Parity time symmetry in two dimensional chiral optical lattice, via positive and negative refraction

The parity time symmetry and positive/negative refraction is investigated in chiral optical lattice. Significant parity time symmetry is reported in five level chiral optical lattice which satisfied the conditions Re(n(r)((+/-))(x,y)) = Re(n(r)(*(+/-))(-x, -y) and Im(n(r)((+/-)) (x, y)) = -I m(n(r)*((+/-)) (-x, -y) for left and right circularly polarized beams. The related group indices, phase shifts and divergent angle are also satisfied the parity time symmetry conditions n(g) ((+/-)) (x, y)) = n(g)*((+/-)) (-x, -y) phi((+/-)) (-x, -y)) = phi*((+/-)) (-x, -y) and theta(d,g)* (-x, -y) for left and right circularly polarized beams. Maximum negative group index is calculated to -25000. The maximum phase and group divergent angles are reported to 0.001 radian and -0.9 radian. The phase shifts in LCP and RCP beams are investigated to +/- 0.004 radian at a length L = 10 lambda. The modified results have potential application in nanotechnology.