Abstract
This work presents a new theoretical framework that extends the standard theory of quasi continuous-wave (CW) rare-earth-doped fibres to the ultrashort pulsed regime. We derive a time dependent, spectrally-resolved, nonlinear propagation equation for the coupled spectral components of the amplified pulse, within the rate-equation approximation. Our approach combines in a unified manner the effects of gain saturation, gain dispersion, fibre dispersion, fibre nonlinearity, stimulated Raman scattering, spontaneous Raman emission (with its temperature dependence) and amplified spontaneous emission (ASE). We also present theoretical models for rare-earth-codoped fibre lasers and amplifiers, in which the donor ions absorb a significant fraction of the pump power, delivering it to the acceptor ions through- an efficient energy transfer mechanism. In particular, we consider the rate-equation model for the Er3+-Yb3+ codoped system with and without Er3+ clustering, which takes into account energy transfer between the (donor) Yb3+ and the (acceptor) Er3+ ions. We also derive rate-equations for the Nd3+-Yb3+ codoped system that includes energy transfer between Nd3+ and Yb3+ ions, interactions among Nd3+ ions, single-ion transitions, and ASE due to Nd3+ and Yb3+ ions. An approximate, quasi-analytical solution to the model equations is derived for CW lasers. Previous theoretical works on short pulse amplification in doped fibres were derived mainly from the generalized nonlinear Schroedinger equation in the time domain. Furthermore, works on high-power rare-earth-codoped fibres have been limited mainly to CW Er3+-Yb3+ codoped fibre lasers and amplifiers. Using our new formulation, we extend previous works on short pulse amplification in doped fibres to the mixed spectrotemporal domain, allowing the full spectral resolution of both the incident pulse and the fibre parameters. We also apply our theoretical models to extend previous works on short length Er3+-Yb3+ codoped fibre amplifiers (EYDFA) to the quasi-CW regime and to study CW Nd3+-Yb3+ codoped fibre lasers (NYDFL). To this end, we solve numerically the rate-propagation equations and investigate various system design parameters of practical interest. The effects of the most important pulse and fibre parameters (e.g., incident pulse wavelength, pulse peak power, pulse chirp, fibre length and pump power) on the spectral and temporal characteristics of short amplified pulses are studied, both in the anomalous and in the normal fibre dispersion regimes. We analyze transient dynamic effects (e.g., amplifier stability) in short length, high-concentration, all-optical gain-clamped EYDFAs, in response to input signal modulations. We also study the effects of key parameters (e.g., fibre length, pump and laser wavelengths, output mirror reflectivity and dopant concentrations) on the output power, efficiency and optimal design (e.g., optimal fibre length and optimum dopant concentrations) of high-power CW NYDFLs. Key words: Optical fibre theory, optical fibre amplifiers, optical fibre dispersion, optical pulse amplifiers, Raman scattering, gain clamping, wavelength-division-multiplexing (WDM), optical fibre lasers, Erbium (Er), Ytterbium (Yb), Neodymium (Nd).