Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry

We propose and demonstrate a novel technique for simultaneous measurement of the phase index, $n_p$, the group index, $n_g$, and the thickness, $t$, of transparent plates by use of a low-coherence interferometer. The output light from a superluminescent diode is focused upon the front plane of a transparent plate that is used as the sample. The sample stage is subsequently moved until the light is focused upon the rear plane of the plate. Measurement of the stage movement distance and the corresponding optical path difference allows us to determine both $n_p$ and $n_g$. By placing the sample between two glass plates, we measured $n_p$, $n_g$, and $t$ simultaneously, with an error of 0.3% or less, for nearly 1-mm-thick transparent plates, including glass and electro-optic crystals.