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We develop a theoretical framework for modeling of continuous wave Yb-doped fiber lasers with highly nonlinear cavity dynamics. The developed approach has shown good agreement between theoretical predictions and experimental results for particular scheme of Yb-doped laser with large spectral broadening during single round trip. The model is capable to accurately describe main features of the experimentally measured laser outputs such as power efficiency slope, power leakage through fibre Bragg gratings, spectral broadening and spectral shape of generated radiation.

A ground-based laser system for space-debris cleaning will use powerful laser pulses that can self-focus while propagating through the atmosphere. We demonstrate that for the relevant laser parameters, this self-focusing can noticeably decrease the laser intensity on the target. We show that the detrimental effect can be, to a great extent, compensated for by applying the optimal initial beam defocusing. The effect of laser elevation on the system performance is discussed. Keywords: laser; self-focusing; space debris INTRODUCTIONThe proliferation of satellites in Earth orbit, which are increasing in both number and value, makes the problem of collisions with orbital debris very real. One of the most practical solutions to this problem is debris removal facilitated by a ground-based pulsed laser. In this approach, laser pulses ablate debris material, change the debris velocity and move the debris to a lower orbit, where natural burn-up occurs (Figure 1). This method of debris removal has been analyzed by the 'Orion' project; 1,2 in this analysis, requirements for the laser and optical and tracking systems were summarized, and the role of nonlinear effects was discussed. Two aspects of the situation have changed since the completion of that project. First, the risk of valuable-asset damage has increased and is now so serious that governments may be willing to spend money on orbital-debris removal. Second, a significant advance in powerful pulsed-laser technology has taken place, mainly at Lawrence Livermore National Laboratory, with the completion of the National Ignition Facility Project.3 Systems designed for inertial-confinement-fusion applications are a near-perfect fit for orbital-debris-removal applications.We begin the analysis with the requirements for the laser pulse on the target. Then, we discuss beam propagation and focusing to more completely define the requirements for the laser. Based on these more specific requirements, we specify a range of parameters for laser operation. We demonstrate that the laser-pulse power substantially exceeds the critical power for self-focusing in air. However, because the laser light is propagated almost vertically, the self-focusing length is much longer than the thickness of the atmosphere. Our numerical calculations demonstrate that the spatial structure of the beam on the target is smooth, without filaments, but the nonlinear effects noticeably decrease the peak intensity. We demonstrate that the atmosphere can be treated as an additional focusing lens and that preliminary beam defocusing can significantly compensate for the detrimental effects of the atmosphere.