When a beam experiences a total internal reflection, a lateral shift exists between the reflected
and the incident beams. It is called Goos and Hänchen effect, named after its discoverers. For decades, the phenomenon has been a research topic attracting considerable amount of efforts for its intriguing physical nature. It gained renewed attention in recent years when plasmonic materials
and metamaterials are involved. Sensor schemes based on GH shift has also been proposed, and have led to sensors of biochemical, thermal and wavelength monitoring applications. The sensitivity in these sensors are directly related to the amount of GH shift, thus, to achieve a large GH shift (positive or negative) is of practical interests.
In reference paper , the possibility to use the guided mode resonance to achieve giant GH shift was proposed. As shown in Figure 1, the incidence comes from the substrate side of the grating at an angle greater than the critical angle of the substrate and will be totally reflected from the surface of the substrate decorated by the dielectric grating. When the incidence couples to the leaky mode of the grating, strong energy flow inside the waveguide exists, thus giant GH shift could be realized. When the leaky mode is a negative propagating one (i.e. the energy flow is anti-parallel to the wave vector of the mode), negative GH shift is expected.
Figure 1. Schematic of a dielectric grating and the GH shift under a total internal reflection. The grating specs are Γ = a/ Λ (duty cycle), Λ = 0.43um, Γ = 0.93, t = 0.11um, ɛh = 12.12, ɛl = ɛc = 1(free space), ɛs = 2.09(SiO2).
The GH shift is defined as:
Figure 4. The Instantaneous distribution of electric field Ey and Poynting vector at kx = 0.38×2π/ L (negative GH shift of maximum magnitude).