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We investigate a unique type of zero-index medium with both gain and loss(ZIMGL), whose effective permittivity and permeability are purely imaginary andof opposite signs. We show analytically that, by using a slab of ZIM-GL withequal magnitude of loss and gain, coherent perfect absorber (CPA) and laser,i.e. the socalled CPA-laser, can be achieved simultaneously. CPA-laser has beenfound previously in parity-time (PT) symmetric systems. However, the underlyingphysics in a PT-symmetric system is distinct from that in a ZIM-GL. Bydesigning a photonic crystal (PC) composed of core-shell rods, with loss andgain distributed in either the core or the shell, we have realized such aZIM-GL. The CPA-laser functionality of such a PC is also confirmed in ournumerical simulations. Our work provides a different approach for simultaneousrealization of CPA and laser besides PTsymmetric systems.

Simultaneous Realization of Coherent Perfect Absorber and Laser by Zero-Index Media with both Gain and Loss