Efficient techniques for scattering from planar and cylindrical structures with edges

In this work, we present rigorous and efficient methods for analyzing scattering from the following structures • Tandem Slit loaded with homogeneous material • Eccentrically loaded cylinder with multiple slits • Semicircular cylinder and slit • Dielectric loaded Wedge shaped cylinder • Circular cylinder with resonant cavities and resonant cavities on circular arc. For analyzing the material loaded tandem slit configuration, the boundary value problem is formulated into a pair of simultaneous Wiener-Hopf equations via Fourier transformation. After decoupling these equations by elementary transformation, each modified Wiener-Hopf equation is reduced to a Fredholm integral equation of the second kind. The integral equations are then solved approximately to yield the Fourier transform of the diffracted fields. The inverse transform is evaluated asymptotically to obtain the far field expressions. Measurements and numerical simulations are also performed for several different geometric and material configurations. The analytic solutions compare well with measured and simulated results. The possibility of reducing beamwidth and increasing power coupled through the loaded tandem slit is explored. The analysis of the eccentrically loaded cylindrical cavity with multiple slits under plane wave illumination is formulated using two distinct approaches: (1) an integral equation/combined boundary condition (IE/CBC) formulation and (2) an integral equation/Neumann series expansion (IE/NS) formulation. The IE/NS formulation is shown to converge faster than the IE/CBC formulation based on the proper edge behavior exhibited by the Neumann series current expansion functions. Results for the backscattered radar cross section (RCS) of several geometries are presented, and the relationships between the RCS and the scatterer characteristics are explored. The applicability of the Neumann series method to find a fast method for evaluating scattering from a metallic strip and semicircular cylinder is presented. The Neumann series of different periodicity is used for studying scattering from wedge shaped cylinder. The Neumann series is also applied to study scattering from a circular cylinder with resonant cavities and resonant cavities on a circular arc. These resonant cavities on a circular arc have superdirective properties, which are useful for high gain antenna design

Applications of the wave packet method to resonant transmission and reflection gratings

Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive (dispersive and absorbing) media. The algorithm is based on the Hamiltonian formalism in the framework of which Maxwell's equations for passive media are shown to be equivalent to the first-order equation, $\partial \Psi/\partial t = {\cal H}\Psi$, where ${\cal H}$ is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector $\Psi$ built of the electromagnetic inductions and auxiliary matter fields describing the medium response. The initial value problem is then solved by means of a modified time leapfrog method in combination with the Fourier pseudospectral method applied on a non-uniform grid that is constructed by a change of variables and designed to enhance the sampling efficiency near medium interfaces. The algorithm is shown to be highly accurate at relatively low computational costs. An excellent agreement with previous theoretical and experimental studies of the gratings is demonstrated by numerical simulations using our algorithm. In addition, our algorithm allows one to see real time dynamics of long leaving resonant excitations of electromagnetic fields in the gratings in the entire frequency range of the initial wide band wave packet as well as formation of the reflected and transmitted wave fronts.Comment: 23 pages; 8 figures in the png forma

Study of the interaction of surface waves with a metallic nano-slit via the finite-difference time-domain method

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2007-2008.L’étude de l’interférence entre un plasmon polariton de surface (SPP) avec le faisceau plan lumineux incident sur une nano-fente métallique de dimension sous-longueur d’onde est devenue récemment un sujet fondamental de recherche dans le domaine de la plasmonique afin de mieux comprendre le mécanisme du rehaussement de la transmission optique de la nano-fente. Par la méthode de différences-finies dans le domaine de temps (FDTD), nous avons étudié le mécanisme de couplage du SPP dans la fente nanométrique. L’objectif de ce projet consiste dans un premier temps à la conception et l’implémentation d’un algorithme FDTD flexible et robuste, capable de simuler l’interaction de sources électromagnétiques avec des nanostructures de métal. L’algorithme développé sur la plate-forme Matlab permet de modéliser dans un espace bi-dimensionel des structures diélectriques dispersives. Dans un deuxième temps, nous avons employé ce simulateur FDTD pour étudier les mécanismes de couplage entre un SPP et une fente nanométrique percée dans une mince couche d’argent. Notre analyse démontre que le SPP incident à la fente est diffusé par le rebord de la fente et que les charges électriques induites sur les rebords ré-irradient l’énergie électromagnétique à l’intérieur de la fente. De plus, ces charges électriques génèrent des nouveaux SPPs sur les parois de la fente, qui contribuent à la formation de modes Fabry-Pérot le long de l’axe central de la fente. Nous démontrons aussi la formation de modes Fabry-Pérot créés par la multi-réflexion des ondes diffusées entre les parois de la fente. La combinaison de ces deux modes Fabry-Pérot produit une distribution de champ asymétrique dans la fente. Nous démontrons que la phase du SPP, relativement au faisceau incident normal, détermine les conditions d’interférence constructive et destructive correspondant respectivement au rehaussement et à la diminution de la transmission à travers la nano-fente. Finalement, nous avons confirmé la théorie d’interférence entre les champs induits par le SPP incident et le faisceau incident normal par l’addition de leurs amplitudes instantanées.The study of the interference of the surface plasmon polariton (SPP) with the incident plane wave on a subwavelength metallic slit has become recently a fundamental subject of research in the domain of plasmonics. One of the objectives is to better understand the phenomenon of enhanced optical transmission through the nano-slit. Using the numerical method of finite-difference time-domain (FDTD), we have investigated the coupling mechanisms of the SPP inside the nano-slit. The objective of this project first consists in the conception and implementation of a flexible and robust FDTD algorithm capable of simulating the interaction between electromagnetic sources and metallic nanostructures. The algorithm that we have developed on the Matlab platform is able to model two-dimensional dispersive dielectric structures. The second and main objective is to use this FDTD simulator to investigate the coupling mechanisms between the SPP and a nano-slit pierced into a thin silver film. Our analysis demonstrates that the incident SPP is scattered by the inner edge of the slit and that the scattered waves induce oscillating electric charges on the slit edges which reradiate electromagnetic energy inside the slit. Moreover, these electric charges generate new SPPs on the slit walls which contribute to the formation of Fabry-Pérot modes along the central slit axis. We also show the formation of Fabry-Pérot modes set up by the multi-reflections of scattered waves between the slit walls. The combination of these two Fabry-Pérot modes produces an asymmetric field distribution inside the slit. We demonstrate that the phase of the SPP relatively to the normal incident beam determine the conditions of constructive and destructive interference which correspond, respectively, to the enhancement and suppression of the optical transmission through the nano-slit. Finally, we have confirmed the theory of interference between the induced fields by the SPP and incident normal beam via the superposition of their instantaneous fields

Electromagnetic Transmission Through Resonant Structures.

Electromagnetic resonators store energy in the form of oscillatory electric and magnetic fields and gradually exchange that energy by coupling with their environment. This coupling process can have profound effects on the transmission and reflection properties of nearby interfaces, with rapid transitions from high transmittance to high reflectance over narrow frequency ranges, and has been exploited to design useful optical components such as spectral filters and dielectric mirrors. This dissertation includes analytic, numeric, and experimental investigations of three different electromagnetic resonators, each based on a different method of confining electromagnetic fields near the region of interest. First, we show that a structure with two parallel conducting plates, each containing a subwavelength slit, supports a localized resonant mode bound to the slits and therefore exhibits (in the absence of nonradiative losses), perfect resonant transmission over a narrow frequency range. In practice, the transmission is limited by conduction losses in the sidewalls; nevertheless, experimental results at 10 GHz show a narrowband transmission enhancement by a factor of 10^4 compared to the non-resonant transmission, with quality factor (ratio of frequency to peak width) Q~3000. Second, we describe a narrowband transmission filter based on a single-layer dielectric grating. We use a group theory analysis to show that, due to their symmetry, several of the grating modes cannot couple to light at normal incidence, while several others have extremely large coupling. We then show how selectively breaking the system symmetry using off-normal light incidence can produce transmission peaks by enabling weak coupling to some of the previously protected modes. The narrowband filtering capabilities are validated by an experimental demonstration in the long wavelength infrared, showing transmission peaks of quality factor Q~100 within a free-spectral range of 8-15 um. Third, we demonstrate that defect-free periodic structures of finite extent can support extended, surface-avoiding, high-quality factor resonant modes, even without mirror-like structures at the boundaries to confine electromagnetic energy. After discussing the necessary conditions for mode confinement to occur, several numerical examples are given. Finally, an experiment at microwave frequencies (2-9 GHz) demonstrates mode confinement, with quality factors Q~150, in a 12-period array of short dielectric rods.PhDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120859/1/yms_1.pd

A statistical model for the excitation of cavities through apertures

In this paper, a statistical model for the coupling of electromagnetic radiation into enclosures through apertures is presented. The model gives a unified picture bridging deterministic theories of aperture radiation, and statistical models necessary for capturing the properties of irregular shaped enclosures. A Monte Carlo technique based on random matrix theory is used to predict and study the power transmitted through the aperture into the enclosure. Universal behavior of the net power entering the aperture is found. Results are of interest for predicting the coupling of external radiation through openings in irregular enclosures and reverberation chambers.Comment: 12 pages, 11 figures, in press, IEEE Transactions on Electromagnetic Compatibilit

Dynamical Equivalent Circuit for 1-D Periodic Compound Gratings

Metallic compound gratings are studied in this work by means of an analytical equivalent circuit approach in order to obtain its transmission and reflection properties when illuminated by a TM-polarized plane wave. A compound grating consists of the periodic repetition of a finite number of slits carved out of a thick metal slab (reflection grating) or connecting two separated open regions through groups of slits in the metal slab (transmission grating). The equivalent circuit is rigorously obtained starting from a simplified version of the integral equation for the electric field at the slits apertures. That equivalent circuit involves transmission-line sections that account for the fundamental and lowest order diffracted modes (which does give the 'dynamical' nature to the present equivalent circuit), and lumped components to model the effect of all the higher order diffracted modes. All the relevant and complex features of the spectra can be satisfactorily explained in terms of the topology and characteristics of the equivalent circuit. In contrast with some previously reported circuit models, all the dynamical and quasi-static circuit elements are analytically and explicitly obtained in terms of the geometric and electrical parameters of the grating. The accuracy of the approximate circuit model is very good over a very wide band, as it is demonstrated by comparison with full-wave data computed with commercial electromagnetic solvers.Ministerio de Economía y Competitividad TEC2013- 41913-PJunta de Andalucía P12-TIC-143