Counterintuitive dispersion violating Kramers-Kronig relations in gain slabs

To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...

In column chromatography, when an analyte is introduced as a narrow band at the top of the column, the solutes begin to separate and broaden, developing a Gaussian profile. This broadening occurs due to various factors, such as longitudinal diffusion.
Longitudinal diffusion occurs when the solute molecules in the mobile phase diffuse from the more concentrated center of the chromatographic band to the more dilute regions on either side, both towards and against the flow direction. This...

Inductively coupled plasma–mass spectrometry (ICP–MS) is a highly selective and sensitive technique for accurate elemental analysis. Though the analysis of ICP–MS mass spectra is comparatively straightforward, it is affected by spectroscopic and non-spectroscopic interferences. Spectroscopic interferences arise when the plasma contains ionic species with an m/z value the same as the analyte ion. Spectroscopic interference can be categorized as isobaric, polyatomic ions, and...

The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
A broadband decoupling technique is used to simplify these complex, sometimes overlapping, signals. Broadband decoupling relies on a...