This analysis reveals distinct constraints on constitutive relations in isotropic media, suggesting new approaches to initial value problems.
We first compare the space-time and momentum descriptions of electromagnetic signals in isotropic, homogeneous, chiral media. The two descriptions supply constraints of a different type on constitutive relations and we give an hyperbolicity criterion for the second-order partial differential equations supplied by these constraints in space-time. Then, we prove that the Laplace transform is a natural tool to tackle initial value problems in space-time and we carefully discuss the solutions obtained with this transform.
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Pïerre Hillion (1996) studied this question.
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