General Coupling Properties of Complex-Valued Refractive Index Fiber Couplers

In this paper, coupling properties of directional fiber couplers using complex-valued refractive index fibers were discussed and extended to complex-valued owing to the complex-valued refractive index. We have derived the optical intensity distributions along the fiber direction, particularly on the energy transmission which includes coupling process and amplification process between conventional index guided (passive) fiber core and gain guided and index antiguided (active) fiber core, where gain effect is averaged into two cores.