By Toralf Scharf
Polarized gentle in Liquid Crystals and Polymers bargains with the linear optics of birefringent fabrics, equivalent to liquid crystals and polymers, and surveys mild propagation in such media with certain realization to functions. it's certain in treating mild propagation in micro- and nanostructured birefringent optical components, corresponding to lenses and gratings composed of birefringent fabrics, in addition to the spatial various anisotropic constructions usually present in miniaturized liquid crystal units.
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Additional resources for Polarized Light in Liquid Crystals and Polymers
Sample text
5 PROPAGATION ALONG A PRINCIPAL AXIS The dielectric displacement D is perpendicular to k and 0 1 D0x B C D ¼ @ D0y A: 53 (3:41) 0 The electric field can be calculated by using the inverse dielectric tensor. 33) leads to 11 0 1 1 00 1 0 1À1 1À1 0 10 xx xy 0 D0x 0 D0x B B C C 1À1 0 A@ D0y AA ¼ v2 m0 m10 @ D0y A, (3:44) À@ 0 A Â @@ 0 A Â @ 1À1 yx yy 0 0 nk0 nk0 0 0 1À1 zz 0 and further equating one finds in the following the final form, which can be explicitly written as 0 1 1 D0x A ¼ v2 m0 m10 @ D0y A: À1 n2 k02 @ 1À1 yx D0x þ 1yy D0y 0 0 À1 1À1 xx D0x þ 1xy D0y 0 (3:45) Two equations result, and with k0 ¼ v/c they can be written, conveniently, in the form 0 B @ 1À1 xx À 1À1 yx 1 n2 1 C D0x ¼ 0: 1 A D0y 1yy À xx n2 1À1 xy (3:46) 54 DESCRIPTION OF LIGHT PROPAGATION WITH RAYS This wave equation can be transformed to a diagonal form and delivers the eigenpolarizations D1 and D 2, as well as two refractive indices corresponding to them.
As well as using the normal surface, there are other ways of graphically representing different aspects of the propagation of an electromagnetic plane wave through an anisotropic medium. 7, there are several surfaces and representations that are suitable for describing different issues. Assume that the three principal values 1x, 1y, and 1z have been measured and are known. As the refractive index in the different main directions is given by n2i ¼ 1i, the main refractive indices n2x , n2y , and n2z are known too.
3), provides À Á À Á k02 n2 À jrSðrÞj2 aðr Þ þ r2 aðrÞ À ik0 2rSðr Þ Á raðrÞ þ aðrÞr2 Sðr Þ ¼ 0: (3:5) The real and imaginary parts of the left-hand side must both vanish. Equating the real part to zero and using k0 ¼ 2p/l0, we obtain l0 jrSðr Þj ¼ n þ 2p 2 2 2 r2 aðr Þ , aðrÞ (3:6) l0 one can where jrSj2 ¼ rS Á rS. 1 The wavefronts are surfaces of constant S(r) and are shown as deformed surfaces. Ray trajectories are normal to that surface. 2 The rays of ray optics are orthogonal to the wavefronts of wave optics.
