  Conjugate metamaterials, in which the permittivity and the permeability are
complex conjugates of each other, possess the elements of loss and gain
simultaneously. By employing a conjugate metamaterial with a purely imaginary
form, we propose a mechanism for realizing both coherent perfect absorber (CPA)
and laser modes, which have been widely investigated in parity-time symmetric
systems. Moreover, the general conditions for obtaining CPA and laser modes,
including obtaining them simultaneously, are revealed by analyzing the wave
scattering properties of a slab made of purely imaginary conjugate
metamaterials. Specifically, in a purely imaginary conjugate metamaterial slab
with a sub-unity effective refractive index, perfect absorption can be realized
for the incident wave from air.
