With the rapid expansion of the Internet of Things (IoT), ensuring the security of personal and group information has become increasingly crucial. However, conventional optical scattering physical unclonable function (OS-PUF) faces challenges due to its linear scattering behavior. In this article, we propose a non-linear OS-PUF (NOS-PUF) that integrates electro-optic materials. By leveraging random refractive index fluctuations generated by the NOS-PUF, we mitigate modeling attacks based on the OS-PUF and bolster the overall security of the authentication process. Moreover, we introduce a novel modeling attack methodology based on scattering invariant modes (SIMs) that poses a significant threat to conventional OS-PUF and NOS-PUF authentication systems. Through extensive simulations, we demonstrate that our NOS-PUF achieves a remarkably lower false accept rate for modeling attacks utilizing SIMs, surpassing the entropy limit imposed by the Gabor filtering algorithm by more than five orders of magnitude. These results highlight the heightened security and increased information entropy offered by the proposed NOS-PUF, making it particularly suitable for applications demanding robust and high-security authentication measures.