Model of light collimation by photonic crystal surface modes

We propose a quantitative model explaining the mechanism of light collimation by leaky surface modes that propagate on a corrugated surface around the output of a photonic crystal waveguide. The dispersion relation of these modes is determined for a number of surface terminations. Analytical results obtained on the basis of the model are compared to those of rigorous numerical simulations. Maximum collimation is shown to occur at frequency values corresponding to excitation of surface modes whose wave number retains a nonzero real part.Comment: 6 pages, 7 figures. Version 2: corrected sign of k_x' (sections 4-6, fig. 2), minor clarifications in section 2. Version 3: significant changes, including reformulation of the model using the theory of aperture antennas, as well as extended discussion of the accuracy of the mode

A modal approach to modelling spin wave scattering

Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their computational cost is high, and the complexity of their output hinders insight into the physics of the simulated system, especially in the case of multimode propagating wave-based devices. We propose a finite-element modal method allowing an efficient solution of the scattering problem for dipole-exchange spin waves propagating perpendicularly to the magnetisation direction. The method gives direct access to the scattering matrix of the whole system and its components. We extend the formula for the power carried by a magnetostatic mode in the Damon-Eshbach configuration to the case with exchange, allowing the scattering coefficients to be normalised to represent the fraction of the input power transferred to each output channel. We apply the method to the analysis of spin-wave scattering on a basic functional block of magnonic circuits, consisting of a resonator dynamically coupled to a thin film. The results and the method are validated by comparison with micromagnetic simulations

Advanced magnon-optic effects with spin-wave leaky modes

We numerically demonstrate the excitation of leaky spin waves (SWs) guided along a ferromagnetic stripe by an obliquely incident SW beam on the thin film edge placed below the stripe. During propagation, leaky waves emit energy back to the layer in the form of plane waves and several laterally shifted parallel SW beams. This resonance excitation, combined with interference effects of the reflected and re-emitted waves, results in the magnonic Woods anomaly and significant increase of the Goos-Hanchen shift magnitude. Hence, we provide a unique platform to control SW reflection and to transfer SWs from a 2D platform into the 1D guiding mode that can be used to form a transdimensional magnonic router

Semi-analytical design of antireflection gratings for photonic crystals

This article concerns the design of antireflection structures which, placed on a photonic crystal surface, significantly diminish the fraction of energy lost to reflected waves. After a review of the classes of these structures proposed to date, a new method is presented in detail for the design of antireflection gratings operating in a wide range of angles of incidence. The proposed algorithm is illustrated by means of several examples, showing the advantages and limitations.Comment: Submitted to Phys. Rev.

Application of the multiple-scattering method to analysis of systems with semi-infinite photonic waveguides

We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as reflection and transmission coefficients, of PC functional elements. Rather than a modification of the MS computational algorithm, our approach involves postprocessing of results obtained by the MS method. We derive analytical formulas for the fields excited in a finite system, taking explicitly into account the spurious reflections occurring at the artificial system boundaries. The intrinsic parameters of the investigated functional element are found by fitting the results of MS simulations to those obtained from the formulas derived. Devices linked with one and two semi-infinite waveguides are analyzed explicitly; possible extensions of the formalism to more complex circuits are discussed as well. The accuracy of the proposed method is tested in a number of systems; the results of our calculations prove to be in good agreement with those obtained independently by other authors.Comment: 8 pages, 5 figure

Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals

By exploiting the concepts of magnetic group theory we show how unidirectional behavior can be obtained in two-dimensional magneto-photonic crystals (MOPhC) with uniform magnetization. This group theory approach generalizes all previous investigations of one-way MOPhCs including those based on the use of antiparallel magnetic domains in the elementary crystal cell. Here, the theoretical approach is illustrated for one MOPhC example where unidirectional behavior is obtained by appropriately lowering the geometrical symmetry of the elementary motifs. One-way transmission is numerically demonstrated for a photonic crystal slice.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Conception et modélisation numérique de composants optiques en nanophotonique intégrée

This thesis is devoted to the design and theoretical and numerical analysis of a number of photonic crystal (PC) components. In its first part we study the influence of the surface structure of two-dimensional (2D) PCs on their optical properties. We formulate an effective-medium model of such PCs, able to reproduce the commonly observed strong dependence of their effective parameters on the position of their truncation plane. We then develop an algorithm for the design of compact wide-angle antireflection gratings for 2D PCs and show them to improve significantly the transmission through a PC flat lens. In the second part of the manuscript we introduce a new approach to the design of resonant cavities to be used in compact magneto-optical circulators. In contrast to structures proposed previously, they are devoid of oppositely-polarised magnetic domains, which significantly facilitates their fabrication. We show that these cavities need not be embedded in PCs, but can be coupled directly with standard rib waveguides. Some numerical techniques developed in the course of this thesis are presented in the last part of the manuscript. We extend the multiple-scattering method to the case of gyrotropic materials and introduce a straightforward and extremely accurate method for the calculation of band structures of 2D PCs composed of circular cylinders, based on Fourier-Bessel expansions. Finally, we describe the implementation of the finite-element method for the calculation of eigenmodes of open, axisymmetric, three-dimensional cavities containing gyrotropic materials.Cette thèse est consacrée à la conception et l'analyse théorique de différents composants en optique intégrée. Nous présentons un modèle de milieu effectif pour les cristaux photoniques (CPs) 2D qui rend compte des effets de surface, puis un algorithme pour la conception de réseaux antiréfléchissants grand-angle pour ces CPs. Ces réseaux permettent d'améliorer significativement la transmission à travers une lentille plate d'indice négatif. Nous proposons une nouvelle génération de circulateurs magnétooptiques compacts, fonctionnant dans un champ magnétique extérieur uniforme et constitués d'une cavité résonnante en anneaux circulaires couplée directement à des guides d'ondes standards. Nous généralisons la méthode multipolaire 2D aux matériaux gyrotropiques et la formulons sans « lattice sums » pour les structures périodiques. Enfin, nous décrivons en détail la méthode des éléments finis pour le calcul des modes propres des cavités 3D en anneaux circulaires et matériaux gyrotropiques