Electromagnetic Metasurfaces. Christophe Caloz

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Parameters Medium Reciprocal upper D overbar overbar equals 0 comma upper S overbar overbar equals 0 comma upper A overbar overbar not-equals 0 Omega nu overbar overbar equals 0 upper D overbar overbar equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar equals 0 Pseudochiral kappa overbar overbar not-equals 0 upper D overbar overbar equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar not-equals 0 Pseudochiral omega upper D overbar overbar not-equals 0 comma upper S overbar overbar equals 0 comma upper A overbar overbar equals 0 Pasteur (or biisotropic) upper D overbar overbar not-equals 0 comma upper S overbar overbar equals 0 comma upper A overbar overbar not-equals 0 Chiral omega upper D overbar overbar not-equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar equals 0 Anisotropic chiral upper D overbar overbar not-equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar not-equals 0 General reciprocal Nonreciprocal upper D overbar overbar equals 0 comma upper S overbar overbar equals 0 comma upper A overbar overbar not-equals 0 Moving nu overbar overbar not-equals 0 upper D overbar overbar equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar equals 0 Pseudo Tellegen kappa overbar overbar equals 0 upper D overbar overbar equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar not-equals 0 Moving pseudo Tellegen upper D overbar overbar not-equals 0 comma upper S overbar overbar equals 0 comma upper A overbar overbar equals 0 Tellegen upper D overbar overbar not-equals 0 comma upper S overbar overbar equals 0 comma upper A overbar overbar not-equals 0 Moving Tellegen upper D overbar overbar not-equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar equals 0 Anisotropic Tellegen upper D overbar overbar not-equals 0 comma upper S overbar overbar not-equals 0 comma upper A overbar overbar not-equals 0 Nonreciprocal nonchiral

      where upper D overbar overbar is a diagonal tensor and upper N overbar overbar is a traceless tensor that can be further split into a symmetric part, upper S overbar overbar, and an antisymmetric part, upper A overbar overbar, where

      (2.87)upper S overbar overbar equals StartFraction upper N overbar overbar plus upper N overbar overbar Superscript normal upper T Baseline Over 2 EndFraction and upper A overbar overbar equals StartFraction upper N overbar overbar minus upper N overbar overbar Superscript normal upper T Baseline Over 2 EndFraction comma

      (2.88)upper M overbar overbar equals upper D overbar overbar plus upper S overbar overbar plus upper A overbar overbar period

      1 1 Each of the four tensors in (2.3) contains susceptibility components, amounting to a total of susceptibilities.

      2 2 Note that some materials, such as glass, can often be assumed to be dispersionless within a limited frequency range given the negligible variations of their constitutive parameters across that range.

      3 3 Here, the tildes are used to differentiate the time-domain susceptibilities from their frequency-domain counterparts.

      4 4 The local field is defined as the total field, at the position of the particle, minus the field produced by the particle itself.

      5 5 In the time domain, time reversal consists in replacing the variable by . Therefore, a function becomes . In the frequency domain, the time-reversal operation consists in taking the complex conjugate of the Fourier transform of , i.e. in transforming into , where the plus sign is for a time-even quantity while the minus sign is for a time-odd

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