White-light spectral interferometric techniques used to measure the group dispersion of isotropic and anisotropic optical elements

摘要

We present two different white-light spectral interferometric techniques employing a low-resolution spectrometer for a direct measurement of the group dispersion of isotropic and anisotropic optical elements. First, the dispersion of the group refractive index for glass plate is measured in a Michelson interferometer with the plate of known thickness inserted in one of the interferometer arms. The technique utilizes the spectrometer to record a series of spectral interferograms for measuring the equalization wavelength as a function of the displacement of the interferometer mirror from the reference position, which corresponds to a balanced Michelson interferometer. The use of the technique is extended for measuring the dispersion of the group refractive indices for the ordinary and extraordinary polarizations in a quartz crystal. We confirm that the measured group dispersions agree well with those resulting from the semiempirical dispersion equations. We also show that the measured mirror displacement depends, in accordance with the theory, linearly on the theoretical group refractive index and that the slope of the corresponding straight line gives precisely the thickness of the quartz crystal. Second, the group dispersion of the quartz crystal is measured in an unbalanced Mach-Zehnder interferometer with the adjustable path length when the crystal is inserted in the test arm. The use of the second technique is extended for measuring the differential group dispersion of a glass of a holey optical fiber.