Time-dependent coupled-power equations describing the transmission of light in multimode optical fibers are discussed, and a new method, using the temporal moments of transmitted light pulses, is described. This method, as well as showing details of a fiber's steady state and how it is reached, yields approximate equations for the length-dependence of pulse broadening in long chains of nonuniform fibers with mode mixing. These approximations are based on closed-form solutions for a two-mode waveguide, but they are generalized and seem to be useful as a mathematical model for long optical cables.
The transmission bandwidth of optical fibers is usually described by their 3-dB bandwidth. This is however problematic if the fiber is operated close to the wavelength λ 0 where its dispersion becomes zero and its bandwidth maximum. It is shown that in this case (or more precisely: if λ 0 is within the spectrum of the optical source) the useful bandwidth is well below the 3-dB bandwidth, and that the so-called 1/5 σ-bandwidth, which is related to the rms width σ of the fiber's impulse response, is both a more realistic and a more convenient figure for characterizing fiber performance at any wavelength.
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