In this work, we propose and analyze a plasmonic sensor with a three-layer waveguide structure. We consider the transverse spin-dependent shift (SDS) of the horizontal photonic spin Hall effect (PSHE) in the waveguide at a given wavelength (1557 nm) for a TM (transverse magnetic or p-polarized) mode. The sensor structure is analyzed in two ways. First, under the normal methods, that is, angular and intensity interrogation methods, for which the results indicate that the maximum figure of merit (FOM) of 4007.0 RIU ⁻¹ is attained for an optimum thickness ( $d_{2}=51$ nm) of the gold layer and this FOM is significantly greater than the corresponding FOM (413.7 RIU ⁻¹ ) reported earlier (for a 50 nm thick gold layer). Also, the average sensitivity increases from 0.0005 to 0.002°/Oe when the volume fraction of Fe ₃ O ₄ particles ( $c$ ) in the magnetic fluid is increased from 1.48% to 1.93%. Correspondingly, a considerably finer value of the resolution (0.046 Oe) is obtained when the volume fraction is increased to 1.93% (compared to 0.199 Oe at 1.48%). Second way is the proposed method of PSHE, for which the analysis indicates that transverse SDS of the horizontal PSHE is the maximum for $d_{2} = 51$ nm leads to the maximum sensitivity $6.25 \times 10^{7}~\mu$ m/RIU for an amplified angle $\Delta = 0.1^{\circ}$ and $1.09 \times 10^{6}~\mu$ m/RIU for $\Delta = 0.1$ rad in the conventional weak measurements. The corresponding finest possible resolution of magnetic field detection at 1.93% is $1.5 \times 10^{-6}$ Oe in the conventional weak measurements for $\Delta = 0.1^{\circ}$ and $7.8 \times 10^{-8}$ Oe in the modified weak measurements for $\Delta = 0.5$ rad, which are significantly finer than those existing in the related state of the art. The above resolution is also superior to those found under normal methods mentioned earlier. Furthermore, the effect of temperature (24.3 °C–60 °C) on PSHE-based magnetic field sensor’s performance is also analyzed which indicates that the proposed PSHE-based magnetic field sensor should be operated in a thermally controlled milieu.

中文翻译：

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硅波导等离子体传感器中利用光子自旋霍尔效应的红外区高灵敏度磁场检测

在这项工作中，我们提出并分析了具有三层波导结构的等离子体传感器。我们考虑了在给定波长 (1557 nm) 下，对于 TM（横磁或 p 极化）模式，波导中水平光子自旋霍尔效应 (PSHE) 的横向自旋相关位移 (SDS)。从两个方面分析传感器结构。首先，在常规方法下，即角度和强度询问方法，结果表明对于最佳厚度获得了4007.0 RIU ^-1的最大品质因数（FOM） （ $d_{2}=51$ nm) 的金层，并且该 FOM 明显大于 早先报道的相应 FOM (413.7 RIU ^-1 )（对于 50 nm 厚的金层）。此外，当 Fe ₃ O ₄颗粒的体积分数 （ $c$ ) 在磁流体中从 1.48% 增加到 1.93%。相应地，当体积分数增加到 1.93% 时（与 1.48% 时的 0.199 Oe）相比，获得了相当精细的分辨率值 (0.046 Oe)。第二种方法是提出的 PSHE 方法，对于该方法，分析表明水平 PSHE 的横向 SDS 是最大的 $d_{2} = 51$ nm 导致最大灵敏度 $6.25 \times 10^{7}~\mu$ m/RIU 放大角度 $\Delta = 0.1^{\circ}$ 和 $1.09 \times 10^{6}~\mu$ 米/RIU 为 $\Delta = 0.1$ rad 在传统的弱测量中。1.93% 的磁场检测的相应最佳分辨率为 $1.5 \times 10^{-6}$ Oe 在传统的弱测量中 $\Delta = 0.1^{\circ}$ 和 $7.8 \times 10^{-8}$ Oe 在修改后的弱测量中 $\Delta = 0.5$ rad，其明显比现有技术中存在的那些更精细。上述分辨率也优于前面提到的常规方法中发现的分辨率。此外，还分析了温度（24.3 °C–60 °C）对基于 PSHE 的磁场传感器性能的影响，这表明所提出的基于 PSHE 的磁场传感器应在热控环境中运行。