The analytical propagation functions for partially coherent vortex cosine-hyperbolic-Gaussian beams (PCvChGB) propagating through uniaxial crystal orthogonal to the optical axis are derived, and numerical examples analyze their spreading properties. It's shown that the intensity distribution of the PCvChGB is astigmatic and related to the initial beam parameters, namely the decentered parameter b and topological charge M, the coherence length <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11082_2025_8047_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\sigma_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, and the ratio of refractive index <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11082_2025_8047_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">${{n_{e} } \mathord{\left/ {\vphantom {{n_{e} } {n_{0} }}} \right. \kern-0pt} {n_{0} }}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>n</mi> <mi>e</mi> </msub> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <msub> <mi>n</mi> <mi>e</mi> </msub> <msub> <mi>n</mi> <mn>0</mn> </msub> </mpadded> </mphantom> </mfenced> </mrow> <msub> <mi>n</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>. The obtained results could be beneficial for application of partially coherent beam in anisotropic medium.

Propagation properties of partially coherent vortex cosine-hyperbolic-Gaussian beams in uniaxial crystal orthogonal to the optical axis

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发表日期：

2025年2月6日

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M. Lazrek,
M. Yaalou,
Z. Hricha,
A. Belafhal

摘要

The analytical propagation functions for partially coherent vortex cosine-hyperbolic-Gaussian beams (PCvChGB) propagating through uniaxial crystal orthogonal to the optical axis are derived, and numerical examples analyze their spreading properties. It's shown that the intensity distribution of the PCvChGB is astigmatic and related to the initial beam parameters, namely the decentered parameter b and topological charge M, the coherence length $\sigma_{0}$ $σ_{0}$ , and the ratio of refractive index ${{n_{e} } \mathord{\left/ {\vphantom {{n_{e} } {n_{0} }}} \right. \kern-0pt} {n_{0} }}$ $n_{e} /) n_{0}$ . The obtained results could be beneficial for application of partially coherent beam in anisotropic medium.