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<p>In this paper, we investigate theoretically the fourth-order dispersion (FOD) influence on the modulation instability (MI) gain spectra in the presence of higher-order effects in the triple-core oppositely directed coupler with positive–negative-positive index material (PIM-NIM-PIM) channels. Based on the linear stability analysis, an analytical dispersion relation is derived and the main characteristics of MI gain are analyzed for both anomalous and normal dispersion instances. The results allow us to evaluate the MI gain in the presence of higher-order dispersion coefficients. Moreover, the influence of self-steepening, intrapulse Raman scattering, second-order nonlinear dispersion (SOND, characterized by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S_{j+3}\)</EquationSource> </InlineEquation>) and modified saturable nonlinearity on MI gain spectra is discussed. More specifically, it is found that the instability gain in the PIM-NIM-PIM triple-core coupler is crucially enhanced by the combined impact of FOD and system parameters. In the normal GVD regime, a negative FOD coefficient (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta _4 &lt; 0\)</EquationSource> </InlineEquation>) imposes a threshold on the MI gain spectrum with respect to the ratio <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> and tends to suppress and strongly perturb the instability bands, whereas a positive <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\beta _4 &gt;0\)</EquationSource> </InlineEquation> allows MI to persist across all <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation>. In the anomalous GVD regime, the MI gain develops predominantly under the condition <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\beta _4 S_{j+3} &lt; 0\)</EquationSource> </InlineEquation>, while <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\beta _4 S_{j+3} &gt; 0\)</EquationSource> </InlineEquation> suppresses MI. Understanding fourth-order dispersion effects in triple-core couplers directly informs the design and optimization of high-speed, high-power, and ultra-broadband optical devices, ensuring better control over pulse dynamics, spectral properties, and nonlinear interactions in advanced photonic systems.</p>

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Impact of fourth-order dispersion on modulation instability in a triple-core PIM-NIM-PIM-coupler with saturable function

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Mati Youssoufa,
  • Aboukar,
  • Ousmanou Dafounansou,
  • Alim,
  • Alidou Mohamadou

摘要

In this paper, we investigate theoretically the fourth-order dispersion (FOD) influence on the modulation instability (MI) gain spectra in the presence of higher-order effects in the triple-core oppositely directed coupler with positive–negative-positive index material (PIM-NIM-PIM) channels. Based on the linear stability analysis, an analytical dispersion relation is derived and the main characteristics of MI gain are analyzed for both anomalous and normal dispersion instances. The results allow us to evaluate the MI gain in the presence of higher-order dispersion coefficients. Moreover, the influence of self-steepening, intrapulse Raman scattering, second-order nonlinear dispersion (SOND, characterized by \(S_{j+3}\) ) and modified saturable nonlinearity on MI gain spectra is discussed. More specifically, it is found that the instability gain in the PIM-NIM-PIM triple-core coupler is crucially enhanced by the combined impact of FOD and system parameters. In the normal GVD regime, a negative FOD coefficient ( \(\beta _4 < 0\) ) imposes a threshold on the MI gain spectrum with respect to the ratio \(f\) and tends to suppress and strongly perturb the instability bands, whereas a positive \(\beta _4 >0\) allows MI to persist across all \(f\) . In the anomalous GVD regime, the MI gain develops predominantly under the condition \(\beta _4 S_{j+3} < 0\) , while \(\beta _4 S_{j+3} > 0\) suppresses MI. Understanding fourth-order dispersion effects in triple-core couplers directly informs the design and optimization of high-speed, high-power, and ultra-broadband optical devices, ensuring better control over pulse dynamics, spectral properties, and nonlinear interactions in advanced photonic systems.