Controlling photonic spin Hall effect based on tunable surface plasmon resonance with an $N\text{−}\mathrm{type}$ coherent medium

We propose a scheme to control the spin Hall effect (SHE) of light reflected from a Kretschmann configuration containing an N-type coherent atomic medium. Owing to the excitation of surface plasmon resonance (SPR), enhanced spin splitting occurs in the reflection dip for TM-polarized incident light. The magnitude and sign of the transverse shifts of spin components depend on the system internal damping which is closely related to the absorption coefficient of atoms. There is an optimal absorption around which the spin components undergo large transverse displacements. We also show that the direction of the photonic spin accumulations can be switched between positive and negative values by adjusting the system parameters. In addition, the resonance angle of SPR varies linearly with the refractivity of the medium. We can therefore coherently control the peak position of the transverse shift. Compared to the conventional SPR-based systems, the proposed scheme provides a more flexible pathway for manipulating and enhancing the SHE of light without changing the structure. This tunable SHE may find applications in spin photonic devices.

Figure 1

(a) Schematic setup of a three-layer Kretschmann configuration composed of a prism, a metal film, and a coherent atomic medium. Spin-dependent splitting occurs for a TM-polarized incident light reflected from the prism-metal interface. (b) Four-level N-type atomic system driven by three lasers: probe field, coupling field, and driving field.

Figure 2

(a) Reflectivity $|r_p|$ and (b) transverse shift of left-handed circularly polarized light ${\delta }_p^{+}$ as a function of incident angle $\theta$ with various Rabi frequencies of driving field ${\mathrm{\Omega }}_d$. Parameters are ${\varepsilon }_1=2.25$, ${\varepsilon }_2=-13.3+0.883i$, $d=40\mathrm{nm}$, ${\mathrm{\Gamma }}_3={\mathrm{\Gamma }}_4\equiv \mathrm{\Gamma }$, $\mathcal{N}=0.04\mathrm{\Gamma }$, ${\mathrm{\Delta }}_p=0$, ${\mathrm{\Delta }}_c=0$, ${\mathrm{\Delta }}_d=0$, and ${\mathrm{\Omega }}_c=2\mathrm{\Gamma }$.

Figure 3

(a) Probe susceptibility $\chi$, (b) internal and radiation dampings ${\mathrm{\Gamma }}^{\mathrm{int}}$ and ${\mathrm{\Gamma }}^{\mathrm{rad}}$, and (c) dip reflectivity and peak values of transverse shift ${\delta }_p^{+}$ versus Rabi frequency of driving field ${\mathrm{\Omega }}_d$. Parameters are the same as those in Fig. 2.

Figure 4

(a) Reflectivity $|r_p|$ and (b) transverse shift of left-handed circularly polarized light ${\delta }_p^{+}$ as a function of incident angle $\theta$ with various Rabi frequencies of coupling field ${\mathrm{\Omega }}_c$. The Rabi frequency of the driving field is ${\mathrm{\Omega }}_d=0.5\mathrm{\Gamma }$, and other parameters are the same as those in Fig. 2.

Figure 5

(a) Probe susceptibility $\chi$, (b) internal and radiation dampings ${\mathrm{\Gamma }}^{\mathrm{int}}$ and ${\mathrm{\Gamma }}^{\mathrm{rad}}$, and (c) dip reflectivity and peak values of transverse shift ${\delta }_p^{+}$ versus Rabi frequency of driving field ${\mathrm{\Omega }}_d$. Parameters are the same as those in Fig. 4.

Figure 6

(a) Reflectivity $|r_p|$ and (b) transverse shift ${\delta }_p^{+}$ as a function of incident angle $\theta$ with various Rabi frequencies of driving field ${\mathrm{\Omega }}_d$. (c) Probe susceptibility $\chi$, (d1) resonance angle ${\theta }_{\mathrm{res}}$, and (d2) dip reflectivity and peak values of ${\delta }_p^{+}$ versus ${\mathrm{\Omega }}_d^2$. Parameters are ${\mathrm{\Omega }}_c=\mathrm{\Gamma }$, ${\mathrm{\Delta }}_d=40\mathrm{\Gamma }$, and other parameters are the same as those in Fig. 3.

Figure 7

Probe susceptibility $\chi$, resonance angle ${\theta }_{\mathrm{res}}$, reflectivity at ${\theta }_{\mathrm{res}}$, and maximum (minimum) of ${\delta }_p^{+}$ versus ${\mathrm{\Omega }}_c^{-2}$. Parameters are ${\mathrm{\Omega }}_d=4\mathrm{\Gamma }$, ${\mathrm{\Delta }}_d=40\mathrm{\Gamma }$ for (a1–a3), and ${\mathrm{\Delta }}_d=-40\mathrm{\Gamma }$ for (b1–b3). Other parameters are the same as those in Fig. 3.