Kelvin's chirality of optical beams

Geometrical chirality is a property of objects that describes a three-dimensional mirror-symmetry violation and therefore it requires a nonvanishing spatial extent. In contrary, optical chirality describes only the local handedness of electromagnetic fields and neglects the spatial geometrical structure of optical beams. In this Letter we put forward the physical significance of geometrical chirality of spatial structure of optical beams, which we term Kelvin's chirality. Furthermore, we report on an experiment revealing the coupling of Kelvin's chirality to optical chirality upon transmission of a focused beam through a planar medium. Our work emphasizes the importance of Kelvin's chirality in all light-matter interaction experiments involving structured light beams with spatially inhomogeneous phase and polarization distributions.

Figure 1

Schematic illustration of the system. The incoming beam, propagating from left to right, is focused and collimated by two confocally aligned aplanatic microscope objectives (MOs). The sample is positioned normally to the $z$ axis between the MOs. The red arrows depict the local polarization of the beam before and after the introduction of a relative phase of $\pi /2$ between radial and azimuthal polarization components.

Figure 2

Experimental setup. A linear polarizer and a q-plate of charge 1/2 convert the incoming Gaussian beam into the desired mode. Two confocally aligned microscope objectives focus the incoming beam onto the sample and collimate it subsequently. Two liquid crystal variable retarders, a linear polarizer and a lens are used to perform a polarization resolved imaging of the back focal plane of the second microscope onto a camera.

Figure 3

Measurements for six input polarizations: (a) radial, (b) spiral ${\mathrm{SP}}_1$, (c) azimuthal, (d) spiral ${\mathrm{SP}}_2$, (e) linear $x$, and (f) linear $y$. (I) Intensity distributions before entering the first microscope objective. The local polarization state is indicated by red arrows. Stokes parameters $S_0^{\text{tr}}$(II) and $S_3^{\text{tr}}$(III), measured in transmission through the stratified medium. Theoretical counterparts are plotted as insets. $S_0^{\text{tr}}$(IV) and $S_3^{\text{tr}}$(V) correspond to transmission through a glass substrate.