A simple theoretical model for erbium doped PCF ring lasers design

Abstract

In this paper a simple theoretical model is presented where the energy conservation principle is used. The model is based on semi-analytical equations describing the behaviour of an erbium-doped photonic crystal fibre (PCF) inside a ring laser. These semi-analytical equations allow the characterisation of the erbium-doped PCF. Spectral absorption and emission coefficients can be determined through the measurement of the gain in the PCF as a function of pump power attenuation for several fibre lengths by means of a linear fitting. These coefficients are proportional to the erbium concentration and to the corresponding absorption or emission cross section. So if the concentration is known the erbium cross sections can be immediately determined. The model was successfully checked by means of two different home-made erbium doped PCFs. Once the fibres were characterised the values of the spectral absorption and emission coefficients were used to simulate the behaviour of a back propagating ring laser made of each fibre. Passive losses of the components in the cavity were previously calibrated. A good agreement was found between simulated and experimental values of efficiency, pump power threshold and output laser power for a wide set of experimental situations (several values of the input pump power, output coupling factor, laser wavelength and fibre length).