  We present generation of asymmetric aberration laser beams (aALBs) with
controlled intensity distribution, using a diffractive optical element (DOE)
involving phase asymmetry. The asymmetry in the phase distribution is
introduced by shifting the coordinates in a complex plane. The results show
that auto-focusing properties of aALBs remain invariant with respect to the
asymmetry parameters. However, a controlled variation in the phase asymmetry
allows to control the spatial intensity distribution of aALBs. In an ideal ALB
containing equal intensity three bright lobes (for $m=3$), by introducing
asymmetry most of the intensity can be transferred to any one of single bright
lobe, and forms a high-power density lobe. A precise spatial position of
high-power density lobe can be controlled by the asymmetry parameter $\beta$
and $m$, and we have determined the empirical relations for them. We have found
that for the specific values of $\beta$, the intensity in the high-power
density lobe can be enhanced by $\sim$6 times the intensity in other bright
lobes. The experimental results show a good agreement with the numerical
simulations. The findings can be suitable for applications such as in optical
trapping and manipulation as well as material processing.
