Research on materials at high pressure is today carried out largely in the diamond anvil cell (DAC), in which the sample is compressed between two transparent anvils and therefore remains accessible to optical measurements. The pressure inside the cell is measured indirectly, most often from the fluorescence of ruby added to the sample. A promising complement to these sensors are transparent spherical microresonators. In them light circulates just below the surface in whispering gallery modes (WGM), whose wavelengths are sharply defined and depend only on the radius of the microresonator and on the refractive indices of its material and of the surrounding medium. Such a microresonator is therefore by construction a sensor of both pressure and refractive index. It has been shown so far that such resonators are usable as pressure sensors, but not as gauges of refractive index.
The aim of this thesis was to calibrate these microresonators as sensors of pressure and of the refractive index of the liquid medium in a DAC. I carried out three experiments with microresonators of europium-doped barium titanate glass, suspended together with spherical rubies in the pressure-transmitting medium, which gave the pressure. The experiment in the 4:1 methanol-ethanol mixture failed, so I carried out the calibration in silicone oil and then tested it in distilled water. Fitting an approximate modal equation to the measured spectra yields two quantities at every pressure, the optical radius, that is the product of the radius of the microresonator and its refractive index, and the ratio $N$ between the refractive index of the microresonator and that of the medium. The pressure dependence of the refractive index obtained from the calibration agrees with the published value for this glass.
As a pressure sensor the optical radius proved imprecise, because the compression of the microresonator and the rise of its refractive index almost cancel in it. The deviation from the ruby scale, that is from the established relation between pressure and the shift of the ruby fluorescence line, is about 1 GPa even at best, and in a blind test on the measurements in water the calibration curve has no solution at all for most readings. The ratio $N$ is considerably more sensitive, but it requires a known medium and is therefore not an option as a stand-alone pressure gauge. This sensitivity, however, is an advantage when the microresonator is used as a gauge of the refractive index of the medium, which enters only through the ratio $N$. From the calibrated optical radius and the measured ratio $N$ I reconstructed the refractive index of water without any assumption about water entering the calculation. The values obtained agree with the published ones to within a few percent. With the microresonators I also measured the ice VI${}\to{}$ice VII phase transition, since at the transition pressure they all independently show a jump in the refractive index whose magnitude is consistent with the expected one. Only microresonators within a narrow range of sizes are usable for this, a range set by the refractive index ratio and not by size alone. I have thus shown that microresonators are not particularly suited to measuring pressure, but that they are very useful as gauges of refractive index, which opens up new possibilities for simpler measurements of various substances at high pressure.
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