  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.
