Eigenpolarizations for Giant Transverse Optical Beam Shifts

We show how careful control of the incident polarization of a light beam close to the Brewster angle gives a giant transverse spatial shift on reflection. This resolves the long-standing puzzle of why such beam shifts transverse to the incident plane (Imbert-Fedorov shifts) tend to be an order of magnitude smaller than the related Goos-Hänchen shifts in the longitudinal direction, which are largest close to critical incidence. We demonstrate that with the proper initial polarization the transverse displacements can be equally large, which we confirm experimentally near Brewster incidence. In contrast to the established understanding, these polarizations are elliptical and angle dependent. We explain the magnitude of the Imbert-Fedorov shift by an analogous change of the symmetry properties for the reflection operators as compared to the Goos-Hänchen shift.

Figure 1

Experimental setup. A collimated light beam from a single-mode fiber (SMF) coupled superluminescent diode (SLED) is prepared in each of the illuminating polarization states ${\mathit{f}}_{\pm }$ alternately, using a polarizer and wave plates. After reflection at the air-glass interface, its transverse position is determined with a quadrant detector (QD).

Figure 2

Measured and calculated shifts: The graph shows the differential spatial IF shifts $d_{+}-d_{-}$ (black) and the individual shifts $d_{\pm }$ (blue, red) as functions of the incidence angle $\theta$ above the Brewster angle ${\theta }_B=56.49°$ for $n=1.5103$. Black dots indicate experimentally measured values ($d_{+}-d_{-}$), diamonds numerically obtained values ($d_{\pm }$). Solid lines correspond to theoretical curves from (6). The plot also shows polarization ellipses for the eigenvectors ${\mathit{e}}_{\pm }$ (bold) and the illuminating polarizations ${\mathit{f}}_{\mp }$ (thin) corresponding to $d_{\pm }$, which tend to linear on approaching ${\theta }_B$. The small arrows indicate the handedness of the elliptical polarization.

Figure 3

Measured and calculated beam profiles for $\theta =56.53°$: Split screen comparison of the beam profiles after reflection corresponding to the eigenpolarizations ${\mathit{e}}_{+}$ (left panel) and ${\mathit{e}}_{-}$ (right panel). (a) Experimental beam profiles recorded with a beam profiler. We also give the Stokes parameter of ${\mathit{e}}_{\pm }$ and the polarization ellipses for both ${\mathit{e}}_{\pm }$ and the illuminating eigenpolarizations ${\mathit{f}}_{\mp }$. (b) Numerically calculated beam profiles at a magnification of 500 to highlight the displacement of the center of the beam. This illustrates that the transverse spatial shift does not lead to any beam deformations.