Anomalous refractive index modulation and giant birefringence in 2D ferrielectric CuInP$_2$S$_6$

2D ferroelectric (FE) materials have opened new opportunities in non-volatile memories, computation and non-linear optics due to their robust polarization in the ultra-thin limit and inherent flexibility in device integration. Recently, interest has grown in the use of 2D FEs in electro-optics, demanding the exploration of their electronic and optical properties. In this work, we report the discovery of an unprecedented anomalous thickness-dependent change in refractive index, as large as $\delta n$ $\sim$ 23.2$\%$, in the 2D ferrielectric CuInP$_2$S$_6$, far above the ultra-thin limit, and at room temperature. Furthermore, CuInP$_2$S$_6$ exhibits a giant birefringence in the blue-ultraviolet regime, with a maximum $\vert n_{OOP} - n_{IP}\vert$ $\sim$ 1.24 at $t \sim$ 22 nm and $\lambda$ = 339.5 nm, which is, to the best of our knowledge, the largest of any known material in this wavelength regime. We relate changes in CuInP$_2$S$_6$ optical constants to changes in the Cu(I) FE polarization contribution, influenced by its ionic mobility, opening the door to electronic control of its optical response for use in photonics and electro-optics.