In this article, we investigate the spectral broadening of cosh-Gaussian pulses which is induced by self-phase modulation (SPM) within the tunneling-induced transparency (TIT) window in an asymmetric multiple-quantum-well system. The study demonstrates how a single laser field, combined with a steady static electric field, enables dynamic control of absorption and dispersion profiles of the system, offering precise control of the group velocity of the applied field. The multiple-quantum-well system exhibits a large Kerr nonlinearity (approximately ${10}^6{\text{W}}^{-1}{\text{m}}^{-1}$), which enhances the SPM effect under the TIT window. Our exploration of SPM using cosh-Gaussian pulses demonstrates that higher probe laser powers result in broader spectral widths and increased internal oscillations, especially under strong tunneling strengths. These results suggest promising applications for fine-tuning light propagation in quantum-well systems and offer a more economical approach for optical light-matter interaction experiments, minimizing the need for extensive optics and optomechanical components.

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• Nonlinear optical susceptibility