Operator Formalism in the Theory of Effective Parameters of Plane Stratified Bianisotropic Structures

Spectral and polarization effects in deterministically non-periodic multilayers containing optically anisotropic and gyrotropic materials

“…Therefore one can rewrite (B.6-B.7) in the form analogous to (14) and (24): On the other hand, one can take Taylor of (B.2-B.5) in another manner, excluding the propagation phase ϕ rather than the polarization plane rotation φ from decomposition. Making use of the fact that iǫ µ (ǫ ∓ δǫ) sin kd µ (ǫ ± δǫ) ≃ i (ǫ ± δǫ) µ (ǫ ± δǫ) sin kd µ (ǫ ± δǫ) + O δǫ 2 and likewise neglecting αδǫ, we obtain This formula is used in the text as (27).…”

“…To advance from a single layer to a multilayer structure, let us investigate what happens when propagators in the form (14) are multiplied. Naturally, we assume different ε, µ, d, and α (if any) for the two adjacent layers.…”

“…Compared to a birefringent evolution operator (24), there is an antisymmetric addition proportional to α (and, more generally, this α comes from decomposition of sin kdα). We know from (14) that such a term in the propagator is responsible for polarization plane rotation.…”

“…We can see that the polarization of the transmitted wave is rotated by the angle of φ = kdα, while the values of t and t ′ (which contribute to the transmittance) remain the same. Besides, it can be stated that the propagator structure for the bi-isotropic layer in (14) explicitly contains the value of φ.…”

“…In addition, interesting results have been recently obtained with weakly modulated periodic structures made of anisotropic and gyrotropic materials [12]. Extensive ongoing analytical research of anisotropic and gyrotropic multilayers [13][14][15], as well as studies of a simpler case of chiral media in 2D [16] and 3D [17] photonic crystals, is also restricted to periodic systems.…”