Analysis of anisotropic dielectric gratings

Electromagnetic Formalisms for Optical Propagation in Three-Dimensional Periodic Liquid-Crystal Microstructures

“…Considering the continuum of tangential fields on interfaces, these fields emitted from the ℓ th layer hence can be straightforwardly treated as the incident fields fˆt ,ℓ+1 for the (ℓ + 1) th layer, and allow to follow the next transfer matrix S ℓ+1 to describe the sequential propagations of fields through the (ℓ + 1) th layer as in Equation (13). For the matrices S ent and S ext defined for the (isotropic) uniform incident (ℓ = 0) and emitted (ℓ = N + 1) regions, respectively, the eigen-modes are specially chosen (and symbolized) as E + q and M + q ( E − q and M − q ) (Ho et al (2011);Rokushima & Yamakita (1983)), representing the physical forward (backward) TE and TM waves as the above-mentioned. In which the transform matrix T (i) ε I between the eigen-mode components and the tangential components fˆt ,0 =[ e x,0 h y,0 e y,0 h x,0 ] t for the isotropic incident region (ℓ = 0) is given as: Will-be-set-by- IN-TECH in which m gh =(n yh n yh + n xg n xg ) 1/2 , ξ gh =(ε I − n yh n yh − n xg n xg ) 1/2 ,andε I = n 2 I have been applied for the incident region.…”

“…A further step in LC optics is to consider rigorously the LC variation both along the cell normal and along a single transverse direction, leading to a two-dimensional treatment of light propagation. This step is fulfilled by implementing the finite-difference time-domain method (Kriezis et al (2000a); Witzigmann et al (1998)), the vector beam propagation method (Kriezisa & Elston (1999 ); Kriezis & Elston (2000b)), coupled-wave theory (Galatola et al (1994); Rokushima & Yamakita (1983)), and an extension of the Berreman approach (Zhang & Sheng (2003)), and has proven to be successful in demonstrating the strong scattering and diffractive effects on the structures with transverse LC variation lasting over the optical-wavelength scale. For three-dimensional LC medium with arbitrary normal and transverse LC variations, Kriezis et al (2002) proposed a composite scheme based on the finite-difference time-domain method and the plane-wave expansion method to evaluate the light propagation in periodic liquid-crystal microstructures.…”

Theory of electron diffraction from planar ideal crystals

“…In summary, the rigorous coupled-wave analysis was developed (i) for electron diffraction from a crystal based upon the (first-order) Dirac equation (Gevers & David, 1982), and (ii) for electromagnetic wave diffraction from gratings with a single grating vector based upon the (second-order) Helmholtz equation (Moharam & Gaylord, 1981, 1983a) and the (first-order) Maxwell equations (Moharam & Gaylord, 1983b;Rokushima & Yamakita, 1983). Transmittance and reflectance are defined in all these theories.…”

Magneto-Optic Periodic Strip Structures

“…The metho d was devel oped by Mo hara m and G aylo rd f or the case of isotro pi c gra ti ng structures and subsequentl y general i zed to ani sotro pi c slanted gra ti ng s by R okushi ma and Y amakita [4]. Recentl y, the anal ysi s of converg ence pro perti es l eadi ng to the im pro ved p erform ance of the m etho d wa s carri ed out by Li [5].…”

“…The structure was magneti zed i n p ol ar geom etry (the m agneti zati on i s p erp endi cul ar to the surf ace of the sam pl e) a nd i t was studi ed using m agneto-opti cal el li psometry . D uri ng the m easurem ent of the Kerr e˜ect, the spectra l dependence of p Kerr ro ta ti on was obta i ned i n the spectra l regi on 240 nm to 1 4 ). The geom etri c para m eters of the sampl es are sum mari zed i n Tabl e. The exp eri ments were carri ed out under the condi ti on tha t the sampl eswere m agneti zed to thei r satura ti on sta te.…”