transmittance and reflectance, the imaginary part can be determined from transmittance data alone. It is possible to use Kramers-Kronig analysis to calculate the real part if the imaginary part is known over a sufficiently broad range. We show that the delta calculated from reflection and transmission data without taking into account roughness may underestimate the real part of the refractive i...

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained ar...

We demonstrate the counterintuitive dispersion effect that the peaks (dips) in the gain spectrum correspond to abnormal (normal) dispersion, contrary to the usual Kramers-Kronig point of view. This effect may also lead to two unique features: a broadband abnormal dispersion region and an observable Hartman effect. These results are explained in terms of interference and boundary effects. Finall...

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 veloc...