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<p>Airyprime beams form a novel family of structured light that retain the diffraction free and self-accelerating features of conventional Airy beams while showing distinctive interference enhanced dynamics. We investigate the propagation of two Airyprime like beams—the Cos Airyprime and Cosh Airyprime—inside a periodic parabolic potential well. Using the nonlinear Schrödinger framework together with a Mathieu function expansion, we obtain analytical propagation expressions and validate them with numerical simulations. We analyze how transverse displacement <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x_{0}\)</EquationSource> </InlineEquation>, cosine modulation <i>β</i>, and hyperbolic cosine factor <i>γ</i> qualitatively affect intensity profiles, centroid motion, and effective beam width. Results show that both beam types undergo periodic breathing and robust spatial confinement imposed by the lattice, with symmetry, localization and breathing amplitude strongly determined by initial parameters. These findings offer clear guidelines for parameter selection in optical field control, photonic lattice engineering, and quantum simulation platforms based on Airyprime type beams.</p>

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Influence of bound state parameters on the propagation properties of Airyprime pulses in a periodic potential well

  • 期刊论文

  • 发表日期：

    2026年4月3日

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  • Lixiong Li,
  • Zhenhua Cai

摘要

Airyprime beams form a novel family of structured light that retain the diffraction free and self-accelerating features of conventional Airy beams while showing distinctive interference enhanced dynamics. We investigate the propagation of two Airyprime like beams—the Cos Airyprime and Cosh Airyprime—inside a periodic parabolic potential well. Using the nonlinear Schrödinger framework together with a Mathieu function expansion, we obtain analytical propagation expressions and validate them with numerical simulations. We analyze how transverse displacement \(x_{0}\) , cosine modulation β, and hyperbolic cosine factor γ qualitatively affect intensity profiles, centroid motion, and effective beam width. Results show that both beam types undergo periodic breathing and robust spatial confinement imposed by the lattice, with symmetry, localization and breathing amplitude strongly determined by initial parameters. These findings offer clear guidelines for parameter selection in optical field control, photonic lattice engineering, and quantum simulation platforms based on Airyprime type beams.