Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation

The recent fabrication of thin-film helicoidal bianisotropic mediums (HBMs) has created an impetus for understanding their electromagnetic response. Using the Oseen transformation, we have derived a 4×4 matrix ordinary differential equation for oblique (i.e. non–axial) propagation in general linear HBMs. A perturbational technique is presented for almost-axial propagation; and two other techniques—one semi–analytic and the other analytic—are presented for general oblique propagation. All three techniques yield exact closed-form results for axial propagation. Our use of the Oseen transformation amounts to viewing oblique propagation not by itself but as a graft on axial propagation, and is thus responsible for the stability of all three techniques.

[1]  C. F. Hayes,et al.  Optical Rotatory Power of a Cholesteric Liquid Crystal for Obliquely Incident Light Using Multiple Scaling , 1977 .

[2]  E. J. Post,et al.  Formal Structure of Electromagnetics , 1963 .

[3]  Akhlesh Lakhtakia,et al.  Lorentz covariance, Occam's razor, and a constraint on linear constitutive relations , 1996 .

[4]  Thomas K. Gaylord,et al.  Diffraction regimes of transmission gratings , 1978 .

[5]  Thomas K. Gaylord,et al.  Analysis of multiwave diffraction of thick gratings , 1977 .

[6]  V. A. I︠A︡kubovich,et al.  Linear differential equations with periodic coefficients , 1975 .

[7]  Akhlesh Lakhtakia,et al.  Reflection at the Motohiro-Taga interface of two anisotropic materials with columnar microstructures , 1994 .

[8]  A. Lakhtakia,et al.  Axial propagation in general helicoidal bianisotropic media , 1993 .

[9]  H. Hochstadt.  Differential Equations: A Modern Approach , 1964 .

[10]  P. Allia,et al.  4×4 matrix approach to chyral liquid-crystal optics , 1986 .

[11]  C. Oseen,et al.  The theory of liquid crystals , 1933 .

[12]  D. Pozar,et al.  Theory of electromagnetic waves , 1984, IEEE Antennas and Propagation Society Newsletter.

[13]  Vijay K. Varadan,et al.  Normally incident plane waves on a chiral slab with linear property variations , 1991, Optics & Photonics.

[14]  C. Mauguin.  Sur la représentation géométrique de Poincaré relative aux propriétés optiques des piles de lames , 1911 .

[15]  Akhlesh Lakhtakia,et al.  On light propagation in helicoidal bianisotropic mediums , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[16]  Anders E Boström,et al.  Transformation properties of plane, spherical and cylindrical scalar and vector wave functions , 1991 .

[17]  G. Meier,et al.  Optical Properties of Cholesteric Liquid Crystals , 1973 .

[18]  Elio Miraldi,et al.  Dispersion relation for propagation of light in cholesteric liquid crystals , 1983 .

[19]  P. Allia,et al.  Optical-properties of Anisotropic Periodic Helical Structures , 1985 .

[20]  Lakhtakia,et al.  Constraint on linear, homogeneous, constitutive relations. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  O. Parodi.  LIGHT PROPAGATION ALONG THE HELICAL AXIS IN CHIRAL SMECTICS C , 1975 .

[22]  K. Vedam,et al.  Effect of preparation conditions on the morphology and electrochromic properties of amorphous tungsten oxide films , 1993 .

[23]  Uniformity constraint on recently conceptualised linear uniaxial bianisotropic media , 1994 .

[24]  Kevin Robbie,et al.  FIRST THIN FILM REALIZATION OF A HELICOIDAL BIANISOTROPIC MEDIUM , 1995 .

[25]  Kevin Robbie,et al.  Fabrication of thin films with highly porous microstructures , 1995 .

[26]  Scalarisation of maxwell's equations in general inhomogeneous bianisotropic media , 1987 .

[27]  Vladimir E. Dmitrienko,et al.  Optics of cholesteric liquid crystals , 1979 .

[28]  I. Abdulhalim.  Light propagation along the helix of chiral smectics and twisted nematics , 1987 .

[29]  J. Silcox,et al.  COLUMNAR STRUCTURE IN THIN VACUUM‐CONDENSED Pd FILMS , 1966 .

[30]  T Motohiro,et al.  Thin film retardation plate by oblique deposition. , 1989, Applied optics.

[31]  P. G. de Gennes,et al.  Theory of magnetic suspensions in liquid crystals , 1970 .

[32]  Claude Brezinski,et al.  Some new convergence acceleration methods , 1982 .

[33]  C. Krowne,et al.  Electromagnetic theorems for complex anisotropic media , 1984 .