Gain-guided optical fibre refractive index synthesis starting from arbitrary modal electric field

Novel results on how to reconstruct gain-guided optical fibres starting from arbitrary modal electric fields are presented. It is known that gain-guided optical fibre refractive index profiles are described in terms of complex numbers. Therefore, to achieve the design of such fibres from a knowledge of modal electric fields one is required to use complex refractive index profile waveguides, where one can determine the required refractive index profile on both real and imaginary parts of the refractive index. The novelty here is that the reconstruction starts by using complex-valued desired electric fields. This inverse problem is solved via modelling the waveguide transversely as a transmission line and working inversely from the electric field. Example reconstructions of refractive index profiles are offered which are useful for high-power lasers, in designing optical fibres for sensors, where one may require specifically shaped electric fields from a waveguide, and also in refractive index profiling instrumentation.