Experimental measurements of the second order susceptibilities for the second harmonic generation are reported for YAl3(BO3)4 (YAB) single crystals for the two principal tensor components xyz and yyy. First principles calculation of the linear and nonlinear optical susceptibilities for Yttrium Aluminum Borate YAl3(BO3)4 (YAB) crystal have been carried out within a framework of the full-potential linear augmented plane wave (FP-LAPW) method. Our calculations show a large anisotropy of the linear and nonlinear optical susceptibilities. The observed dependences of the second order susceptibilities for the static frequency limit and for the frequency may be a consequence of different contribution of electron-phonon interactions. The imaginary parts of the second order SHG susceptibility chi_{123}^{(2)}(omega), chi_{112}^{(2)}(omega), chi_{222}^{(2)}(omega), and chi_{213}^{(2)}(omega) are evaluated. We find that the 2(omega) inter-band and intra-band contributions to the real and imaginary parts of chi_{ijk}^{(2)}l(omega) show opposite signs. The calculated second order susceptibilities are in reasonably good agreement with the experimental measurements.
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