The motion of a charged particle in a space- and time-dependent potential and the motion of an optical pulse in an inhomogeneous anisotropic medium coincide when the dispersion surfaces are the same. For the trajectories in space to coincide, it is sufficient that the wave vectors be proportional. It follows from the general expression of the average stress-energy density
denotes the average lagrangian density and
denotes the 4 wave vector, that radiation forces are proportional to wave vectors for charged particles as well as for optical pulses. Because of these relations, many results in mechanics are applicable to optics. In particular, the constancy of the horizontal component of the velocity of a bullet on earth has, as a counterpart in optics, the constancy of the axial component of the group velocity of optical pulses propagating in thick tapered dielectric slabs. It follows from this observation that thick tapered dielectric slabs are not suited for long-distance communication, because of the large pulse spreading that they introduce. Slabs with moderate thickness, however, may exhibit low pulse spreading.
© 1975 Optical Society of America
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