Time Dispersion in Dielectric Waveguides

In multimode dielectric waveguides operating at optical frequencies, the primary cause of time dispersion of narrow pulses can be mode conversion. In a geometrically perfect guide with more than a single mode, energy initially launched in a given mode remains in that mode as it propagates down the guide. Physical guides have imperfections from perfect geometric shape (e.g., roughness at the core-cladding interface of a nominally right circular cylindrical guide) which allows energy to couple between modes during propagation down the guide'. Since group velocities differ in general amongst the modes, a pulse of energy initially launched in a single mode or combination of modes will be broadened due to the spread of propagation times of different parts of the energy. 843 844 T H E BELL SYSTEM TECHNICAL JOURNAL, MARCH 1971 In this paper we argue that under certain assumptions, a dielectric waveguide acts as a linear system in intensity as well as in voltage. That is, we show that the relationship between the input intensity and output intensity of the guide is defined in terms of an intensity impulse response. We argue that this intensity impulse response, for sufficiently long guides, has a mean-square width about its mean which increases only linearly with length. Further, in the limit of very long guides, we argue that the response shape is gaussian. We also show that the greater the coupling between modes, the less the time dispersion--a result which at first contradicts intuition.