We provide a new unified formalism for the analogy between fiber-optics and mechanics. It is based on the scalar theory of light for an optical fiber with length-independent refractive index, and the mechanics of a particle in a time-independent potential. Illustrative examples such as tunneling and precession are given. We also mention the conceptual analogies that arise when we include (i) polarization and (ii) length or time-dependent variations. This should prove useful both in teaching and as a bridge between research areas.
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Black et al. (1985) studied this question.