Continuous Goos-Hänchen Shift of Vortex Beam via Symmetric Metal-Cladding Waveguide

Goos-Hänchen shift provides a way to manipulate the transverse shift of an optical beam with sub-wavelength accuracy. Among various enhancement schemes, millimeter-scale shift at near-infrared range has been realized by a simple symmetrical metal-cladding waveguide structure owing to its unique ultrahigh-order modes. However, the interpretation of the shift depends crucially on its definition. This paper shows that the shift of a Gaussian beam is discrete if we follow the light peak based on the stationary phase approach, where the M-lines are fixed to specific directions and the beam profile is separated near resonance. On the contrary, continuous shift can be obtained if the waveguide is illuminated by a vortex beam, and the physical cause can be attributed to the position-dependent phase-match condition of the ultrahigh-order modes due to the spatial phase distribution