  We propose a theoretical scheme in a cold Rubidium-87 ($^{87}$Rb) atomic
ensemble with a non-Hermitian optical structure, in which a lopsided optical
diffraction grating can be realized just with the combination of single
spatially periodic modulation and loop-phase.~Parity-time ($\mathcal{PT}$)
symmetric and parity-time antisymmetric ($\mathcal{APT}$) modulation can be
switched by adjusting different relative phases of the applied beams. Both
$\mathcal{PT}$ symmetry and $\mathcal{PT}$ antisymmetry in our system are
robust to the amplitudes of coupling fields, which allows optical response to
be modulated precisely without symmetry breaking. Our scheme shows some
nontrivial optical properties, such as lopsided diffraction, single-order
diffraction, asymmetric Dammam-like diffraction, etc. Our work will benefit the
development of versatile non-Hermitian/asymmetric optical devices.
