Causality-Based Criteria for a Negative Refractive Index Must Be Used With Care

Abstract

Using the principle of causality as expressed in the Kramers-Kronig relations, we derive a generalized criterion for a negative refractive index that admits imperfect transparency at an observation frequency omega. It also allows us to relate the global properties of the loss (i.e., its frequency response) to its local behavior at omega. However, causality-based criteria rely on the group velocity, not the Poynting vector. Since the two are not equivalent, we provide some simple examples to compare the two criteria.

Frequency-domain simulations of a negative-index material with embedded gain

“…We note, however, that further away from the resonance, both the index of refraction and the extinction coefficient increase due to the gain, thus corresponding to a lowered FOM. These specific simulations are an example showing that a low-loss NIM regime is feasible, and that it can be isolated in wavelength from adjacent regimes of high losses, in agreement with the predictions of [57]. [58].…”

Past achievements and future challenges in the development of three-dimensional photonic metamaterials

“…Other experiments using semiconductor gain in split-ringresonator metamaterials have only achieved partial loss compensation 84,85 . In principle, under stable steady-state conditions, the FOM can approach infinity at a single wavelength 86,87 .…”

Reducing the losses of optical metamaterials

“…There are theoretical debates [129][130][131][132][133] if it is possible to obtain low loss metamaterials with negative refractive index, n. They have used the Kramers-Kronig (KK) relations and we would like to verify that Kramers-Kronig relations work with and without gain. In addition, we need to compare the numerically-retrieved effective permeability, µ, shown in …”