Optical Second-Harmonic Generation in Commensurate-Incommensurate Phase Transitions

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(1) Intensities of optical second-harmonic wave and coherence lengths were measured in the ferroelectric and incommensurate phases of (NH_4) BeF_4 (AFB) , K_2ZnCl_4 (KCZ) , and {N (CH_3)_4}_2ZnCl_4 ((TMA) CZ) crystals. It was found that no appreciable second-harmonics was observed in the incommensurate phase of AFB. While KCZ and (TMA) CZ exhibited weak intensities around their lock-in transition temperatures. The results could be interpreted on the model where nonlinear optical constant modulates with the incommensurate period along the incommensurate axis. It was also found that an annealing effect on the second harmonics was observed in KCZ. Measured coherence lengths were compared with the incommensurate modulation period determined by the Xーray diffraction method. It was found that the coherence lengths were larger than the modulation period by a factor of 10^2-10^3. These facts indicate that the possibility of quasi-phase matching i. e., the coincidence of the coherence length and the modulation period, is excluded in the crystal.(2) All independent components of the second-order nonlinear optical (SHG) tensors and Miller's indices of Ca_2Pb (C_2H_5CO_2)_6 (DLP) were determined in the temperature range from -60^0C to 90^0C Both in paraelectric and ferroelectric phases, the components d11 and d14 which are forbidden by the symmetry and Kleimann's condition were also observed. Precise examination revealed that the phenomenon originated from the symmetry-lowering as a result of strong internal electric field produced in the DLP crystal. By annealing the crystal at 250^0C, the effect of symmetry-lowering could be diminished. Temperature dependences of the SHG tensors were analyzed by the bond-charge theory where Pb-0 and Ca-0 bonds were assumed to contribute mainly to the observed tensors.Opposite sign of the two bond-contributions causes the anomalous temperature dependence of the SHG tensors.