Optical pulse propagation in dispersive systems

A new context for the group delay function is presented describing electromagnetic pulse propagation in a uniform linear dielectric medium. In contrast to the traditional formulation, this new context retains validity for pulses of any bandwidth, propagating in media with arbitrarily complicated resonance structures. The new context defines the arrival time of a light pulse at a point in space (using a time expectation integral over the Poynting vector) and considers the delay between pulse arrival times at two distinct points. This delay consists of two parts: a spectral superposition of group delays and a delay due to spectral reshaping via absorption or amplification. The traditional formulation of group velocity is recovered by taking a narrowband limit of this generalized context. The use of the new context is illustrated for pulses propagating both superluminally and subluminally in amplifying and absorbing media. The inevitable transition to subluminal behavior for any initially superluminal pulse is also demonstrated.; The energy exchanged between an electromagnetic pulse and a linear dielectric medium in which it propagates is also considered. It is this exchange of energy which allows for the superluminal behavior of the centroid of field energy. While group velocity indicates the presence of field energy (the locus of which can move with arbitrary speed), the velocity of energy transport maintains strict luminality. This indicates that the medium exchanges energy differently with the leading and trailing portions of the pulse. The reason for this asymmetric treatment is clearly demonstrated by rewriting the exchange energy in terms of the instantaneous spectrum (i.e., the spectrum of the pulse truncated at each new instant as a given locale in the medium experiences the pulse). This description for the exchange energy directly emphasizes the role of the principle of causality and gives insight into the phenomenon of superluminal pulse propagation.