Theoretical Studies of Optical Metamaterials Jianji Yang To cite this version: Jianji Yang. Theoretical Studies of Optical Metamaterials. Other [cond-mat.other]. Université Paris Sud - Paris XI, 2012. English. NNT : 2012PA112175. tel-00737379 HAL Id: tel-00737379 https://pastel.archives-ouvertes.fr/tel-00737379 Submitted on 1 Oct 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITÉ PARIS XI UFR SCIENTIFIQUE D’ORSAY École Doctorale Ondes et Matières Laboratoire Charles Fabry THÈSE Présentée pour obtenir le grade de DOCTEUR EN SCIENCES DE L’UNIVERSITÉ PARIS-SUD XI Spécialité : Optique et Photonique par Jianji YANG (杨建基) Theoretical studies of optical fishnet metamaterials Soutenue le 14 Septembre 2012 devant la commission d’examen composée de: M. Stéphane COLLIN Membre invité M. Julien DE LA GORGUE DE ROSNY M. Philippe LALANNE Directeur de thèse M. Didier LIPPENS M. Luis MARTIN-MORENO Rapporteur M. Christophe SAUVAN Co-encadrant invité M. Jean-Claude WEEBER Rapporteur M. Saïd ZOUHDI Table of content Introduction 1 1 Introduction to metamaterials 7 1.1 Maxwell equations and material parameters ....................................................................... 8 1.2 Structured electromagnetic materials: metamaterials ..................................................... 9 1.2.1 Development of structured electromagnetic materials ........................................ 9 1.2.2 Metamaterials .........................................................................................................................10 1.3 A brief history of negative refractive-index metamaterials .........................................11 1.3.1 Negative refraction and the perfect lens ....................................................................11 1.3.2 Ingredients for realizing a negative refractive index ...........................................13 1.3.3 Early experimental demonstration of negative-index metamaterials .........17 1.4 Negative-index metamaterials at optical frequencies ....................................................18 1.5 Outline of the thesis ........................................................................................................................20 2 Retrieving the effective parameters of metamaterials from the single interface scattering problem 23 2.1 Introduction ........................................................................................................................................24 2.2 Light scattering at an air/metamaterial interface ............................................................25 2.2.1 Fundamental Bloch mode of a fishnet metamaterial ...........................................27 2.2.2 Scattering coefficients at the air/fishnet interface ................................................28 2.2.3 Single Bloch mode approximation ................................................................................29 2.3 From the single interface to the retrieval of effective parameters ...........................30 2.3.1 Proposal of a retrieval method based on single interface scattering ...........30 2.3.2 Comparison between the S-parameter method and the proposed method ...................................................................................................................................................................31 2.4 Conclusion ...........................................................................................................................................33 3 Closed-form expression for the scattering coefficients at an interface between two periodic media 35 3.1 Introduction and classical least mean square solution ..................................................36 3.2 Electromagnetic theory of light scattering at the interface between two periodic structures ..........................................................................................................................37 3.3 Bloch mode orthogonality ............................................................................................................38 3.4 Closed-form expression for the scattering coefficients of the fundamental Bloch modes ........................................................................................................................................41 3.5 Test of the close-form expressions ..........................................................................................42 3.6 Conclusion ...........................................................................................................................................46 4 Microscopic model for fishnet metamaterials 47 4.1 Introduction ........................................................................................................................................48 4.2 Elementary waveguide structures and scattering events .............................................50 4.2.1 Two elementary waveguide structures in fishnet .................................................51 4.2.2 Elementary plasmon scattering processes ...............................................................53 4.3 Microscopic model: a coupled mode formalism ................................................................54 4.3.1 Metallic hole-chain: TE01 supermode ..........................................................................55 4.3.2 Z-periodic hole-chain ..........................................................................................................56 4.3.3 Fishnet structure ...................................................................................................................58 4.4 Origin of the negative index ........................................................................................................61 4.4.1 Longitudinal (vertical) channel ......................................................................................61 4.4.2 Transversal (horizontal) channel ..................................................................................61 4.4.3 Quantifying the “magnetic” resonance .......................................................................63 4.5 Numerical analysis ..........................................................................................................................63 4.5.1 Numerical analysis ...............................................................................................................64 4.5.2 Numerical accuracy and convergence .........................................................................66 4.6 Conclusion ...........................................................................................................................................67 5 Applications of the microscopic model: Engineering the optical properties of fishnet metamaterials 69 5.1 Introduction ........................................................................................................................................70 5.2 Engineering the fishnet geometrical parameters ..............................................................71 5.2.1 Impact of the transversal period ax ..............................................................................72 5.2.2 Impact of the dielectric layer thickness ......................................................................74 5.2.3 Impact of the dielectric refractive index ....................................................................76 5.3 Incorporation of gain medium for loss-compensation ...................................................77 5.4 Analysis of the main model limitation ....................................................................................80 5.5 Conclusion ...........................................................................................................................................82 6 Ultra-small 3D Metal-Insulator-Metal (MIM) resonators: slow retardation effects in the quasi-static limit 85 6.1 Introduction ........................................................................................................................................86 6.2 Magnetic resonance of a single 3D MIM resonator ..........................................................88 6.3 Fabry-Perot model of the magnetic resonance ..................................................................90 6.3.1 Fabry-Perot model parameters: fundamental mode of the MIM waveguide and facet reflectivity ....................................................................................91 6.3.2 Fabry-Perot equations: phase-matching condition and quality factor ........94 6.3.3 Analysis of the Q factor increase ....................................................................................96 6.4 Fabry-Perot model in the quasi-static limit .........................................................................97 6.5 Conclusion ...........................................................................................................................................99 7 Conclusion and Perspectives 101 7.1 Summary ..........................................................................................................................................