Verification of the Kramers–Kronig relations in optically pumped ruby

Abstract

The real and imaginary parts of the complex index of refraction have been measured in the R1 line of optically pumped ruby. The experiments, which employed a temperature-controlled, single-mode ruby laser as a variable-frequency monochromatic source, were performed near liquid-nitrogen temperature, where the R1 doublet structure is well resolved. R1 absorption profiles were measured for several optical-pumping conditions, ranging from zero up to a pump power that excited a population in the 2E state equal to about 60% of the population of the 4A2 ground state. For each pumping condition, the anomalous-dispersion curve was measured interferometrically. The spectral profiles of the absorption coefficient and the anomalous dispersion display a dependence on the optical-pumping conditions that is more complicated than simple saturation of the R1 transitions, but for given pumping conditions the two quantities are correlated as predicted by the Kramers–Kronig relations.