Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media

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Abstract
Several aspects of electromagnetic wave propagation and scattering in isotropic chiral media (D = ∊E + β∊▽ × E, B = μH + βμ▽× H) are explored here. All four field vectors, E, H, D, and B, satisfy the same governing differential equation, which reduces to the vector Helmholtz equation when β = 0. Vector and scalar potentials have been postulated. Conservation of energy and momentum are examined. Some properties, consequences, and computationally attractive forms of the applicable infinite-medium Green’s function have been explored. Finally, the mathematical expression of Huygens’s principle, as applicable to chiral media, has also been derived and employed to set up a scattering formalism and to establish the forward plane-wave-scattering amplitude theorems. Several of the results given that pertain to the field equations and Green’s dyadic are available for constitutive equations other than those mentioned above; these results, along with some others, have been given now for the above-mentioned constitutive equations. The derivations of Huygens’s principle and other developments described here have not been given earlier, to our knowledge, for any pertinent set of constitutive equations. With advances in polymer science, the formalisms developed here may be useful in the utilization of artificial chiral dielectrics at suboptical and microwave frequencies; application to vision research is also anticipated.

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