratic (or Kerr) electrooptic effects. The amplitude of the modulation of the thickness and the refractive indices is evaluated by a computer fit, and allows the determination of Pockels (r) and Kerr (s) coefficients (Eqs. 28) ... 

Here ai is the frequency of the first strongly absorbing electronic transition in the molecule, and la and at are the fundamental wavelengths in second harmonic generation and for electrooptic coefficient measurements, respectively. The electrooptic effect (Pockels effect) is related to the corresponding second-order NLO susceptibility and by knowing the SHG coefficients, one can also estimate the electrooptic coefficients. 

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