Controlling Enhancement of Transmitted Goos-Hänchen Shifts: From Symmetric to Unidirectional

Abstract: Since the discovery of the Goos-H\"anchen (GH) shift in the 1940s, its deep connections to Fourier transforms and causality have led to widespread interest and applications in optics, acoustics, and quantum mechanics. Control of the shift involves both its magnitude and direction. Although resonance-enhanced GH shift under reflection has significantly expanded and facilitated its observation and application, implementations in transmission scenarios remain scarce. More importantly, discussions on the direction of the GH shift are rare, and the associated degree of freedom for controlling directional asymmetry has not been fully explored. To address these issues, we discuss a control framework for enhancing transmitted GH shifts from symmetric to asymmetric. A design with complete degrees of freedom from symmetric shift enhancement to unidirectional shift enhancement is demonstrated in transmission scenarios. The control dimension associated with directionality significantly enhances the flexibility of beam shift control, with broad application prospects in scenarios such as high-sensitivity sensing, precision measurement, optical isolators, and asymmetric optical switches.