Three-dimensional spin Hall effect of light in tight focusing

Shu, Weixing; Lin, Chuyang; Wu, Jun; Chen, Shizhen; Ling, Xiaohui; Zhou, Xinxing; Luo, Hailu; Wen, Shuangchun

doi:10.1103/physreva.101.023819

Cited by 34 publications

(23 citation statements)

References 54 publications

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“…In Figure , the central basis vectors ( x̂ , ŷ , ẑ ), if rotated along the z axis by ϕ and then along the y axis by θ i , can be transformed into the local ones ( x̂ i , ŷ i , ẑ i ): ( x̂ i , ŷ i , ẑ i ) = ( x̂ , ŷ , ẑ ) R z (ϕ) R y (θ i ). Hence, the transmitted light field can be related with the incident one by transformation , bold-italicẼ o u t = R z ( ϕ ) R y ( θ t ) T R y − 1 ( θ i ) R z − 1 ( ϕ ) bold-italicẼ i n = M bold-italicẼ i n Here R y (θ) and R z (ϕ) denote unitary rotations around the y axis by θ and the z axis by ϕ, respectively R y ( θ ) = [ true cos ⁡ θ 0 sin ⁡ θ 0 1 0 − sin ⁡ θ 0 cos ⁡ θ ] , goodbreak0em0.25em⁣ R …”

Section: Theoretical Formulationmentioning

confidence: 90%

“…In contrast to the previous 2D ones, − the transformation matrix eq is 3D. The difference should be noticeable in specific situations, such as in the near field and tight focusing. , …”

Section: Theoretical Formulationmentioning

confidence: 99%

“…In Figure 1, the central basis vectors (x, y, z), if rotated along the z axis by ϕ and then along the y axis by θ i , can be transformed into the local ones (x̂i, ŷi, ẑi): (x̂i, ŷi, ẑi) = (x, y, z)R z (ϕ)R y (θ i ). Hence, the transmitted light field can be related with the incident one by transformation 34,45…”

Section: ■ Theoretical Formulationmentioning

confidence: 99%

“…The difference should be noticeable in specific situations, such as in the near field and tight focusing. 31,34 Topological SOI through a Uniaxial Crystal. For a general linear polarization, let us consider an x-polarized light E ̃in = |x⟩ (ϑ = π/4, φ = 0 in eq 1) for simplicity.…”

Section: ■ Theoretical Formulationmentioning

confidence: 99%

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Topological Differential Microscopy Based on the Spin–Orbit Interaction of Light in a Natural Crystal

2022

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We experimentally demonstrate a two-dimensional topological differential microscopy based on the spin–orbit interaction of light through a thin uniaxial crystal slab. First, a three-dimensional propagation theory is established for the light propagating through a uniaxial material. Then it is found that, due to the spin–orbit interaction, the two circularly polarized components of incident light are imposed with opposite topological charges, leading to the azimuthal splitting of spin states. Consequently, the cross-polarized field approximately amounts to the second-order spatial differentiation of the incident field. Finally, such an optical differentiation performed by a lithium niobate crystal is successfully applied to edge detection in microscopy. Further experiments validate its good performance in edge enhancement of both amplitude and phase objects. The results provide an economic, simple but robust approach to real-time, colorful, and high-contrast biological imaging in living systems.

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Section: Theoretical Formulationmentioning

confidence: 90%

“…In contrast to the previous 2D ones, − the transformation matrix eq is 3D. The difference should be noticeable in specific situations, such as in the near field and tight focusing. , …”

Section: Theoretical Formulationmentioning

confidence: 99%

Section: ■ Theoretical Formulationmentioning

confidence: 99%

Section: ■ Theoretical Formulationmentioning

confidence: 99%

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Topological Differential Microscopy Based on the Spin–Orbit Interaction of Light in a Natural Crystal

2022

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“…Usually, the Hall effect in optics is observed when light is reflected from a medium interface [11] or when it passes through multilayer media [4], crystals [12], or a metasurface [13]. At the same time, publications concerned with the Hall effect at the tight focus of laser light [14,15] or in the focal plane vicinity [16] are rather sparse.…”

Section: Introductionmentioning

confidence: 99%

High-Order Orbital and Spin Hall Effects at the Tight Focus of Laser Beams

Kotlyar

Stafeev²,

Козлова³

et al. 2022

Photonics

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In this paper, using a Richards–Wolf method, which describes the behavior of electromagnetic waves at the sharp focus, we show that high-order spin and orbital Hall effects take place at the focal plane of tightly focused laser beams. We reveal that four local subwavelength regions are formed at the focus of a linearly polarized optical vortex with unit topological charge, where the spin angular momentum behaves in a special way. Longitudinal projections of the spin angular momentum are oppositely directed in the adjacent regions. We conclude that this is because photons falling into the neighboring regions at the focus have the opposite spin. This newly observed phenomenon may be called a spin Hall effect of the 4-th order. We also show that tightly focusing the superposition of cylindrical vector beams of the m-th and zero-order produces 2m subwavelength regions in the focal plane, such that longitudinal projections of the orbital angular momentum are oppositely directed in the neighboring regions. This occurs because photons falling into the neighboring regions at the focus have the opposite signs of the on-axis projections of the orbital angular momentum. This phenomenon may be termed an orbital Hall effect of the 2m-th order.

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