Abstract
Spin Hall effect of light, which is normally explored as a transverse spin-dependent separation of a light beam, has attracted enormous research interests. However, it seems there is no indication for the existence of the longitudinal spin separation of light. In this paper, we propose and experimentally realize the spin separation along the propagation direction by modulating the Pancharatnam-Berry (PB) phase. Due to the spin-dependent divergence and convergence determined by the PB phase, a focused Gaussian beam could split into two opposite spin states, and focuses at different distances, representing the longitudinal spin separation. By combining this longitudinal spin separation with the transverse one, we experimentally achieve the controllable spin-dependent focal shift in three dimensional space. This work provides new insight on steering the spin photons, and is expected to explore novel applications of optical trapping, manipulating, and micromachining with higher degree of freedom.
Highlights
For a light beam with polarization state A, assuming it is linearly polarized along x axis, its polarization state eA is described by eA = ex, where ex denotes the unit vector along the x axis. This light beam can be considered as a composition of two spin states L and R, corresponding to the left-handed (LH) and right-handed (RH)
It has to be emphasized that the longitudinal spin separation of light occurs whether the polarization transformation happens after or before this lens, because the spin-dependent divergence and convergence can work in the both cases
For the PB phase described by Eq 4, it provides the general idea to simultaneously focus two spin states to spots at customizable longitudinal and transverse locations
Summary
If B is another linear polarization state and its polarization direction along angle θ, it meets eB = cos θex + sin 2θey, where eB is the unit vector of polarization state B This light beam could be decomposed in two spin states L and R, i.e. eB = (e−iθeL + eiθeR)/ 2. Another typical selection of Φ is the phase factor of a spherical wave, i.e. Φ = αr[2], where r denotes the radial coordinate, and α is a nonzero constant In this case, the two output spin states would carry phase factors of converging and diverging spherical waves The LH and RH components would obtain diverging and converging phase factors, representing defocusing and focusing propagations, respectively. We set E0 as a focused Gaussian profile [with the phase factor e−i α0r α0 > 0]
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