The photonic structure of a two-dimensional square lattice with square colu
mns rotated by 45 degrees is theoretically studied. For a range of dielectr
ic filling factors around f=0.5 (for which the lattice reduces to a chessbo
ard) a photonic band gap common to s and p polarizations is found. The comp
lete band gap occurs for a wide range of values of the dielectric contrast
and is maximum fur relatively low values of the contrast.