This paper presents a generalized Drude-Lorentz model that complies with the requirements of the singularity expansion method (SEM) for describing the dielectric permittivity of optical materials. The model is derived by treating the permittivity as a meromorphic transfer function, which can be expanded in terms of complex singularities. This approach allows for the derivation of a generalized expression of the Debye-Drude-Lorentz model that satisfies the constraints of physical systems and the requirements of complex analysis. The model is validated using experimental data for a wide range of materials, including metals, 2D materials, and dielectrics. The accuracy of the model is assessed by comparing the calculated permittivity with experimental data, and it is shown that the model provides a highly accurate description of the permittivity across a broad spectral range. The generalized Drude-Lorentz model is derived by expanding the permittivity in terms of complex singularities and expressing it as a sum of Drude and Lorentz terms. The model includes additional frequency-dependent imaginary terms that account for the contribution of the first derivative of the electric field to the displacement field in the temporal domain. These terms are essential for the model to comply with the requirements of the SEM. The model is then used to retrieve the parameters of the permittivity from experimental data using an optimization method based on auto-differentiation. This method is applied to nine materials, including oxides, metals, and 2D materials, and it is shown that the model provides highly accurate results with a small set of poles. The distribution of the poles in the complex frequency plane is used to characterize the behavior of the materials at different frequencies. The poles associated with Drude and Lorentz terms are used to identify the resonances and anti-resonances in the permittivity. The model is shown to be effective in characterizing the behavior of materials, including metals and dielectrics, and it is demonstrated that the poles can be used to determine the nature of the material. The model is also shown to be applicable to a wide range of materials, including non-isotropic media, due to its compliance with complex analysis. The study concludes that the generalized Drude-Lorentz model provides a highly accurate description of the dielectric permittivity of optical materials and that the model can be used to characterize the behavior of materials based on the distribution of their poles in the complex frequency plane. The model is shown to be efficient and accurate, and it is demonstrated that the inclusion of additional frequency-dependent imaginary terms in the model allows for a more accurate description of the permittivity with a smaller number of singularities. The model is validated using experimental data and is shown to provide excellent results for a wide range of materials.This paper presents a generalized Drude-Lorentz model that complies with the requirements of the singularity expansion method (SEM) for describing the dielectric permittivity of optical materials. The model is derived by treating the permittivity as a meromorphic transfer function, which can be expanded in terms of complex singularities. This approach allows for the derivation of a generalized expression of the Debye-Drude-Lorentz model that satisfies the constraints of physical systems and the requirements of complex analysis. The model is validated using experimental data for a wide range of materials, including metals, 2D materials, and dielectrics. The accuracy of the model is assessed by comparing the calculated permittivity with experimental data, and it is shown that the model provides a highly accurate description of the permittivity across a broad spectral range. The generalized Drude-Lorentz model is derived by expanding the permittivity in terms of complex singularities and expressing it as a sum of Drude and Lorentz terms. The model includes additional frequency-dependent imaginary terms that account for the contribution of the first derivative of the electric field to the displacement field in the temporal domain. These terms are essential for the model to comply with the requirements of the SEM. The model is then used to retrieve the parameters of the permittivity from experimental data using an optimization method based on auto-differentiation. This method is applied to nine materials, including oxides, metals, and 2D materials, and it is shown that the model provides highly accurate results with a small set of poles. The distribution of the poles in the complex frequency plane is used to characterize the behavior of the materials at different frequencies. The poles associated with Drude and Lorentz terms are used to identify the resonances and anti-resonances in the permittivity. The model is shown to be effective in characterizing the behavior of materials, including metals and dielectrics, and it is demonstrated that the poles can be used to determine the nature of the material. The model is also shown to be applicable to a wide range of materials, including non-isotropic media, due to its compliance with complex analysis. The study concludes that the generalized Drude-Lorentz model provides a highly accurate description of the dielectric permittivity of optical materials and that the model can be used to characterize the behavior of materials based on the distribution of their poles in the complex frequency plane. The model is shown to be efficient and accurate, and it is demonstrated that the inclusion of additional frequency-dependent imaginary terms in the model allows for a more accurate description of the permittivity with a smaller number of singularities. The model is validated using experimental data and is shown to provide excellent results for a wide range of materials.