Magnetic field sensor based on multiple Fano resonance in metal-insulator-metal waveguide coupled with cross-shape resonator

Abstract In this paper, an innovative plasmonic magnetic field sensor (MFS) that exploits a Metal-insulator-Metal (MIM) waveguide configuration with an asymmetric cross-shaped resonator is constructed. The design enables the observation of double Fano resonance in the transmission spectrum, resulting from the coupling between continuous spectrum and discrete spectrum. By incorporating magnetic fluid in the asymmetric cross-shape resonator, the Fano line shapes can be tuned by the external magnetic field. Finite-Difference Time-Domain (FDTD) is used to simulate the spectra response to external magnetic fields and geometrical sizes. The proposed structure exhibits remarkable magnetic field sensitivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>12.1</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>p</mml:mi> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mi>O</mml:mi> <mml:mi>e</mml:mi> </mml:math> within the detection range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>15</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>O</mml:mi> <mml:mi>e</mml:mi> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>199</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>O</mml:mi> <mml:mi>e</mml:mi> <mml:mo>.</mml:mo> </mml:math> The resolution of MIM magnetic field sensors can reach <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.0826</mml:mn> <mml:mspace width="0.5em"/> <mml:mi>O</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> <mml:mo>.</mml:mo> </mml:math> The optimal figure of merit (FOM) and maximum Q factor of the Fano dip are about <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>6.9</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mo>/</mml:mo> <mml:mspace width="0.5em"/> <mml:mi>O</mml:mi> <mml:mi>e</mml:mi> </mml:math> and 66.74, respectively. Meanwhile, The proposed Fano resonance MFS has some advantages, including compact size, high sensitivity, and cost-effectiveness. A strong linear relationship between the magnetic field and resonance wavelength indicates that the proposed structure can find potential applications in diverse fields such as magnetic field sensors, aircraft navigation, and even nuclear energy generation.