We study the electromagnetics of media described by identical inhomogeneous relative dielectric and magnetic tensors, .  m = Such media occur generically as spatial transformation media, i.e. electromagnetic media that are defined by a deformation of space. We show that such media are completely described by a refractive index n r s , ( ˆ) that depends on position r and direction s, ˆbut is independent of polarization. The phase surface is always ellipsoidal, and n r s , ( ˆ) is therefore represented by the radius vector to the surface of the ellipsoid. We apply our method to calculate the angular dependence of the refractive index in the well-studied cylindrical cloak and to a new kind of structurally chiral medium induced by a twist deformation. By way of a simple example we also show that media for which  m = do not in general preserve the impedance properties of vacuum. The implications of this somewhat surprising conclusion for the field of transformation optics are discussed.

We employ coupled wave theory to enumerate the lasing modes of structurally chiral lasers. The elliptical modes are shown to be fundamentally distinct from those of a scalar distributed feedback laser. High threshold modes are shown to lase with the opposite chirality as the active medium, in contrast to their low-threshold counterparts that lase with the same chirality as the active medium. The lasing mode structure suggests the intriguing possibility of dynamically changing the polarization handedness of a chiral laser, as well as the possibility of lasing within the forbidden band-gap region. These observations arise from the fundamental interplay between the distributed chirality-preserving reflections within the active medium and the localized chirality-reversing reflections at the medium's boundaries.

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