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Journal of the Optical Society of America

Verification of the Kramers–Kronig relations in optically pumped ruby

Brent L. Bean, Jerald R. Izatt

Published Jul 1, 1973• 2 citations
Publisher

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.

DOI
10.1364/josa.63.000832

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Journal of the Physical Society of Japan•Jul 1, 1966•52 citations
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.
The real and imaginary parts of the complex index of refraction in the R-line region of ruby have been measured near liquid-nitrogen temperature with sufficient resolution that the R-line doublet structure was well resolved. A modification of the usual Babinet compensator technique was used for the refractive-index measurements, which were found to correlate with the absorption measurements as predicted by the Kramers-Kronig relations. An attempt at direct quantitative verification of the dispersion relations for an optically pumped sample is also described.
High-resolution measurements have been made of the anomalous dispersion associated with the two Stark components of the R sub l absorption line in ruby. These preliminary measurements suggest that the R sub l dispersion obeys the Kronig-Kramers relations; however, it is superposed on a background which is itself anomalous because the refractive index increases with increasing wavelength. These measurements cover a wavelength interval of about 0.5 A, and the change in background index is of the order of 0.001 while the R sub l dispersion curve deviates from the background value by about 0.0001 at the maximum. A second surprising feature of the measurements is the observation that coherent radiation from a ruby laser, which was used to illuminate the ruby sample, is absorbed less in traversing the sample than would be expected on the basis of absorption measurements made with incoherent light. Highly accurate measurements have been made of the temperature dependence of the ruby laser emission between 63K and 116K and in a second interval between 196K and 207K. Light shielding is described which has been designed and tested to minimize pump light and ruby fluorescence at the detector in experiments with the sample optically pumped. (Author)
Studies of the resonant interaction of radiation from a liquid-nitrogen-cooled ruby laser with a ruby crystal in the temperature range 4.2°–100°K are described. The interaction was measured by observation of the change which occurs in the Cr3+ ground state EPR absorption on laser irradiation. At low radiation intensities, the temperature dependence of this change is shown to be determined by the well-known thermal tuning behavior of the R lines. Precise measurement of the relative laser and ruby-sample absorption frequencies by this technique of double-resonance spectroscopy is described. Under optical saturation conditions, additional temperature-dependent pumping effects occur at low temperatures. In particular, as the ruby temperature is increased from 4.2° to 40°K, the laser-induced change in EPR absorption is observed to undergo a large increase. This increase cannot be explained by a relative thermal shift of the laser and absorption frequencies which is known to be very small in this temperature range. The phenomena are attributed in part to the temperature-dependent homogeneous linewidth which determines the widths of the holes burnt into the inhomogeneous strain-broadened R lines. Calculations indicate that the related temperature-dependent thermalization process which redistributes excited Cr3+ among the 2E levels quantitatively accounts for most of the increase.
A high resolution study has been made of the R(1) doublet in the absorption spectrum of pink ruby, using a temperature-controlled ruby laser as a variable frequency monochromatic source. The source and sample crystals were oriented for measurement of the absorption of alpha-polarized radiation, and the measurements were made near liquid nitrogen temperature. The observed absorption coefficient was found to decrease as the intensity of the incident beam was increased, indicating that significant depletion of the ground state was effected by the resonant pumping action of the laser beam. The highest laser beam intensity employed was approximately 100 J/cm(2). At this intensity level a significant reduction in the spectral spacing of the R(1)(+/-3/2) and R(1)(+/-(1/2)) components of the absorption doublet was also observed. Time-resolved spectral measurements showed, moreover, that at similar intensity levels, temporally smooth incident beams at frequencies near the absorption line peaks emerged from the sample temporally structued. The observed reduction in the absorption coefficient agrees well with calculations based on a simple model for ground state depletion, but no detailed theoretical explanation of the other observed phenomena has yet been developed.
Bistability, differential gain, discriminator, clipper, and limier actions were observed using a plano-concave Fabry-Perot cavity containing ruby. Input powers were approximately 20 mW from a cw ruby laser. Operation wa anticipated near 77 °K where the R1 transition was nearly resonant with the laser. However, the device functioned at room temperature. The refractive index of ruby depends on the fractional ground-state population. Driving the R lines leads to a nonlinear refractive index due to dispersive contributions from nonresonant pump and charge-transfer bands, which explains the room-temperature operation.
Absorption transitions between two excited optical states in ruby have been studied by comparing the absorption coefficients measured under optically pumped and unpumped conditions. The spectrum has been determined in the π-and σ-polarizations in the photon energy range from 5,500 to 45,000 cm -1 . Several absorption bands have been found which arise from the transitions from the excited states t 2g 3 2 E g and t 2g 3 2 T 1g of the Cr 3+ ion. From the locations and intensities of these bands, the terminal states of the observed transitions are assigned to the charge transfer state, the t 2g 3 2 T 2g state, and the doublet states belonging to the electron configuration t 2g 3 e g . Calculated energies between these states and the metastable states, t 2g 3 2 E g and t 2g 3 2 T 1g , are in good agreement with the peak energies of the observed absorption bands. The present experiment gives new information inaccessible by the ordinary ground state absorption measurement, such as the locations of several doublet states with the configuration t 2g 2 e g and the intensities of doublet-doublet transitions in ruby.