Second harmonic coefficient measurement

Second harmonic coefficients of the poled films were measured at... 

The nonlinear optical properties of thin films of the polymers were investigated through measurement of second-harmonic generation, and exhibit second-harmonic coefficients, d33, in the range 4.1-34 pm/V. 

It has been established experimentally that the origin of the electro-optic effect in organic materials is largely electronic. This implies that the linear electro-optic coefficient can be estimated from the second harmonic coefficient. By properly accounting for the dispersion (using a two level model), the electronic contribution to the electro-optic coefficient is calculated to be r5 3 - 2.4 0.6 x 10 m/V at X-O.S m. Measured values of the electro-optic coefficient are in agreement within experimental uncertainty. These values compare favorably with that of GaAs (r4i - 1.2 x 10 m/V). 

The refractive indices of M(CeH5)4 crystals (M = Si to Pb) are in the 1.58 0.05 range. The crystals are transparent from 325 to 1200 nm and are Class B second harmonic generators. Measurements of linear electro-optic effects show the rg3 coefficients to be in the range (17 + 1) X 10 m/V with half-wave retardation voltages of 5 kV [24]. 

CB04. The spontaneous polarisation was measured by the pulse pyroelectric technique (Ps = 46 nC/cm ). The piezoelectric coefficient evaluated for CB04 was dsi = 1.6 pC/N. The estimation of the efficiency of the second harmonic generation for compound CB04 gives the value three times more than for quartz. 

This effect, which is in a loose sense the nonlinear analog of linear optical rotation, is based on using linearly polarized fundamental light and measuring the direction of the major axis of the ellipse that describes the state of polarization of the second-harmonic light. For a simple description of the effect, we assume that the expansion coefficients are real, as would be the case for nonresonant excitation within the electric dipole approximation.22 In this case, the second-harmonic light will also be linearly polarized in a direction characterized by the angle... 

Figure 9.9 Simulated normalized line shapes of -polarized (a-c) and p-polarized (if-/) second-harmonic signals for quarter waveplate measurements (a) and (if) hypothetical achiral surface (hs = 0.5 fp = 0.75, gp = —0.5), (b) and (if) hypothetical chiral surface with in-phase chiral coefficient (fs = 0.75, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25), (c) and (/) hypothetical chiral surface with out-of-phase chiral coefficient ( fs = 0.75 0.25i, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25z). Upper (solid line) and lower (dashed line) sign in expansion coefficients correspond to two enantiomers. Rotation angles of 45° and 225° (135° and 315°) correspond to right-hand (left-hand) circularly polarized light and are indicated for one of enantiomers with open and filled circles, respectively.

The coefficients /, g, and h are unique for each second-harmonic signal and depend on the three susceptibility tensors. We normalize the relative values of the tensor components to = 1- The task is then to determine the complex values of the other 14 tensor components (see Table 9.2). A sufficient number of 8 independent measurements is provided by the p- and s--polarized components of the reflected and transmitted second-harmonic signals for the two orientations of the sample shown in Figure 9.17. The change in sample orientation corresponds to a coordinate transformation that reverses the... 

The nonlinearity of the sample was analyzed using the experimental procedure described in Section 3.3 The polarization of the fundamental beam of a YAG laser was continuously varied by means of a quarter waveplate, and the intensity of the second-harmonic signal was measured as a function of the rotation angle of the quarter waveplate. The obtained polarization pattern were then fitted to Eq. (42), which yields the relative values of the expansion coefficients /, g, and h. The experimental results for the transmitted, glass-side-incidence, s-polarizcd signal are shown in Figure 9.20. 

Calculations which ascribe nonlinear optical polarizabilities in LilOa to the individual I-O bonds and relate experimentally measured second harmonic generation coefficients x 311 and X313 to theoretical results for the structure of LilOs, have been performed by Jeggo ii). 

Both theoretical analysis and dipole moment measurements indicated that sulfonyl-substituted compounds may have ft coefficients similar in magnitude to their nitro analogues. Therefore, we have measured p for several sulfonyl- and nitro-substituted compounds using electric-field-induced second-harmonic generation method (EFISH) (11,25). In this experiment, one measures an effective third-order nonlinearity rEFISH for a solution containing the compound of interest, given by... 

Before we close this section, let us emphasize the importance of the degeneracy factor D in Eq. (28). This factor takes different values depending on the nature of the nonlinear optical process. For instance, in the case of second harmonic generation its value is unity, while for an electro-optic process it takes the value 2. Therefore, great care must be taken in reconciling experimental values of nonlinear coefficients measured using different experiments. 

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) ... 

We measured SHG efficiencies tjconv = P toipm ( pto inside of the film) for the conversion of a fundamental TEo-mode (X = 926 nm) into a second-harmonic TEi-mode of up to 6-10 3 (pto = 30W, nonlinear optical coefficient djj = 12.9 pm/V, beam width 0.5 mm, interaction length 2 mm) yielding a ncmnalized conversion efficiency of iJnorm = 0.5%W cm 2 (0.02%W ). This corresponds reasonable to the calculated conversion efficiency iJcalc - 2.2%W lcm if one considers the attenuation of the modes that was neglected in the theory. 

A quite direct method for measuring x is based on second harmonic generation, SHG. Figure 3.3 depicts a typical set-up used to determine the SHG coefficients and d, defined as d=x l2, by way of SHG measurements. 

Nonlinear optical properties. The optical nonlinearity was characterized by two experiments second harmonic generation (SHG) and electro-optic measurements. All of the results are listed in Table n. The second harmonic generation (SHG) for the poled polyimides was conducted to determine the second harmonic generation coefficients (das). PI 1 possessed the highest value of SHG... 

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