Doubly skew: A new class of non-birefringent media

Abstract

We introduce a new class of non-birefringent, linear media. These media are based on skewonic materials (media that violate the Post constraint), complemented by a skew-symmetric contribution to the principal part of the constitutive relation. The class may be parametrized in terms of a 4 × 4 matrix, whose symmetric part defines the quadratic Fresnel surface, and two space vectors.

Decomposable Medium Conditions in Four-Dimensional Representation

“…The medium has no birefringence if the symmetric parts of these two dyadics are multiples of one another. When in addition A is a multiple of B, the medium coincides with the doubly-skew medium of [22].…”

“…Since the principal part is not complete, i.e., it does not have an inverse, some trouble in interpreting the medium in terms of three-dimensional medium dyadics may be expected. If A = B is chosen in (66) and (67), SDCM reduces to a simplified class of media, previously called that of doubly-skew media [22].…”

The non‐birefringent limit of all linear, skewonless media and its unique light‐cone structure

“…In the context of this paper, this property has little relevance, since a vanishing skewon implies that either Q = −Q T or Q = Q T . Insomuch as the former case leads to an unspecified wave (co-)vector [18], only the latter case can be accepted. Thus, Q can henceforth be considered to be a "constitutive" metric, converging to g for the vacuum (16).…”

“…A comparison with χ 0 in Eq. (16) reveals that, at this point, only two quantities can still be adjusted: the impedance (18), with the sign s Q , and an axion term. Even so, when probing an interface with empty space, selecting…”