Wide-angle giant photonic spin Hall effect

The photonic spin Hall effect is a manifestation of the spin-orbit interaction of light and can be measured by a transverse shift $\delta$ of photons with opposite spins. The precise measurement of transverse shifts can enable many spin-related applications, such as precise metrology and optical sensing. However, this transverse shift is generally small (i.e., $\delta /\lambda <{10}^{-1}$, where $\lambda$ is the wavelength), which impedes its precise measurement. To date, proposals to generate a giant spin Hall effect (namely, with $\delta /\lambda >{10}^2$) have severe limitations, particularly its occurrence only over a narrow angular cone (with a width of $\mathrm{\Delta }\theta <1^{\circ }$). Here we propose a universal scheme to realize the wide-angle giant photonic spin Hall effect with $\mathrm{\Delta }\theta >{70}^{\circ }$ by exploiting the interface between free space and uniaxial epsilon-near-zero media. The underlying mechanism is ascribed to the almost-perfect polarization splitting between $s$ and $p$ polarized waves at the designed interface. Remarkably, this almost-perfect polarization splitting does not resort to the interference effect and is insensitive to the incident angle, which then gives rise to the wide-angle giant photonic spin Hall effect.

Figure 1

Wide-angle giant photonic spin Hall effect from a specially designed interface. The interface is between an isotropic medium (e.g., air) and a uniaxial medium with a relative permittivity of ${\overline{\overline{\varepsilon }}}_r=\left[{\varepsilon }_{\left|\right|},{\varepsilon }_{\left|\right|},{\varepsilon }_{\perp }\right]$, where ${\varepsilon }_{\left|\right|}\to 1$ and ${\varepsilon }_{\perp }\to 0$. (a) Schematic of the photonic spin Hall effect. This effect is featured with a spin-dependent transverse shift ${\delta }_{\pm }$, where the subscript $+$ ($-$) corresponds to the reflected light with left-handed (right-handed) circular polarization. (b) Schematic of reflection. The reflection coefficient for TE ($s$-polarized) or TM ($p$-polarized) waves is denoted as $r_s$ and $r_p$, respectively. (c) and (d) $|r_p|/|r_s|$ and normalized transverse shift $|{\delta }_{\pm }|/\lambda$ as a function of the incident angle. In (c) and (d), $\lambda =632.8$ nm is the wavelength in free space, ${\varepsilon }_{\left|\right|}=1-{10}^{-4}$ and ${\varepsilon }_{\perp }={10}^{-4}$, and the beam width of $w={10}^4\lambda$ is chosen for the incident $s$-polarized Gaussian beam. The giant photonic spin Hall effect with $|{\delta }_{\pm }|/\lambda \ge {10}^2$ occurs within a wide incident angular range—namely, from ${\theta }_{\min }=1.1^{\circ }$ to ${\theta }_{\max }=75.6^{\circ },$ as shown in (d). For comparison, the reflection and the photonic spin Hall effect at the regular air–glass interface are also studied in (c) and (d), where the refractive index of glass is $n=1.515$.

Figure 2

Influence of the uniaxial medium on the wide-angle giant photonic spin Hall effect at the air–uniaxial medium interface. The uniaxial medium has a relative permittivity of ${\overline{\overline{\varepsilon }}}_r=\left[{\varepsilon }_{\left|\right|},{\varepsilon }_{\left|\right|},{\varepsilon }_{\perp }\right]$, where ${\varepsilon }_{\left|\right|}\to 1$ and ${\varepsilon }_{\perp }\to 0$. (a) Influence of ${\varepsilon }_{\left|\right|}$ on the transverse shift, under the scenario of ${\varepsilon }_{\perp }={10}^{-4}$. (b) Influence of ${\varepsilon }_{\perp }$ on the transverse shift, by setting ${\varepsilon }_{\left|\right|}=1-{10}^{-4}$.

Figure 3

Reflection coefficients. Here ${\varepsilon }_{\left|\right|}=1-{10}^{-4}$, and the structural setup is the same as in Fig. 2. (a) Influence of ${\varepsilon }_{\perp }$ on the magnitude $|r_{p,s}|$ of reflection coefficients. (b) Influence of ${\varepsilon }_{\perp }$ on the phase ${\phi }_{p,s}=Arg\left(r_{p,s}\right)$ of reflection coefficients. In Figs. 3 and 3, we plot ${\delta }_{+}/\lambda$, instead of $|{\delta }_{\pm }|/\lambda$, as a function of the incident angle. (c) ${\varepsilon }_{\perp }={10}^{-3}$. (d) ${\varepsilon }_{\perp }={10}^{-2}$ .

Figure 4

Influence of the beam width on the wide-angle giant photonic spin Hall effect. The other structural setup is the same as in Fig. 1, except for the width $w$ of the incident Gaussian beam.

Figure 5

The wide-angle giant photonic spin Hall effect from uniaxial slabs with a subwavelength thickness. (a) Schematic of the photonic spin Hall effect. The surrounding environment is free space. The other structural setup is the same as Fig. 1, except for the slab thickness $d$. (b) Influence of the slab thickness on the transverse shift.

Figure 6

The influence of slab thickness and loss on the transverse spin shift. For conceptual demonstration, the uniaxial medium has ${\varepsilon }_{\left|\right|}=1-{10}^{-4}$ and ${\varepsilon }_{\perp }={10}^{-4}$. (a) The thickness of slab $d/\lambda =15$ and (b) $d/\lambda =30$, and (c) is the loss influence $[\mathrm{Im}\left({\varepsilon }_{\left|\right|,\perp }\right)\ne 0$.] on the transverse shift.

Figure 7

Gas sensors based on the measurement of the angular position of the dip in Fig. 2. Here ${\varepsilon }_{\left|\right|}=1-{10}^{-4}$ and ${\varepsilon }_{\perp }={10}^{-2}$. We assume the region (e.g., free space with gases with different densities) above the uniaxial epsilon-near-zero medium has a refractive index of $1+\mathrm{\Delta }n$. The other setup is the same as that in Fig. 1. (a) Influence of $\mathrm{\Delta }n$ on the transverse shift. (b) The angular position of the dip (namely, ${\theta }_{\mathrm{dip}}$) as a function of $\mathrm{\Delta }n$. ${\theta }_{\mathrm{dip}}$ is sensitive to the slight variation of $\mathrm{\Delta }n$.