Crystal optical properties of incommensurate phases in the plane-wave modulation region

Abstract

Crystal optical properties of anisotropic optical materials of which the dielectric tensor is spatially modulated with a sinusoidal wave form are studied in the framework of the Jones calculus. Propagation of polarized light along the directions parallel to and far from the optical axes is considered. Polarization of the normal waves of the medium and the Jones matrix of a finite modulated crystal are derived, enabling us to ascertain the parameters of the apparent macroscopic optical activity. The developed model should describe the optical effects in a planewave region of incommensurate phases with the average inversion symmetry, occurring in the A 2 BX 4 family crystals. The boundary conditions for the phase of the modulation wave, which play a key role in crystal optics of incommensurate phases, are discussed. The model predicts a relatively small optical activity in the birefringent crystal sections and negligible or zero effect in the optical axis directions. The conclusions agree well, at least, with the non-contradictory experimental results on optical rotatory power of the A 2 BX 4 crystals. A comparison with the results derived earlier for the square modulation wave proves that the main conclusions of the model do not depend on the exact modulation shape.

On the Propagation of Light in Incommensurately Modulated Dielectric Crystals

“…Moreover, a cumbersome relation N 2 dNadz Àw 2 ac 2 e T derived in [5] in the assumption of a complete equivalence of equations (1) and (5) has in general to be regarded as incorrect. It is easy to prove with, e.g., inserting into the equation the N matrices for the modulated materials derived in [8] according to their definition (i.e. on the basis of the relation [2] between N and the well-known integral Jones matrices).…”

“…A proper electromagnetic analysis of the problem has to be based on accounting for the macroscopic inhomogeneity of the dielectric tensor [6,8,18], first of all, the components where j qz j 0 is the phase of the modulation wave. Being related to the order parameter of an incommensurate phase transition, the structural modulation is a quite feeble effect, and the non-modulated components e (see e.g.…”

“…Being related to the order parameter of an incommensurate phase transition, the structural modulation is a quite feeble effect, and the non-modulated components e (see e.g. [6,8,14]). As shown above, the inequality (7) is no longer true in this case and the operator approach used in [6 to 8] turns out to be insufficient.…”

“…As shown above, the inequality (7) is no longer true in this case and the operator approach used in [6 to 8] turns out to be insufficient. For this reason we have recalculated the main results of [8], employing the approximate ªwave equationº (5) which may be now written as…”

Non-reciprocity of Faraday rotation in gyrotropic crystals

“…Such a superposition is known to may lead to some effects impossible for observing in a plane case of pure circular birefringence. A relevant example may be the influence of periodic structural modulation in crystals on their optical anisotropy characteristics, which cannot be reduced to that for the case of light propagation strictly along an optic axis direction [16]. Still closer to our subject is another example related to multiple light reflections in anisotropic dielectric media [17]: contrary to the case of the Faraday rotation, those reflections do not affect the optical rotation due to pure optical activity, though the effect appears whenever a small accompanying linear birefringence exists.…”