Which group velocity of light in a dispersive medium?

TL;DR

This paper investigates how the group velocities of transmitted and reflected light pulses in a dispersive medium are constrained by energy conservation, showing they depend on the medium's dispersive and transmission properties.

Contribution

It provides a theoretical analysis linking energy conservation to the group velocities of light in dispersive media, highlighting their dependence on environmental and structural properties.

Findings

Transmitted and reflected pulses have group velocities constrained by energy conservation.

Group velocities depend on dispersive properties of the environment and transmission characteristics.

One detailed example illustrating the theoretical results is discussed.

Abstract

The interaction between a light pulse, traveling in air, and a generic linear, non-absorbing and dispersive structure is analyzed. It is shown that energy conservation imposes a constraint between the group velocities of the transmitted and reflected light pulses. It follows that the two fields propagate with group velocities depending on the dispersive properties of the environment (air) and on the transmission properties of the optical structure, and are one faster and the other slower than the incident field. In other words, the group velocity of a light pulse in a dispersive medium is reminiscent of previous interactions. One example is discussed in detail.