BYU Physics and Astronomy

Abstract: A new context for the group delay function (valid for pulses of arbitrary bandwidth) is presented for electromagnetic pulses propagating in a uniform linear dielectric medium. The traditional formulation of group velocity is recovered by taking a narrowband limit of this generalized context. The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points consists of two parts: a spectral superposition of group delays and a delay due to spectral reshaping via absorption or amplification. The use of the new context is illustrated for pulses propagating both superluminally and subluminally. The inevitable transition to subluminal behavior for any initially superluminal pulse is also demonstrated. (C) 2001 Optical Society of America.

Abstract: We examine the energy exchanged between an electromagnetic pulse and a linear dielectric medium in which it propagates. While group velocity indicates the presence of field energy ( the locus of which an move with arbitrary speed), the velocity of energy transport maintains strict luminality. This indicates that the medium treats the leading and trailing portions of the pulse differently. The principle of causality requires the medium to respond to the instantaneous spectrum, the spectrum of the pulse truncated at each new instant as a given lo ale in the medium experiences the pulse. (C) 2001 Optical Society of America.

Abstract: Without approximation the energy density in Poynting's theorem for the generally dispersive and passive dielectric medium is demonstrated to be a system total dynamical energy density. Thus the density in Poynting's theorem is a conserved form that by virtue of its positive definiteness prescribes important qualitative and quantitative features of the medium-field dynamics by rendering the system dynamically closed. This fully three-dimensional result, applicable to anisotropic and inhomogeneous media, is model independent, relying solely on the complex-analytic consequences of causality and passivity. As direct applications of this result, we show (1) that a causal medium responds to a virtual, "instantaneous" field spectrum, (2) that a causal, passive medium supports only a luminal front velocity, (3) that the spatial "center-of-mass" motion of the total dynamical energy is also always luminal and (4) that contrary to (3) the spatial center-of-mass speed of subsets of the total dynamical energy can be arbitrarily large. Thus we show that in passive media superluminal estimations of energy transport velocity for spatially extended pulses is inextricably associated with incomplete energy accounting.