The refractive index and wave vector in passive or active media

Abstract

Materials that exhibit loss or gain have a complex valued refractive index $n$. Nevertheless, when considering the propagation of optical pulses, using a complex $n$ is generally inconvenient -- hence the standard choice of real-valued refractive index, i.e. $n_s = \RealPart (\sqrt{n^2})$. However, an analysis of pulse propagation based on the second order wave equation shows that use of $n_s$ results in a wave vector \emph{different} to that actually exhibited by the propagating pulse. In contrast, an alternative definition $n_c = \sqrt{\RealPart (n^2)}$, always correctly provides the wave vector of the pulse. Although for small loss the difference between the two is negligible, in other cases it is significant; it follows that phase and group velocities are also altered. This result has implications for the description of pulse propagation in near resonant situations, such as those typical of metamaterials with negative (or otherwise exotic) refractive indices.

Phys. Rev. A, to appear (2009)

References in corpus (8)

• Fresnel equations and the refractive index of active media
• On the electromagnetic properties of active media
• Causality-based criteria for a negative refractive index must be used with care
• Few cycle pulse propagation
• On resolving the refractive index and the wave vector
• Forward-backward equations for nonlinear propagation in axially-invariant optical systems
• Limits of the uni-directional pulse propagation approximation
• Negative refraction in active and passive media: a discussion of various criteria

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