Nonlinear electrooptic coefficients

LiNbOj is a widely used ferroelectric crystal with various applications in the nonlinear optics and integrated optics (10). Another attractive material for 10 devices is LiTaOs. Its electrooptic (EO) and nonlinear (NL) coefficients are comparable to those of LiNbOj, and its photorefractive damage threshold is more than an order of magnitude higher than that of LiNbOj in the visible range. 

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) ... 

For the sake of illustration, the determination of the electrooptic coefficient for a uniaxial crystal is described below. Considering the nonlinear uniaxial medium of Figure 11, a D.C. electric field is applied in the z direction. The effect of the electric field is to modify the refractive index in the z direction by an amount proportional to the electric field, the modified ellipsoid is given as... 

The linear and nonlinear optical behaviors of poly-(1,6-heptadiyne)s containing NLO chromophores was summarized in Table 22. It was found that n of the copolymers gave higher values than that of poly-76 not bearing any chromophore while the values of Amax were similar to each other. This result clearly shows the effects of incorporation of chromophore into the polymer backbone. The values of electrooptic coefficients, r33, for poled film samples of poly-77 to poly-81 by using a simple reflection technique reported by Teng et al. was measured. Table 22 shows the measured electrooptic coefficients of polymer films at... 

It was pointed out that the performance of photorefractive polymer composites is too large to be explained by the simple electrooptic photorefractive effect alone. A theoretical model was offered where both the birefringence and electrooptic coefficient are periodically modulated by the space-charge field due to the orientational mobility of the nonlinear chromophores at ambient temperatures. 

Sugie, M., and Tada, K, Measurements of the linear electrooptic coefficients and analysis of the nonlinear susceptibilities in cubic GaAs and hexagonal CdS, Jpn. Appl. Phys., 15, 421 (1976). 

Landolt-Bomstein Tables, Neue Serie Vol. III/30a (Editor D.F. Nelson), Springer Verlag. Cook, Jr. WR, Nelson DF, Vedan K (1996) High Frequency Properties of Dielectric Crystals. Piezooptic and Electrooptic Coefficients and Nonlinear Dielectric Susceptibilities. 

Third-order nonlinear optical properties (namely, quadratic electrooptic coefficient) of this polymeric system at different dye concentrations have been measured using a modified Michelson interferometer at 633nm. For this measurement, the polymer film was spin-coated from the filtered solution on an indium-tin-oxide (FTO) coated glass plate where the ITO layer was used as an electrode. A gold layer of 500A thickness was thermally evaporated onto the polymer film to form the second electrode. The experimental set-up of this modified Michelson interferometer is schematically shown in (Figure 7). 

The semiconducting properties of the compounds of the SbSI type (see Table XXVIII) were predicted by Mooser and Pearson in 1958 228). They were first confirmed for SbSI, for which photoconductivity was found in 1960 243). The breakthrough was the observation of fer-roelectricity in this material 117) and other SbSI type compounds 244 see Table XXIX), in addition to phase transitions 184), nonlinear optical behavior 156), piezoelectric behavior 44), and electromechanical 183) and other properties. These photoconductors exhibit abnormally large temperature-coefficients for their band gaps they are strongly piezoelectric. Some are ferroelectric (see Table XXIX). They have anomalous electrooptic and optomechanical properties, namely, elongation or contraction under illumination. As already mentioned, these fields cannot be treated in any detail in this review for those interested in ferroelectricity, review articles 224, 352) are mentioned. The heat capacity of SbSI has been measured from - 180 to -l- 40°C and, from these data, the excess entropy of the ferro-paraelectric transition... 

However, its was found possible to infer all four microscopic tensor coefficients from macroscopic crystalline values and this impossibility could be related to the molecular unit anisotropy. It can be shown that the molecular unit anisotropy imposes structural relations between coefficients of macroscopic nonlinearities, in addition to the usual relations resulting from crystal symmetry. Such additional relations appear for crystal point group 2,ra and 3. For the monoclinic point group 2, this relation has been tested in the case of MAP crystals, and excellent agreement has been found, triten taking into account crystal structure data (24), and nonlinear optical measurements on single crystal (19). This approach has been extended to the electrooptic tensor (4) and should lead to similar relations, trtten the electrooptic effect is primarily of electronic origin. 

The "r" coefficient characterizes the low frequency electrooptic nonlinearity and the "d" coefficient the optical frequency nonlinearity. The conversion from "r" coefficients to "d" or "x" coefficients must take into account the frequency dependence of the dielectric properties. 

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...

It is difficult to compare the second order nonlinear response of different materials because of its dependence on processing and the electrical poling process. Nevertheless, we have collected the SHG values of d33(= f 33/2) tensor components and electrooptic 33 coefficients for a number of SCPs containing NLO mesogenic groups in Table 22. 

In the first part of this paper we describe the properties of amorphous copolymer with a pending group with large hyperpolarizability. These amorphous copolymers show high optical nonlinear coefficients after poling under an electric field. We have used these copolymers for the manufacture of an electrooptic modulator working at 1.3 xm at a frequency of 1 GHz. 

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