Spatial dispersion in incommensurately modulated insulators

Abstract

Peculiarities of the non-local responses of spatially inhomogeneous insulating media to electromagnetic waves are considered within a phenomenological approach. In the case of a weak spatial dispersion (SD), a ‘quasi-local’ constitutive equation is derived, which allows one to isolate the effects of SD in relation to non-uniformities of the wavefield and the material properties of the medium. The symmetry of the material tensors is clarified. The material contribution to the SD suggests a novel mechanism for optical activity. The SD in crystalline media is described in terms of dielectric permittivity dependent upon a single argument which is a specific combination of the light wavevector and the reciprocal lattice vectors. The conditions and materials for which the relevant effects can be notable are pointed out. The character of the normal light wave polarization in dielectric crystals of the A2BX4 group with incommensurately modulated superstructure is analysed and the effective crystal optical parameters are derived. It is shown that the first-order material SD effects associated with the bulk macroscopic properties of these crystals could be of practical importance.

A Superspace Formalism for the Electromagnetism of Generic Nonlocal Continuous Metamaterials: Principal Structures and Applications

“…For example, from the perspective of general thermodynamics, see [29], [30]. Some of the topics reexamined within the framework of a general nonlocal fieldmatter interaction theory include the applicability of optical reciprocity theorems [31]- [34], energy/power balance [35], quantization [36]- [38], operator methods [39], extension of spatial dispersion to include inhomogeneous media [12], and alternative formulations of spatial dispersion in terms of the Jones calculus [40].…”

“…Quasi-inhomogeneous or smoothly-inhomogeneous nonlocal media are some of the simplest possible prototypes of general (inhomogeneous) nonlocal materials where the spatial dispersion model ε(k) with only a dependence on one variable k is not adequate to the description of the physics of the problem [12], [39]. In general, there has been quite few investigations aimed at going beyond spatial dispersion in homogeneous media.…”

A Superspace Formalism for the Electromagnetism of Generic Nonlocal Continuous Metamaterials: Principal Structures and Applications

“…which is the standard constitutive relation of linear electromagnetic materials. Clearly, (12) says that only the exciting field F(r) data at r is needed to induce a response at the same location. In a nutshell, locality implies that the natural configuration space of the electromagnetic problem is just the point-like spacetime manifold D ⊂ R 3 or the entire Euclidean space R 3 .…”

“…In general, dealing with topics such as supergravity, supersymmetry, superfields, superstrings, and noncommutative geometry often requires the use of one superspace formalism or another [8]. More related to the subject of nonlocal MTMs is the original superspace concept introduced earlier for the analysis of deformed crystal [11] and subsequently utilized for fundamental investigations of EM nonlocality in incommensurate (IC) superstructures in insulators [12]. Such modulatedstructure materials possess spaces with dimensions greater than spacetime [13].…”

Band pattern of commensurate modulated periodic structures

“…The relation between the competing periods d, (d′) and δ plays an important role in the response of the structure to an incoming electromagnetic wave. Previous evidence shows that the modulation has a profound impact on the unmodulated EBGs [10,11]. One of the effects is the splitting in a (large) number of new EBGs [7].…”