Role of group velocity in tracking field energy in linear dielectrics

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.

Steady-state analysis of signal transmission in evanescent channels

“…Only the power coupling accompanying a measurement has been shown to be responsible for limiting the transmission velocity of the measured physical quantity below or equal . A generalization of some of the results presented in this contribution to the case of wideband signals can be found in the recent publications [17] and [18] which comprehensively deal with the problem of linear energy transfer in dielectrics.…”

Group Delay Description For Broadband Pulses

“…For small displacements, ∆t G is negative since the near-resonance components of the pulse spectrum still affect the expectation in Eq. (6). As the pulse propagates further into the medium and experiences absorption, the longer delay times of the off-resonance components dominate the expectation resulting in the eventual subluminal delay times generally observed for broadband pulses.…”

“…Note that the distribution ρ (r, ω) is evaluated at the final point, so that only the spectral components that actually arrive at r contribute to the delay. Equation (6) explicitly demonstrates the connection between the delay time for a pulse and the group delay function. Note the close resemblance between Eq.…”

“…(1) and Eq. (6). Both are expectation integrals, the former being executed as a 'centerof-mass' integral in time, the later being executed in the frequency domain on the group delay function, ∂ Re k/ ∂ω · ∆r.…”

“…Because of this failure, traditional group delay suffers severe shortcomings when applied to broadband pulse propagation. [1][2][3][4] We recently introduced a method for describing pulse delay 5,6 in which the group delay function naturally arises. In contrast to the traditional formulation of group delay, this method retains validity for pulses of arbitrary bandwidth propagating in linear dielectrics (including cases where the spectrum overlaps resonances in the medium).…”