Ten years past the Post

Abstract

The Post constraint for linear electromagnetic materials arises from two basic tenets of modern electromagnetism. The first is the microscopic basis of all electromagnetic phenomenons. The second is thatẼ (x, t) andB (x, t) are the fundamental fields, whereasD (x, t) andH (x, t) are merely secondary constructs. The latter is in contrast to the older version of electromagnetism, wherein the roles ofB (x, t) andH (x, t) are the opposite, and which does not admit the Post constraint. A comprehensive view of the Post constraint is presented. REDISCOVERY OF THE POST CONSTRAINTA little over ten years ago, I was busy finishing a monograph on electromagnetic fields in isotropic, linear, chiral mediums [1]. The electromagnetic response properties of these materials are direction-independent. At any given frequency, three constitutive scalars are needed to describe these properties. It was known that the general, linear, isotropic medium requires four constitutive scalars [2,3]. The difference is that while the threeparameter mediums are Lorentz-reciprocal, the four-parameter mediums are not [4]. This difference produces a dilemma: How can the characteristics of propagation in the forward and the backward directions be different from each other in a linear medium with direction-independent response properties? For two years, I had searched in vain for a way out of this dilemma.While my monograph had gone to the publishers and I was suffering from what could be described as a post partum depression, I began leafing through a slender volume on the formal structure of electromagnetism [5]. I had occasionally consulted this book for over a decade, and did not expect to find anything new. This time, however, my attention was arrested by Eq. 6.18b for this book, which seemed to have emerged from Eq. 6.18. If this equation were true, modern electromagnetism would not admit an isotropic, linear, four-parameter medium. Furthermore, this equation would assert that all linear isotropic materials must be Lorentz-reciprocal, although it would not outlaw Lorentz-reciprocity for linear anisotropic materials. My notes indicate that I sent three e-mails on March 26, 1994 to my friend and collaborator, Werner S. Weiglhofer (University of Glasgow) describing the situation. Within three weeks, both of us had checked and confirmed my initial thoughts. The Post constraint had been rediscovered. On May 2, 1994, we submitted a note for publication [6].We also communicated with Frédéric Guérin, one of the organizers of the conference Chiral '94 . He agreed to let us deliver a post-conference presentation on May 20, 1994. There is no record of our presentation in the official proceedings of that conference [7]. The air was thick with excitement after our joint delivery. Many sentiments were freely expressed by others. Werner and I thoroughly enjoyed the hullabaloo. My depression vanished.Ever since then, the Post constraint has been the subject of ongoing discussion in the complex-mediums electromagnetics research community. During the first severa...

Measuring a piecewise constant axion field in classical electrodynamics

“…In Post [21] it was argued that the axion piece has to vanish, i.e., α = 0 (and even dα = 0). For this reason, Lakhtakia [7,8] (and references given there) called α = 0 the Post constraint and advocated it as a condition each medium has to fulfill. We quoted in [4] literature in which materials are described (Cr 2 O 3 and Fe 2 TeO 6 ) that carry an axion piece.…”

Numerical Modeling of Electromagnetic Wave Propagation Through Bi-Isotropic Materials

“…While reciprocal chiral materials have been extensively researched during the last years, and different geometries and fabrication techniques have been designed [5,6], nonreciprocal materials have stayed mainly in the plane of theoretical discussion. In [12,13], Lakhtakia and Weiglhofer affirmed, using a covariance requirement deduced by Post (the so-called "Post constraint" [14]), that a bi-isotropic medium must be reciprocal, so the Tellegen parameter should always be 0. This opened a discussion on the theoretical possibility of the existence of such materials that lasted more than a decade, mainly between Lakhtakia and Weiglhofer [12,13,[15][16][17][18] and Lindell, Sihvola, Tretyakov et al [3,4,[19][20][21][22][23].…”

“…After that (13) is discretized in the same way than (11) y (12). The resulting equations are coupled to (16).…”

Linear media in classical electrodynamics and the Post constraint

“…Since the metric of spacetime is the gravitational potential in general relativity, it is gratifying to know that there is a gravity-free way of formulating the Maxwell equations. Accordingly, the Maxwell equations (12), (13) are valid in a flat Minkowski spacetime (in any coordinates), in a curved Riemannian spacetime, and even in the Riemann-Cartan spacetime of the Poincaré gauge theory of gravitation. Needless to say that this beautiful formalism has great practical value for applying electrodynamics in accelerated reference frames, for instance.…”

“…The most notorious one is the so-called Post constraint, which requires the sum of the traces of the matrices C b a and D b a to vanish, i.e., C a a + D a a = 0. There is an ongoing dispute mainly in the electrical engineering community, see Lakhtakia & Weiglhofer [12,13,14,15,16,50,51] and Lindell, Sihvola, Tretyakov, et al [20,21,22,23,24,38,43,49] whether this constraint is valid or not. We will address this question.…”