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<p>A novel mathematical approach to model a Bragg grating element is studied in the present article, expressed as an individual cell TF in the Z domain. The modelling considers a uniform cell width or delay length and periodic strong index contrast between the adjacent cells, and the periodic cell RI difference is acknowledged by a phase term in the TF polynomials. The grating element is viewed as cascade connections of the high-index contrast cells, and the modelling explores the optical delay-line signal processing and the unity delay concept. The Z-transform technique is an effective tool in modern-day optical communication, and the entire modelling is carried out in the Z-domain. The MATLAB environment is used for the simulation work and obtains both the reflection and the transmission responses. The reflection spectrum profile of the HCBG for three different grating lengths is also captured, while the Opti-FDTD designer platform is used to validate the proposed mathematical modelling. The spectral properties, including peak reflection, sidelobe magnitude, and FWHM bandwidth, are evaluated for three different grating lengths and are highlighted in a tabular format.</p>

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Z-domain transfer function extraction and opti-FDTD verification of high-contrast grating

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • Suraj Saha,
  • Sanjoy Mandal

摘要

A novel mathematical approach to model a Bragg grating element is studied in the present article, expressed as an individual cell TF in the Z domain. The modelling considers a uniform cell width or delay length and periodic strong index contrast between the adjacent cells, and the periodic cell RI difference is acknowledged by a phase term in the TF polynomials. The grating element is viewed as cascade connections of the high-index contrast cells, and the modelling explores the optical delay-line signal processing and the unity delay concept. The Z-transform technique is an effective tool in modern-day optical communication, and the entire modelling is carried out in the Z-domain. The MATLAB environment is used for the simulation work and obtains both the reflection and the transmission responses. The reflection spectrum profile of the HCBG for three different grating lengths is also captured, while the Opti-FDTD designer platform is used to validate the proposed mathematical modelling. The spectral properties, including peak reflection, sidelobe magnitude, and FWHM bandwidth, are evaluated for three different grating lengths and are highlighted in a tabular format.