We present a theoretical investigation of the Goos-Hänchen shift in an optical cavity containing a three-level atomic medium. Unlike conventional approaches that require external control or pump fields, transparency in our system is induced by the vacuum field itself through a phenomenon known as vacuum-induced transparency, distinguishing it from the traditional electromagnetically induced transparency. Inspired by this mechanism, we introduce the concept of the vacuum-induced Goos-Hänchen (VIGH) shift, where the lateral displacement of the reflected beam is governed by vacuum field interactions. Additionally, we explore the influence of a microwave field on the atomic medium, demonstrating its ability to modulate both the magnitude and direction of the VIGH shift. Notably, we establish a tunable control over positive and negative VIGH shifts through the microwave field, with the shifts in magnitude further influenced by the photon number inside the cavity. Moreover, we examine the impact of Doppler broadening, revealing a unique deviation in VIGH shift behavior. In contrast to the Doppler-free case, where the microwave field can transition the VIGH shift between positive and negative regimes, Doppler broadening suppresses this transition, enhancing only the magnitude of the negative VIGH shift as microwave strength increases. Our findings provide deeper insights into light-matter interactions at the quantum level and open pathways for precision control of optical shifts in cavity-based quantum systems.

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• Quantum optics