Ultimate efficiency of the quasi-perfect CPA laser constructed of a one-dimensional finite periodic parity-time-symmetric optical waveguide network

In this paper, the ultimate efficiency of the coherent perfect absorber and laser (CPA laser) generated by a one-dimensional (1D) two-connect two-material finite periodic parity-time (PT) symmetric optical waveguide network is studied. It is found that producing a perfect CPA laser four conditions need to be satisfied, but unfortunately they cannot be filled simultaneously, and consequently, a perfect CPA laser is impossible to be achieved. Nevertheless, for a optical waveguide network with given material and unit cell structure, the quasi-perfect CPA laser that generates ultimate efficiency can be designed by means of high-order infinitesimal constraint conditions. The maximal transmissivity and minimal overall output coefficient produced by our designed quasi-perfect CPA laser reach 3.81 x 1015 and 1.19 x 10-14, respectively, which are, respectively, 9 orders of magnitude larger and 7 orders of magnitude smaller than the corresponding best reported results. It may possess potential applications in integrated optics, high power lasers, optical signal pulse recovery, highly sensitive optical coherent filters and linear optical switches, etc.