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A thorough review of metasurfaces (2D planar counterpart of metamaterials) based on electromagnetic (EM) classification i.e., <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-negative (ENG), <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-negative (MNG), and double-negative (DNG) materials is presented in this paper. The concept of left-handedness in metasurfaces which comprise of ENG, MNG, and DNG is demonstrated through basic Maxwell&#x2019;s equations. This concept is then explained by designing unit cells of each category along with numerical extractions of parameters through Kramers-Kronig rule (for ENG) and Nicholson-Ross-Weir (NRW for MNG and DNG), thereby verifying unit cell designs. This helps the reader to have complete insight regarding the design, simulation, and mathematical verification of ENG, MNG, and DNG-based metasurfaces used in antenna applications for gain enhancement, absorbers to reduce radar cross-section and beam forming. Moreover, the paper also provides a thorough review of the state-of-the-art research based on these metasurfaces in antenna applications delineated above. A comparison of the state of the art is drawn at the end of this review.

Review of Metasurfaces Through Unit Cell Design and Numerical Extraction of Parameters and Their Applications in Antennas