PLASMONICS NANOFOCUSING BASED ON LONGRANGE SURFACE PLASMON POLARITONS

Table of ContentsPreface1Abstract2List of Figures5List of Symbols7List of Abbreviations8Introduction9Chapter 1 Basics of Surface Plasmon Polaritons111.1Maxwell’s Equations111.2 Surface Plasmon Polaritons at Metal-Insulator Interfaces131.2.1 The Wave Equation of TM Mode and TE Mode131.2.2 Surface Plasmon Polaritons at a Single Interface171.2.3 Multilayer Systems and the Long Ranging Modes191.3 Excitation Methods231.3.1 Prism Coupling231.3.2 Grating Coupling251.3.3 End-fire Coupling Excitation27Chapter 2 Demand for nanofocusing, an idea and supporting results292.1 The Increasing Demand of Nanofocusing and an Idea292.2 Supporting Results302.2.1 Extended Long Range Surface Plasmon Polaritons302.2.2 Apertureless Nanotip312.2.3 Plasmonic Nanofocusing Based on a Metal Coated Axicon Prism32Chapter 3 FDTD simulation353.1 FDTD Simulation353.2 Numerical Dispersion413.3 Numerical Stability – The Courant-Friedrichs-Lewy Stability Criterion423.4 Perfect Electric Conductors433.5 Dielectric-Dielectric Interface433.6 Terminating The Simulation Domain46Chapter 4 Waveguide structure, simulation results and discussions534.1 Centre symmetric longrange plasmonics waveguide.534.2 Asymmetric MDM waveguide for long-range surface wave excitation.544.3 Combination of centre symmetric MDM and two side-asymmetric plasmonic waveguide.564.4 Waveguide Structure594.5 Simulation results614.3 The Dependence of the Field Magnification Factor and the Beam Side on Parameters67Conclusion71References72 List of FiguresFigure 1.1 Definition of a planar wave guide geometry..15Figure 1.2 Geometry for SPP propagation at a single interface between a metal and a dielectric.18Figure 1.3 Geometry of a three-layer system consisting of a thin layer I20Figure 1.4 Dispersion relation of the coupled odd and even modes.22Figure 1.5 Prism coupling to SPPs using attenuated total internal reflection24Figure 1.6 Prism coupling and SPP dispersion.24Figure 1.7 Phase-matching of light to SPPs using a grating.26Figure 1.8 End-fire coupling technique for exciting SPPs.27Figure 2.1 Scheme of the analyzed apertureless SNOM probe [8].32Figure 2.2 Schematic for the localization of photons by a metal-coated axicon prism [10]33Figure 2.3 Intensity distributions on a gold-coated axicon prism for radially polarized incident light [10].34Figure 3.1 Discretization of the model into cubes and the position of field.37Figure 3.2 Basic flows for implementation of Yee FDTD scheme.38Figure 3.3 The three-dimensional computational region for FDTD simulation.41Figure 3.4 An example with PEC on the top surface of Cube (i, j, k).43Figure 3.5 Four adjacent cubes with different permittivity and conductivity.44Figure 3.6 A closed loop C crossing four cubes with different permittivity and conductivity.44Figure 3.7 Boundary E field component between two layers of different dielectrics.52Figure 4.1 Centre symmetric waveguide structure53Figure 4.2 A 3D view of longrange surface plasmon polariton excited in a MDM structure.54Figure 4.3 A 2D view of longrange surface plasmon excited in a MDM structure.54Figure 4.4 An asymmetric plasmonic waveguide structure.55Figure 4.5 A 3D view of LRSPPs excitation in an asymmetric structure.55Figure 4.6 A 2D view of LRSPPs excitation in an asymmetric structure.56Figure 4.6 A combination of a symmetric structure with two asymmetric waveguides.56Figure 4.7 Electric field distribution at x-z plane.57Figure 4.8 A 2D view of the electric field distribution at x-z plane.57Figure 4.9a Hy at the x-z plane.58Figure 4.9b Magnetic field distribution at x-z plane.58Figure 4.11 Schematic of the simulated model with an incident wavelength of 1550 nm.59Figure 4.12 Electric field distribution at x-z plane..61Figure 4.12a’ A 3D view of the electric field distribution at x-z plane.61Figure 4.12b Electric field distribution at y-z plane..62Figure 4.12c Poynting vector in z-direction.63Figure 4.12d Magnetic field profile of the guided LRSPPs mode.63Figure 4.12e Magnetic field distribution at the x-z plane.64Figure 4.12f A 3D view of Hy.64Figure 4.12g Electric field (upper) and phase (lower) distribution at the end of the structure.65Figure 4.13 Distribution of electric field at 5nm far from the apex.66Figure 4.14 Electric field profiles of Ez and Ex components at the apex.66Figure 4.15 Dependence of magnification factor and beam side on the outer cladding thickness67Figure 4.16 Dependence of magnification factor and beam side on the exponential coefficient.68Figure 4.17 Dependence of magnification factor and beam side on the tip width.69Figure 4.18 Dependence of magnification factor and beam side on the central film thickness.70List of SymbolsSymbolsExplanationEElectric FieldHMagnetic FieldBMagnetic Flux DensityDDielectric DisplacementJCurrent DensityJextExternal Current Densityλ_0Excitation wavelengthεDielectric ConstantμRelative PermeabilityρCharge Densityρ_extExternal Charge DensityσConductivityχDielectric Susceptibilityk0Wave vectorβPropagation Constant List of AbbreviationsAbbreviationOriginal termSPPsSurface Plasmon PolaritonsLRSPPsLong Range Surface Plasmon PolaritonsFDTDFinite Difference Time DomainBEMBoundary Element MethodFEMFinite Element MethodSNOMsScanning Near-Field Optical Microscopes IntroductionSurface plasmon polaritons (SPPs) are tranverse magnetic polarized optical surface waves that propagate along an interface between a dielectric and a conductor and it exponentially decays in the perpendicular direction. These electromagnetic excitations are excited by coupling of an incident electromagnetic field to oscillations of the conductor’s free electrons. In a metal slab comprised of a sufficiently thin metal film embedded in dielectrics, bound SPPs modes at the upper metal- dielectric interfaces couples to that of the lower one forming two bound super-modes. One of these coupled modes has lower attenuation as the metal film thickness is reduced. It is called long- range surface plasmon polaritons (LRSPPs).In recent explosive progress in nanometric optics, the strong concentration of optical energy, which has been based on the great localization of surface plasmon waves in nanostructures, provides people with a great ability to manipulate substance at nanoscale. It was proposed that smoothly tapered metal plasmonic waveguides focused light energy at its tip due to resonant properties of metal nanoparticles [9-22]. Furthermore, conical dielectric waveguide structures with metal-coating have asserted their ability in nanofocusing with great field enhancement and ultra-high energy confinement based on the constructive interference of surface waves. And in most cases, a transverse magnetic radially polarized optical wave was used due to surface plasmon polaritons excitation and the convergence of photons at the tips of the structures. Recently, some scientits have proposed an excitation method for the localization of photons at the apex of a gold- coated axicon prism. An enhanced spot was generated 5 nm below the apex with a magnification factor of 120 times and confined within 35 nm for an incident wavelength of 632.8 nm. Even though the results are quite impressed, that method consumes high excitation energy and provides quite low field enhancement and large beam side. This thesis proposes another tapered dielectric plasmonic waveguide structure for the convergence of long-range surface plasmon polaritons at the tip of the waveguide in the near infrared (λ0 = 1550 nm). It requires low excitation energy but provides with extreme high field enhancement and small beam side at 5 nm far from the apex.The research bases on the results of a number of computational simulations. Currently, there are some methods to solve electromagnetic problems such as BEM, FDTD. Because of the advantages in near field observation, FDTD is chose to implement the simulations, with a tool named OptiFDTD. In this thesis, all the simulations were executed at 2D level. This thesis consists of 4 chapters, in which the first chapter indicates basic literature of surface plasmon polaritons and methods of excitation. Whereas, chapter 2 illustrates demand for nanofocusing and shows some external results, which support the final design. Next, chapter 3 shows some basic literature of finite difference time domain method used in simulations. Finally, chapter 4 shows output data of the simulation and discussions about these results.

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL OF ELECTRONICS AND TELECOMMUNICATIONS GRADUATE THESIS TOPIC: PLASMONICS NANOFOCUSING BASED ON LONGRANGE SURFACE PLASMON POLARITONS Student: NGUYỄN NGỌC AN Class No.8 – K51 Supervisor: Professor ĐÀO NGỌC CHIẾN, Ph.D Hanoi, May 2011 5/2011 Plasmonics nanofocusing based on longrange surface plasmon polaritons Class No - K51 NGUYỄN NGỌC AN HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL OF ELECTRONICS AND TELECOMMUNICATIONS GRADUATE THESIS TOPIC: PLASMONICS NANOFOCUSING BASED ON LONGRANGE SURFACE PLASMON POLARITONS Student: NGUYỄN NGỌC AN Class No.8 – K51 Supervisor: Professor ĐÀO NGỌC CHIẾN, Ph.D Hanoi, May 2011 MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom - Happiness - PURPOSE OF GRADUATE THESIS Student‟s name: …………….………….…… Student‟s ID: ……………… Key: …………………….School of Electronics and Telecommunications Department: ……………… Thesis title: ……………………………………………… ……………………………………………… ……………………………………………………………………………………………… Initial data: …………………………………… …………………………………………… …… …… ……………………………………………………………………………………………… ……………………………………………………….… ……………………… ………… Contents of explanation and calculation: ……………………………………………………………………………………………… ……………… ….………………………………………………………………………… ………………………………………………………… ….……………………………… ……………………………………………………………………………………………… Figures and graphs (detail types and size of graphs) ……………………………………………………………………………………………… ……………………… ….………………………………………………………………… ……………………………………………………… ……….…………………………… Academic supervisor’s name: ……………………………………………………… … Thesis starting date: ………………………………………………….…………… Thesis finishing date: …………………………………………………………… … June ……,2011 Department Chair Academic Supervisor This acknowledges that this student has completed and submitted this graduate thesis in May……, 2011 Judge MINISTRY OF EDUCAITON AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY - GRADUATE THESIS REVIEW Student‟s name: Student‟s ID: Department: Key: Academic supervisor: Judge: Contents of graduate thesis: Review of judge: May , 2011 Judge ( Signature, detailed fullname ) Preface The research presented in this thesis aims to discover the responses of gold to the excitation in a proposed waveguide structure based on a phenomenon excavated in the time of the Holy Roman Empire It is also the result of intensive efforts to create a potential application for those properties on the current developing field of nanometric optics This thesis has been completed in one year after I came to the Computational Electromagnetic R&D Laboratory By that time, I have worked with a number of great people who contributed in many ways to the research I would like to thank all of them for helping and inspiring me during my graduate study At the first place, I especially want to thank my supervisor, Prof Dao Ngoc Chien, for his essential guidance and endless encouragements during my research and study at Hanoi University of Science and Technology His perpetual energy and enthusiasm in research had motivated all of his students, including me In addition, he was always accessible and willing to help his students with their research in various ways As a result, research life became smooth and rewarding for me I gratefully acknowledge Hoang Van Son for his advice and important supports which made the research much easier I would like to give him the deep thanks for his kind consideration on me All my lab buddies at the Computational Electromagnetic R&D Laboratory made it a convivial place to work In particular, I would like to thank Quang Ngoc Hieu and Nguyen Cong Anh for their constructive comments and helps All other folks had inspired me in research and life through our interactions during the long hours in the lab Finally, my deepest gratitude goes to my family for their eternal love and support throughout my life Abstract In this research, I propose an excitation method for the convergence of longrange surface plasmon polaritons at the tip of a 2D tapered waveguide in the near infrared (λ0 = 1550 nm) The waveguide structure comprises of three thin metal films of finite width which are embedded in dielectrics in order to create both asymmetric and symmetric metal slab waveguides which support long-range surface plasmon polartitons (LRSPPs) The 20 nm width Au film with complex permittivity εr,Au,20 nm = -111.2558 - j17.46 and two different dielectrics, of which the refractive indices are n1 = 1.453 and n2 = respectively, are used to implement the structure Based on the end-fire coupling technique with an incident plane wave source, long range surface plasmon polaritons are excited and propagate along the thin Au films then converge drastically at the tip of the tapered waveguide by constructive interferences causing an extreme field enhancement The simulation was implemented using finite difference time domain method Table of Contents Preface .1 Abstract .2 List of Figures .5 List of Symbols List of Abbreviations Introduction Chapter Basics of Surface Plasmon Polaritons 11 1.1 Maxwell‟s Equations .11 1.2 Surface Plasmon Polaritons at Metal-Insulator Interfaces 13 1.2.1 The Wave Equation of TM Mode and TE Mode .13 1.2.2 Surface Plasmon Polaritons at a Single Interface 17 1.2.3 Multilayer Systems and the Long Ranging Modes 19 1.3 Excitation Methods 23 1.3.1 Prism Coupling .23 1.3.2 Grating Coupling 25 1.3.3 End-fire Coupling Excitation 27 Chapter Demand for nanofocusing, an idea and supporting results .29 2.1 The Increasing Demand of Nanofocusing and an Idea 29 2.2 Supporting Results 30 2.2.1 Extended Long Range Surface Plasmon Polaritons 30 2.2.2 Apertureless Nanotip 31 2.2.3 Plasmonic Nanofocusing Based on a Metal Coated Axicon Prism 32 Chapter FDTD simulation 35 3.1 FDTD Simulation 35 3.2 Numerical Dispersion .41 3.3 Numerical Stability – The Courant-Friedrichs-Lewy Stability Criterion .42 3.4 Perfect Electric Conductors 43 3.5 Dielectric-Dielectric Interface .43 3.6 Terminating The Simulation Domain .46 Chapter Waveguide structure, simulation results and discussions 53 4.1 Centre symmetric longrange plasmonics waveguide 53 4.2 Asymmetric MDM waveguide for long-range surface wave excitation 54 4.3 Combination of centre symmetric MDM and two side-asymmetric plasmonic waveguide 56 4.4 Waveguide Structure .59 4.5 Simulation results 61 4.3 The Dependence of the Field Magnification Factor and the Beam Side on Parameters 67 Conclusion 71 References 72 List of Figures Figure 1.1 Definition of a planar wave guide geometry 15 Figure 1.2 Geometry for SPP propagation at a single interface between a metal and a dielectric .18 Figure 1.3 Geometry of a three-layer system consisting of a thin layer I 20 Figure 1.4 Dispersion relation of the coupled odd and even modes 22 Figure 1.5 Prism coupling to SPPs using attenuated total internal reflection 24 Figure 1.6 Prism coupling and SPP dispersion 24 Figure 1.7 Phase-matching of light to SPPs using a grating 26 Figure 1.8 End-fire coupling technique for exciting SPPs 27 Figure 2.1 Scheme of the analyzed apertureless SNOM probe [8] 32 Figure 2.2 Schematic for the localization of photons by a metal-coated axicon prism [10] .33 Figure 2.3 Intensity distributions on a gold-coated axicon prism for radially polarized incident light [10] .34 Figure 3.1 Discretization of the model into cubes and the position of field 37 Figure 3.2 Basic flows for implementation of Yee FDTD scheme 38 Figure 3.3 The three-dimensional computational region for FDTD simulation 41 Figure 3.4 An example with PEC on the top surface of Cube (i, j, k) 43 Figure 3.5 Four adjacent cubes with different permittivity and conductivity 44 Figure 3.6 A closed loop C crossing four cubes with different permittivity and conductivity 44 Figure 3.7 Boundary E field component between two layers of different dielectrics 52 Figure 4.1 Centre symmetric waveguide structure 53 Figure 4.2 A 3D view of longrange surface plasmon polariton excited in a MDM structure 54 Figure 4.3 A 2D view of longrange surface plasmon excited in a MDM structure .54 Figure 4.4 An asymmetric plasmonic waveguide structure 55 Figure 4.5 A 3D view of LRSPPs excitation in an asymmetric structure 55 Figure 4.6 A 2D view of LRSPPs excitation in an asymmetric structure 56 Figure 4.6 A combination of a symmetric structure with two asymmetric waveguides 56 Figure 4.7 Electric field distribution at x-z plane 57 Figure 4.8 A 2D view of the electric field distribution at x-z plane 57 Figure 4.9a Hy at the x-z plane 58 Figure 4.9b Magnetic field distribution at x-z plane 58 Figure 4.11 Schematic of the simulated model with an incident wavelength of 1550 nm 59 Figure 4.12 Electric field distribution at x-z plane 61 Fig.4.11 illustrates the structure of the proposed plasmonic waveguide Firstly, a thin gold film of 34 nm thick is sandwiched between two dielectric layers which have the refractive index of 1.453 The purpose of this process is to form a symmetric metal slab waveguide at the center of the structure After that, this waveguide is exponentially tapered and then is coated with a thin golden layer which has a width of about 20 nm Gold is used because of its chemical stability Furthermore, the structure is covered with an outer dielectric cladding, which has a refractive index of This process forms two asymmetric metal slabs which are found to effectively sustain long range surface plasmon polaritons in many reseach The outer dielectric cladding also helps to prevent thin gold layers from oxidation which contributed to the plasmon propagation length In addition, it transforms the coupling conditions of light modes propagating in the core into SPP modes at the metal-outer cladding interface Furthermore, it reduces the plasmon wavelength, contributing to the extremely confinement of energy inside the structure Recently, enhanced nanofocusing due to asymmetric field distribution in different dielectrics on both sides of the metal layer was observed by a number of other authors Given that long range plasmon wave modes can be sustained by thin metal films in homogeneous dielectric media with both symmetric and asymmetric structures, the long ranging modes still attenuate due to the damping factor in the metal In order to improve the propagation distance of the long range plasmon mode, a simple way is to reduce the metal layer thickness But it is experimentally difficult to deposit homogeneous metal film of less than 15 nm thickness because gold typically form nanoscale islands in the initial deposition process Thus, the tip of the waveguide is 10 nm wide and the optimal width of the gold- coating is 20 nm in order to reach high coupling efficiency of SPPs and to reduce propagation attenuation of LRSPPs The shape of the structure drastically influences the concentration of LRSPPs at the tip of the structure The utilized curvature parameter α is 13 ensuring extreme convergence of light energy at the centre of the waveguide Long- range surface plasmon polaritons are excited by end- fire coupling technique in order to reach high coupling efficiency, in the near- infrared (λ0 = 1550 nm) with a plane wave 60 source and the complex relative permittivity of gold εr,Au,20 nm = -111.2558 - j17.46 A plane wave can be assumed as a combination of a left hand circularly polarized wave and a right hand circularly polarized wave 4.5 Simulation results Fig.4.12a and a‟ shows the field distribution at vertical plane x-z along the structure axis when a plane wave is incident to the plasmonic waveguide Figure 4.12a Electric field distribution at x-z plane LRSPPs arise and propagate along the structure, then converge at the apex generating an extremely field enhancement Figure 4.12a‟ A 3D view of the electric field distribution at x-z plane 61 As can be seen from the Fig 4.12a, a‟, b, c, d, e, f, g LRSPPs are efficiently excited at the side of the gold coating and the centre thin gold film due to end-fire coupling technique Consequently, these surface waves propagate along the gold layers toward the tip of the waveguide Figure 4.12b Electric field distribution at y-z plane LRSPPs arise and propagate along the structure, then converge at the apex generating an extremely field enhancement The illuminating beam rapidly decays after penetrating through the apex Approaching the apex, the three long range surface plasmon waves constructively interfere together causing an ultra high energy concentration Finally, an enhanced beam penetrated through the tip of the waveguide structure An extremely electric field enhancement is observed at the corner of the apex with a magnification factor of more than 6×103 as shown in Fig.4.12b The excited surface plasmon wave has a wavelength of approximate 520 nm and has the electric component gradually enhanced along the waveguide Fig.4.12.c shows the Poynting vector in z-direction as an evidence of power concentration at the tip of the plasmonic waveguide structure 62 Figure 4.12c Poynting vector in z-direction The guided plasmon mode at each thin metal film has a symmetric magnetic field profile as shown in Fig.4.12d This proves that the coupled mode at each gold layer is long ranging mode Thus, it has the longest propagation distance to approach the tip of the structure Figure 4.12d Magnetic field profile of the guided LRSPPs mode This is the longest range mode 63 Fig.4.12d also points out a fact that a vast majority of light energy was confined within the waveguide structure Figure 4.12e Magnetic field distribution at the x-z plane Figure 4.12f A 3D view of Hy 64 Figure 4.12g Electric field (upper) and phase (lower) distribution at the end of the structure Fig.4.12g takes a closer look at the field and phase distribution at the last 400 nm length of the structure The graphs clearly state that all the requirements were fully provided for a constructive interference After penetrating through the apex, the electric field is exponentially decayed with distance as illustrated in Fig.4.12b As a result, at a lateral cross section nm below the apex, the field enhancement reduces to 3.1×103 as shown in Fig.4.13, and the emergent beam has a full-width-at-half-maximum of 19 nm In comparison, Keisuke Kato and co-workers used an excitation wave with a much higher energy (λ0= 632.8 nm) However, the spot has a full-width-at-half-maximum of 35 nm and peak intensity (E2) that is 1.2 × 102 times larger than at the apex Thus, the proposed method in this thesis is much more energy efficient and effective 65 Figure 4.13 Distribution of electric field at 5nm far from the apex The electric field distribution at the apex in terms of Ex and Ez components is also investigated in details As shown in Fig.4.14, Ex component is extremely magnified at the apex creating a strong energy confinement By contrast, Ez has two peaks of amplitude at the two corner of the tip but nearly vanishes at the center This is due to the destructive interference of two side-LRSPPs Figure 4.14 Electric field profiles of Ez and Ex components at the apex 66 4.3 The Dependence of the Field Magnification Factor and the Beam Side on Parameters We also investigate the dependence of the field magnification factor and the illuminated beam side on four parameters, namely outer cladding thickness, exponential coefficient α, tip width and central film thickness Eventually, the final design is created based on all the optimized parameters Fig.4.15 shows how electric field and beam side vary when outer cladding thickness increases from 85 nm to 145 nm Noticeably, while the beam side remains unchanged at 19 nm, the field amplitude reaches highest value at the outer cladding thickness of 120 nm Thus, we choose 120 nm as the optimum width for the outer dielectric layer Figure 4.15 Dependence of magnification factor and beam side on the outer cladding thickness In fact, the design comprises two parts with respect to its length The first part has a length of 875 nm with no curvature The second one is the exponentially tapered part has a length of 675 nm Actually, only the first part has the outer layer 67 thickness of 120nm On the other hand, the second part takes 120 nm as the starting value for its thickness Another parameter related to the shape of the design is the exponential coefficient α The exponential profile of the design is determined by the formula below f = exp [αx/l]-1, in which l = 675 nm is distance between the start and end points of the curvature and α is the exponential coefficient At the tip, outer layer thickness is 50 nm The dependence of the magnification factor and the beam side on α is illustrated in Fig.4.16 At the range of α from to 13, the beam side seems to be constant at 19 nm However, at α =14 and α 15, the full-width at half- max of the beam roughly climb up to 20 nm and 22 nm, respectively By contrast, the magnification factor steadily increases as the exponential coefficient α increase Thus, α = 13 is chose as the optimal value Figure 4.16 Dependence of magnification factor and beam side on the exponential coefficient 68 The tip width also has a significant effect on the field enhancement and the beam side As can be seen from Fig.4.17, as the tip width varies from 10 nm to 20 nm, the beam side rapidly increases from 19 nm to 29 nm By contrast, the electric field enhancement reduces significantly from 2925 to nearly 2500 Thus, the tip of 10 nm width provides us with smallest beam side and largest magnification factor Figure 4.17 Dependence of magnification factor and beam side on the tip width Finally, we investigate the influence of the central thin film on the field enhancement and side of the penetrating beam as shown in Fig.4.18 While the beam side remains unchanged at 19 nm, the magnification factor slightly increases as the central film thickness increases We conclude that the beam side heavily depends on the exponential coefficient α, and the tip width, on the other hand, the magnification factor is contributed by all four parameters 69 Figure 4.18 Dependence of magnification factor and beam side on the central film thickness 70 Conclusion In conclusion, this thesis proposed a plasmonic waveguide structure in which the constructive interference of LRSPPs excited by end- fire coupling technique creates a strongly focused beam penetrating through the apex The beam has a full-widthat-half-maximum of 19 nm, approximately, for an incident wavelength of 1550 nm The end-fire coupling technique has asserted a high efficiency in exciting LRSPPs at the symmetric and asymmetric metal slab configurations Based on these prospective results, this structure can potentially be used as a pure nanometric light source for scanning microscopy, optical imaging and optical memory, etc However, the design is still a 2-D model due to the limitation of computer ability In order to make it more realistic, future scrutiny must be done with 3D models 71 References [1] Stefan A Maier, 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TOPIC: PLASMONICS NANOFOCUSING BASED ON LONGRANGE SURFACE PLASMON POLARITONS Student: NGUYỄN NGỌC AN Class No.8 – K51 Supervisor: Professor ĐÀO NGỌC CHIẾN, Ph.D Hanoi, May 2011 MINISTRY OF EDUCATION... Abbreviations Introduction Chapter Basics of Surface Plasmon Polaritons 11 1.1 Maxwell‟s Equations .11 1.2 Surface Plasmon Polaritons at Metal-Insulator