<p>Characteristics of photon plasmon coupling in black phosphorus (BP) embedded between chiroferrite layer is analyzed in THz frequency spectrum. The frequency behavior and propagation characteristics of SPPs are analyzed under various physical parameters i.e., chirality parameter (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\xi\)</EquationSource> </InlineEquation>), gyrotropy (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mu}_{2}\)</EquationSource> </InlineEquation>), carrier density (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({n}_{s}\)</EquationSource> </InlineEquation>), and the number of layers (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(N\)</EquationSource> </InlineEquation>). Numerical results indicate the significant dependency of surface plasmon frequency on these parameters along (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{ac}\)</EquationSource> </InlineEquation>) and (<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{zz}\)</EquationSource> </InlineEquation>) conductivities of BP. As chirality parameter (<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\xi\)</EquationSource> </InlineEquation>) increases, the plasmonic frequency increases for both conductivities. While gyrotropy (<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mu}_{2}\)</EquationSource> </InlineEquation>) shifts the plasmonic response, with larger values of <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mu}_{2}\)</EquationSource> </InlineEquation> leading to decrease the plasmonic frequency. The carrier density <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({n}_{s}\)</EquationSource> </InlineEquation> also influences the plasmon frequency, with higher <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({n}_{s}\)</EquationSource> </InlineEquation> values resulting in higher frequencies for both (<InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{ac}\)</EquationSource> </InlineEquation>) and (<InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{zz}\)</EquationSource> </InlineEquation>). Furthermore, the number of BP layers (N) has notable impact, as an increase in N causes a steeper rise in frequency for both (<InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{ac}\)</EquationSource> </InlineEquation>) and (<InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{zz}\)</EquationSource> </InlineEquation>). Propagation loss or imaginary part of propagation constant for different carries density is also analyzed for both conductivities. Based on numerical results <InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{ac}\)</EquationSource> </InlineEquation> is suitable for higher frequencies compared to <InlineEquation ID="IEq17"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{zz}\)</EquationSource> </InlineEquation>​. This suggests that <InlineEquation ID="IEq18"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{ac}\)</EquationSource> </InlineEquation>​ might possess properties that facilitate its performance or responsiveness at higher frequencies in contrast to <InlineEquation ID="IEq19"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{zz}\)</EquationSource> </InlineEquation>​. However, <InlineEquation ID="IEq20"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="340_2025_8528_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\sigma}_{zz}\)</EquationSource> </InlineEquation> exhibits higher effective mode index for the proposed waveguide structure. Additionally, modulating carrier density can control both the phase velocity and propagation length. The proposed waveguide structure holds promising potential for plasmonic community to fabricate nanophotonic devices due to anisotropy of chiroferrite and BP medium in THz frequency regime.</p>

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Photon plasmon coupling in black phosphorus embedded between chiroferrite layers

  • Mohamed Shaban,
  • Sameerah I. Al-Saeedi,
  • A. M. Elbasiony,
  • A. Waleed,
  • Fadhil Faez Sead,
  • Rana Muhammad Zulqarnain

摘要

Characteristics of photon plasmon coupling in black phosphorus (BP) embedded between chiroferrite layer is analyzed in THz frequency spectrum. The frequency behavior and propagation characteristics of SPPs are analyzed under various physical parameters i.e., chirality parameter ( \(\xi\) ), gyrotropy ( \({\mu}_{2}\) ), carrier density ( \({n}_{s}\) ), and the number of layers ( \(N\) ). Numerical results indicate the significant dependency of surface plasmon frequency on these parameters along ( \({\sigma}_{ac}\) ) and ( \({\sigma}_{zz}\) ) conductivities of BP. As chirality parameter ( \(\xi\) ) increases, the plasmonic frequency increases for both conductivities. While gyrotropy ( \({\mu}_{2}\) ) shifts the plasmonic response, with larger values of \({\mu}_{2}\) leading to decrease the plasmonic frequency. The carrier density \({n}_{s}\) also influences the plasmon frequency, with higher \({n}_{s}\) values resulting in higher frequencies for both ( \({\sigma}_{ac}\) ) and ( \({\sigma}_{zz}\) ). Furthermore, the number of BP layers (N) has notable impact, as an increase in N causes a steeper rise in frequency for both ( \({\sigma}_{ac}\) ) and ( \({\sigma}_{zz}\) ). Propagation loss or imaginary part of propagation constant for different carries density is also analyzed for both conductivities. Based on numerical results \({\sigma}_{ac}\) is suitable for higher frequencies compared to \({\sigma}_{zz}\) ​. This suggests that \({\sigma}_{ac}\) ​ might possess properties that facilitate its performance or responsiveness at higher frequencies in contrast to \({\sigma}_{zz}\) ​. However, \({\sigma}_{zz}\) exhibits higher effective mode index for the proposed waveguide structure. Additionally, modulating carrier density can control both the phase velocity and propagation length. The proposed waveguide structure holds promising potential for plasmonic community to fabricate nanophotonic devices due to anisotropy of chiroferrite and BP medium in THz frequency regime.