Enhancing the Goos-Hänchen and spin-Hall shifts in planar and spherical structures through complex-frequency excitations

The scattering of an electromagnetic field oscillating in a complex-frequency plane is known to capture and release energy within a lossless cavity, yielding virtual loss and virtual gain, respectively. In this context, we use electromagnetic with complex frequency to optimize both the longitudinal beam shifts (Goos-H\"anchen shift) and transversal beam shifts (spin-Hall shift) in the transmitted field through the slab and scattered field by the sphere. The results demonstrate a significantly large gradient in the transmission amplitude due to the occurrence of scattering poles in the lower half plane of the complex frequency. In addition, the complex frequency allows the suppression of both forward and backward scattering by the spherical cavity. Consequently, the scattered plane undergoes a substantial shift, leading to an enhanced Goos-H\"anchen shift and spin-Hall shift in both planar and spherical cavities. Importantly, this scheme relies on the incident-beam profile without the need for engineering materials parameters of the cavity. As a result, it surpasses previous methods that rely on materials engineering to optimize the beam shifts. To underscore the broad applicability and versatility of the current formalism, we have chosen to implement it using the commercial software COMSOL and found perfect agreement with the analytical results.