This paper explores the propagation characteristics of Airyprime beams in an inhomogeneous medium with periodic potential, from both theoretical and numerical simulation perspectives. By using the method of separation of variables, the Gross–Pitaevskii equation with periodic potential was solved to obtain the breather soliton solution and breathing period. Additionally, considering the medium and beam parameters, numerical simulations were performed to study the propagation characteristics of Airyprime beams and the superposition between two Airyprime beams. First, the influence of initial medium parameters (modulation intensity P and modulation frequency ω) on the propagation characteristics was studied. Then, the effect of initial beam parameters (initial chirp C and position x0) on the propagation characteristics was analyzed. Finally, the superposition between two Airyprime beams with different phases <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10043_2025_1003_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$\varphi = 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>φ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10043_2025_1003_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$\varphi$</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>, amplitudes A, and initial separations x0 was investigated. By changing the initial medium parameters, the breathing period and central position of the breather soliton can be controlled; by adjusting the initial beam parameters, the deflection direction, size, and maximum intensity of the breather soliton can be manipulated. Changing the phase <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10043_2025_1003_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$\varphi = 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>φ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10043_2025_1003_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$\varphi$</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation>, amplitude A, and initial separation x0 of the two Airyprime beams can form different bound-state breather solitons. The results provide a theoretical foundation for the propagation and control of Airyprime beams, as well as for their potential applications in optical communication.

Transmission dynamics of Airyprime beams in periodic optical lattices

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发表日期：

2025年9月19日

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Lixiong Li,
Guanghao Zeng,
Zhenhua Cai

摘要

This paper explores the propagation characteristics of Airyprime beams in an inhomogeneous medium with periodic potential, from both theoretical and numerical simulation perspectives. By using the method of separation of variables, the Gross–Pitaevskii equation with periodic potential was solved to obtain the breather soliton solution and breathing period. Additionally, considering the medium and beam parameters, numerical simulations were performed to study the propagation characteristics of Airyprime beams and the superposition between two Airyprime beams. First, the influence of initial medium parameters (modulation intensity P and modulation frequency ω) on the propagation characteristics was studied. Then, the effect of initial beam parameters (initial chirp C and position x₀) on the propagation characteristics was analyzed. Finally, the superposition between two Airyprime beams with different phases $\varphi = 0$ $φ = 0$ $\varphi$ $φ$ , amplitudes A, and initial separations x₀ was investigated. By changing the initial medium parameters, the breathing period and central position of the breather soliton can be controlled; by adjusting the initial beam parameters, the deflection direction, size, and maximum intensity of the breather soliton can be manipulated. Changing the phase $\varphi = 0$ $φ = 0$ $\varphi$ $φ$ , amplitude A, and initial separation x₀ of the two Airyprime beams can form different bound-state breather solitons. The results provide a theoretical foundation for the propagation and control of Airyprime beams, as well as for their potential applications in optical communication.