Simple analytical results are obtained for the mode distribution and impulse response of graded index fibres under a variety of excitation conditions relevant to practical systems. It is found that the choice of an optimum refractive index profile depends quite strongly on the source distribution of or, that one can significantly improve the impulse response of a particular profile by appropriate choice of launching conditions. Furthermore the r.m.s. pulse width is not necessarily reduced simply by partially filling the numerical aperture of the fibre.
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