A novel, to the best of our knowledge, optical fiber plasmonic sensor based on a tapered coreless fiber (TCF) coating with rolled-up hyperbolic metamaterials (HMMs) is proposed and theoretically studied. The HMMs are composed mainly of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">g</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">T</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> multi-layer composite materials. We can effectively control the surface plasmon resonance (SPR) wavelengths by adjusting the ratio of metal in two-layer ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>R</mml:mi> </mml:math> ), the number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> ), and thickness ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>T</mml:mi> </mml:math> ) of two-layer on the HMMs. Spectral quality can be improved by changing the core diameter of TCF. According to the effective medium theory and finite element method, HMMs of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>R</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0.3</mml:mn> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>30</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>20</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mtext>µ</mml:mtext> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> can provide an average sensitivity of 9127.86 nm/RIU (refractive index unit) in an external refractive index (ERI) of 1.33–1.40 and have a depth of SPR dip figure of merit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>65.32</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">U</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , which is an order of magnitude higher than 50 nm silver, for an ERI of 1.34–1.35. Also, the optical fiber plasmonic sensor integrated with roll-up HMMs shows performance superior to normal HMMs, thus providing certain guidance for future research.
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