<p>A gain-assisted atomic medium controls and modifies spatial solitons of reflection and transmission of structured light. Structured light pulses of reflection and transmission are generated and analyzed by azimuthal quantum numbers dependent on control driving fields in the medium. The study revealed the formation of spatial bright and dark solitons. The bright and dark soliton splitting regions are linearly increasing according to azimuthal quantum numbers of formula <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16538_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(2\ell\)</EquationSource> </InlineEquation>. Two, four, six, and eight bright and dark soliton regions are investigated with the azimuthal quantum number of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16538_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="100" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell _{1,2}=1,2,3,4\)</EquationSource> </InlineEquation>. The structured light of the reflection pulse maintained a constant shape, exhibiting weak nonlinearity along the <i>x</i>-axis and strong nonlinearity along the <i>y</i>-axis. However, the structured light transmission pulse displayed varying shapes, influenced by the balanced nonlinearities along both the <i>x</i>- and <i>y</i>-axes at higher azimuthal quantum number <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16538_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell _{1,2}=4\)</EquationSource> </InlineEquation>, leading to stable propagation of spatial bright solitons. These findings highlight the significant role of the structured light effect in controlling and stabilizing soliton dynamics, with potential applications in nonlinear optics, traffic flow, signal processing, plasma physics, quantum field theory, and optical soliton interferometry.</p>

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Coherent control of reflection and transmission solitons of structured light via a gain-assisted medium

  • Amir Ali,
  • Mohammad Mahtab Alam,
  • Dragan Pamucar,
  • Abdul Majeed,
  • Zeeshan Ali

摘要

A gain-assisted atomic medium controls and modifies spatial solitons of reflection and transmission of structured light. Structured light pulses of reflection and transmission are generated and analyzed by azimuthal quantum numbers dependent on control driving fields in the medium. The study revealed the formation of spatial bright and dark solitons. The bright and dark soliton splitting regions are linearly increasing according to azimuthal quantum numbers of formula \(2\ell\) . Two, four, six, and eight bright and dark soliton regions are investigated with the azimuthal quantum number of \(\ell _{1,2}=1,2,3,4\) . The structured light of the reflection pulse maintained a constant shape, exhibiting weak nonlinearity along the x-axis and strong nonlinearity along the y-axis. However, the structured light transmission pulse displayed varying shapes, influenced by the balanced nonlinearities along both the x- and y-axes at higher azimuthal quantum number \(\ell _{1,2}=4\) , leading to stable propagation of spatial bright solitons. These findings highlight the significant role of the structured light effect in controlling and stabilizing soliton dynamics, with potential applications in nonlinear optics, traffic flow, signal processing, plasma physics, quantum field theory, and optical soliton interferometry.