  We present design techniques of special optical lattices that allow quantum
simulation of spin frustration in two-dimensional systems. By carefully
overlaying optical lattices with different periods and orientations, we are
able to adjust the ratio between the nearest-neighbor and next-nearest-neighbor
interaction strengths in a square spin lattice and realize frustration effects.
We show that only laser beams of a single frequency is required, and the
parameter space reachable in our design is broad enough to study the important
phases in the $J_1$-$J_2$ frustrated Heisenberg model and checkerboard
antiferromagnet model. By using the polarization spectroscopy for detection,
distinct quantum phases and quantum phase transition points can be
characterized straightforwardly. Our design thus offers a suitable setup for
simulation of frustrated spin systems.
