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Using successively the conventional Gibbs and the differential-form formulations of Maxwell's equations, we analyze the electromagnetic fields in a self-dual chiral material (invariance under the exchanges [(E⇔−H), (D⇔B), (e⇔−μ)]. We prove that such a medium supports pseudo-TE/TM waves (only a component is null with two relations between four of the five other components). An interesting example is supplied by the Courant-Hilbert quasi-undistorted progressing waves: their form does not change along propagation; only their amplitude could change.

Pseudo-TE/TM Waves in a Self-Dual Chiral Medium