Group refractive index of fused silica and white-light spectral interferometry with a dispersive Michelson interferometer

The spectral interference of two beams from a white-light source, a tungsten halogen lamp, is measured at the output of a dispersive Michelson interferometer by a low-resolution miniature fiber optic spectrometer when the interferometer beam splitter is made of fused silica. It is confirmed that the spectral interference fringes are resolved only in the vicinity of the equalization wavelength whose value is dependent on the group optical path difference in the interferometer. Thus, the equalization wavelength is measured as a function of the displacement in the interferometer in the spectral range approximately from 490 to 870 nm. Moreover, when the group refractive index of fused silica is evaluated at the equalization wavelengths by using the Sellmeier dispersion equation, it is confirmed, in accordance with the theory, that the measured displacement as a function of the group refractive index of fused silica is a straight line whose slope gives the effective thickness of the beam splitter. It is also revealed that when the effective thickness of the beam splitter made of fused silica is known with a sufficiently high accuracy, the differential group refractive index of fused silica in a spectral range from 490 to 870 nm can be obtained from the measurement of the equalization wavelength as a function of the displacement in the interferometer.