Improved Photonic Spin Hall Effect by an Induced Polarization Gradient in Anisotropy-Black Phosphorous and Its Application to NO<sub>2</sub> Gas Detection
Vinit Kumar, Rupam Srivastava, Yogendra Kumar Prajapati
Abstract
This study introduces an enhanced and tunable conventional spin-dependent shift (CSDS) resulting from the photonic spin Hall effect (PSHE). The PSHE is caused by the separation of opposite spin states when linearly polarized light incidents on the interface of multilayer structures with a gradient in refractive index (RI). To get the PSHE, the proposed structure consists of silver (Ag), silicon (Si), and anisotropic black phosphorous (BP). Here, Ag is used as a plasmonic layer. Si is utilized to enhance the evanescent field near the interface of the top BP layer and air. Here, the in-plane anisotropy of BP is used as a polarizer to tune the CSDS. The maximum CSDS of 50.67 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> is obtained at the optimal Si thickness, i.e., 13 nm, by tuning the rotation angle ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\phi {)}$ </tex-math></inline-formula> of BP to 34.50° for left-hand horizontal polarization, which is greater in magnitude than the previously reported work on PSHE. In addition, the PSHE-proposed structure is used for nitrogen dioxide (NO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{{2}}{)}$ </tex-math></inline-formula> gas sensing because BP has high molecular adsorption energy for NO2. The spin-dependent sensitivity of 3212.88 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> /RIU is achieved at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\phi $ </tex-math></inline-formula> near of 22° for NO2 gas sensing at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta {n}$ </tex-math></inline-formula> = <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\times 10^{-{3}}$ </tex-math></inline-formula> . In addition, a finer value of limit of detection is also obtained for the proposed sensor (i.e., structure 3) as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9.95\times 10^{-{8}}$ </tex-math></inline-formula> degree.RIU/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> .