Propagation of a Gaussian wave packet in an absorbing medium

Wave Packets and Group Velocity in Absorbing Media: Solutions of the Telegrapher's Equation

“…Thus, their results have confirmed the predictions of Garrett and McCumber [6]. An asymptotic analysis of Gaussian WPs in a Lorentz gas has been performed in [8], where it was shown that the fast propagation with U > c observed by Chu and Wong is characteristic for the early stage of the motion of the WP, while the slow propagation with U < c appears at long traveling distances.…”

“…For the Lorentz model, the group velocity W defined in (5) is complex for real ω. For short traveling distances the velocity of the envelope's maximum V (t) was shown to be close to U [6,8], while for long distances V significantly differs from U. Similar results were obtained in [11,13] for whistler WPs propagating in a magnetized collisional plasma, for which the form of complex dispersion equation is quite different from the one following from the Lorentz model.…”

“…This allows us, on one hand, to ensure the causality of the problem of pulse propagation, and on the other hand, to avoid cumbersome direct calculations of the Fourier integrals for short and moderate traveling distances. It should be noted that for WP solutions obtained in [6,8] for the Lorentz model, the group velocity U was calculated by (6) where ω c is the carrier frequency. For the Lorentz model, the group velocity W defined in (5) is complex for real ω.…”

Coherent Control of Single-Photon Absorption and Reemission in a Two-Level Atomic Ensemble

“…DOI: 10.1103/PhysRevLett.109.263601 PACS numbers: 42.50.Nn, 03.65.Ta, 32.80.Qk, 42.50.Ct Photon absorption and emission are two key probes to study the light-matter quantum interaction, which lays down the foundations for atomic, molecular, and optical physics [1][2][3]. When a coherent optical pulse propagates through a medium, the absorption and emission can coherently modify its spectral components and lead to many interesting and important optical phenomena, such as attenuation, amplification, distortion, and slow and fast light effects [4][5][6][7][8]. For a single photon, causality requires that the absorption and reemission follow the right time order: the reemission can only occur following the absorption.…”

Narrowband Biphotons: Generation, Manipulation, and Applications

“…When an optical pulse propagates through a dispersive medium, the absorption and emission can coherently modify its spectral-temporal components and lead to many fundamental and important optical phenomena, such as attenuation, amplification, distortion, slow and fast light effects [40,42,86,87,88]. For a single photon in the absorptive medium, the remission can only occur after the absorption, as required by the causality.…”