1：Experimental Design and Method Selection:

The study proposes a metal-clad waveguide backed by a coherent atomic medium to achieve tunable giant spatial and angular GH shifts. The methodology involves theoretical modeling and numerical calculations to derive expressions for spatial and angular GH shifts for the reflected light.

2：Sample Selection and Data Sources:

The system consists of a prism, a thin metal-cladding with thickness d2, a dielectric waveguide with thickness d3, and a coherent atomic medium. The permittivity of the coherent medium is written as ε4 = 1 + χ, with χ being the susceptibility.

3：List of Experimental Equipment and Materials:

A silver film is utilized as the cladding metal. The system is modeled using a three-level V-type atomic system for the coherent medium.

4：Experimental Procedures and Operational Workflow:

Light beam is incident upon the prism-silver interface at angle θ and coupled into the waveguide by an evanescent wave when the x-component of the wave vector matches the propagation constant of the guided mode. The spatial and angular GH shifts are calculated based on the complex reflection coefficient of the four-layer structure.

5：Data Analysis Methods:

The study uses numerical calculations to analyze the dependence of GH shifts on various parameters such as waveguide thickness, coupling field Rabi frequency, and detuning.