Average Energy Flow of Optical Pulses in Dispersive Media

Abstract

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 is shown to consist of two parts: a spectral superposition of group delays (inverse of group velocity) and a delay due to spectral reshaping via absorption or amplification. The result provides a context wherein group velocity is always meaningful even for broad band pulses and when the group velocity is superluminal or negative. The result imposes luminality on sharply defined pulses.

Periodic nanostructures for photonics

“…1 For actual physical systems, the notion "lossless" means that the real part of the electric permittivity (magnetic permeability) is much larger than its imaginary part in the relevant spectral region. 2 By construction, the energy velocity [4] is parallel to the Poynting vector. For periodic structures, e.g., for ordinary crystals, metamaterials, and photonic crystals, all quantities are understood as averaged over a unit cell as well as a cycle of light.…”

“…However, this is correct only for a (rather large) class of photonic-crystal structures that exhibit sufficiently symmetric unit cells [10]. 4 In the general case [10], a rigorous proof of the existence of photonic band gaps and the determination of their sizes requires the calculation of the density of states (see Section 2.1.1.2 and Figs. 4 and 5).…”

Slow and Fast Light in Semiconductor Optical Amplifiers for Microwave Photonics Applications

“…We will highlight this last point in the following part. For further details on the definition of the arrival time for optical pulses, you can refer to (Peatross et al, 2000).…”

Group velocity and energy transport velocity near the band edge of a disordered coupled cavity waveguide: an analytical approach

“…This concept is convenient to describe the propagation of a bit of information, but becomes less relevant in the vicinity of dielectric constant resonances [7]. Although v g keeps a physical meaning near a resonance for very specific conditions, such as a small sample thickness to avoid any distortion of the pulse [8][9][10], it cannot be associated with the speed of the energy transport. In addition, all the effects of advance or delay of a pulse observed near a resonance are limited by the initial temporal pulse width, because such effects only result from a reshaping of the pulse instead from a significant rigid temporal shift of all the envelope of the pulse [8,9].…”