The differential theory of diffraction by arbitrary cross-section cylindrical objects is developed for the most general case of an incident field with a wave vector outside the cross-section plane of the object. The fast Fourier factorization technique recently developed for studying gratings is generalized to anisotropic and/or inhomogeneous media described in cylindrical coordinates; thus the Maxwell equations are reduced to a first-order differential set well suited for numerical computation. The resolution of the boundary-value problem, including an adapted S-matrix propagation algorithm, is explained in detail for the case of an isotropic medium. Numerical applications show the capabilities of the method for resolving complex diffraction problems. The method and its numerical implementation are validated through comparisons with the well-established multipole method.
RésuméWe deduce from Monomode Modal Method the analytical expressions of transmission and reflexion Jones matrices of an infinitely conducting metallic screen periodically pierced by subwavelength holes. The study is restricted to normal incidence and to the case of neglected evanescent fields (far-field) which covers many common cases. When only one non-degenerate mode propagates in cavities, they take identical forms to those of a polarizer, with Fabry-Perot-like spectral resonant factors depending on bigrating parameters. The isotropic or birefringent properties are then obtained when holes support two orthogonal polarization modes. This basic formalism is finally applied to design compact and efficient metallic half-wave plates.
Bloch surface waves (BSWs) are recently developing alternative to surface plasmon polaritons (SPPs). Due to dramatically enhanced propagation distance and strong field confinement these surface states can be successfully used in on-chip all-optical integrated devices of increased complexity. In this work we propose a highly miniaturized grating based BSW coupler which is gathering launching and directional switching functionalities in a single element. This device allows to control with polarization the propagation direction of Bloch surface waves at subwavelength scale, thus impacting a large panel of domains such as optical circuitry, function design, quantum optics, etc.
We study a polarizer-analyzer mounting for the terahertz regime with perfectly conducting metallic polarizers made of a periodic subwavelength pattern. We analytically investigate the influence on the transmission response of the multiple reflections which occur between polarizer and analyzer with a renewed Jones formalism. We demonstrate that this interaction leads to a modified transmission response: the extended Malus' Law. In addition, we show that the transmission response can be controlled by the distance between polarizer and analyzer. For particular set-ups, the mounting exhibits extremely sensitive transmission responses. This interesting feature can be employed for high precision sensing and characterization applications. We specifically propose a general design for measuring electro-optical response of materials in the terahertz domain allowing detection of refractive index variations as small as 10 −5 .
The diffraction of an electromagnetic wave by a cylindrical object with arbitrary cross section is studied by taking advantage of recent progress in grating theories. The fast Fourier factorization method previously developed in Cartesian coordinates is extended to cylindrical coordinates thanks to the periodicity of both the diffracting object and the incident wave with respect to the polar angle theta. Thus Maxwell equations in a truncated Fourier space are derived and separated in TE and TM polarization cases. The new set of equations for TM polarization is resolved numerically with the S-matrix propagation algorithm. Examples of elliptic cross sections and cross sections including couples of nonconcentric circles show fast convergence of the results, for both dielectric and metallic materials, as well as good agreement with previous published results. Thus the method is suitable for an extension to conical (out-of-plane) diffraction, which will allow studying mode propagation along microstructured fibers.
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