In the case of optimal excitation of a multimode graded-index fiber by a laser diode, the coupling efficiency κ0 between the Gaussian laser beam and the fundamental mode of the fiber describes the input mode power distribution uniquely. Using this result, fiber impulse responses are calculated for two realistic excitations, first, by a gain-guided laser diode and second, by an index-guided laser diode. Also, the commonly used uniform and stationary excitations are given for comparison. The calculations yielding these results are based on the power diffusion equations and include profile dispersion, material dispersion, mode-dependent attenuation, and mode coupling. The mode group delay times have been computed for a parabolic profile using the scalar wave equation. However, delay times for other profiles can be introduced in the calculations. As κ0 characterizes laser fiber coupling uniquely and because it can simply be measured, we propose the use of κ0 as a characteristic launching parameter which allows easy comparison of measured impulse responses.
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