There has been already a similar question here https://www.researchgate.net/post/What_is_the_refractive_index_of_graphene_in_the_far_infra-red_region

The solution lies in following paper, refer it for a better understanding

Rodrigo, D., Limaj, O., Janner, D., Etezadi, D., De Abajo, F.J.G., Pruneri, V. and Altug, H., 2015. Mid-infrared plasmonic biosensing with graphene. Science, 349(6244), pp.165-168

The below paper [1] gives the formula of wavelength and temperature dependence of graphene. conductivity The relative permittivity can be obtained by conductivity [2].

[1] A. Madani and S. R. Entezar, Optical properties of one-dimensional photonic crystals containing graphene sheets, Physica B 431, 1 (2013).

[2] X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, A Graphene-Based Hybrid Plasmonic Waveguide With Ultra-Deep Subwavelength Confinement, J. Lightwave Technol. 32(21), 3597 (2014).

The below paper [1] gives the formula of wavelength and temperature dependence of graphene conductivity. Then the relative permittivity can be obtained by the conductivity [2].

[1] A. Madani and S. R. Entezar, Optical properties of one-dimensional photonic crystals containing graphene sheets, Physica B 431, 1 (2013). [2] X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, A Graphene-Based Hybrid Plasmonic Waveguide With Ultra-Deep Subwavelength Confinement, J. Lightwave Technol. 32(21), 3597 (2014).

The below paper Ref. [1] [Eq.(1)] gives the formula of wavelength and temperature dependence of graphene conductivity. Then the relative permittivity can be obtained by the conductivity using Eq. (2) in Ref. [2].

[1] A. Madani and S. R. Entezar, Optical properties of one-dimensional photonic crystals containing graphene sheets, Physica B 431, 1 (2013).

[2] X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, A Graphene-Based Hybrid Plasmonic Waveguide With Ultra-Deep Subwavelength Confinement, J. Lightwave Technol. 32(21), 3597 (2014).

Jacek Gosciniak & Dawn T. H. Tan, Theoretical investigation of graphene-based photonic modulators .

Yizhe Li, Limei Qi, Junsheng Yu, Zhijiao Chen, Yuan Yao, and Xiaoming Liu, One-dimensional multiband terahertz graphene photonic crystal filters,

• Article One-dimensional multiband terahertz graphene photonic crystal filters