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Grating Coupling of Surface Plasmon Polaritons at Visible and Microwave Frequencies

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Grating Coupling of Surface Plasmon Polaritons at Visible and Microwave Frequencies GRATING COUPLING OF SURFACE PLASMON POLARITONS AT VISIBLE AND MICROWAVE FREQUENCIES Submitted by ALASTAIR PAUL HIBBINS To the University of Exeter as a thesis for the degree of Doctor of Philosophy in Physics NOVEMBER 1999 This thesis is available for library use on the understanding that it is copyright material and that no quotation from this thesis may be published without proper acknowledgement. I certify that all material in this thesis which is not my own work has been identified and that no material is included for which a degree has previously been conferred upon me. __________________________________________ ABSTRACT ABSTRACT The work presented here concerns the electromagnetic response of diffraction gratings, and the rôle they play in the excitation of surface plasmon polaritons (SPPs) at the interface between a metal and a dielectric. The underlying aim of this thesis is to build on the current understanding of the excitation of SPPs in the visible regime, and extend and develop these ideas to microwave wavelengths. The position and shape of the resonance of the SPP is extremely sensitive to both the interface profile and the properties of the surrounding media and hence, by using a suitable grating modelling theory, this dependence can be utilised to parameterise the profile and optical properties of the media. Indeed, the first two experimental chapters of this thesis present the first characterisations of the dielectric function of titanium nitride, and non-oxidised indium using such a grating-coupled SPP technique. Experimental reflectivities measured at visible frequencies are normally recorded as a function of the angle measured from the normal to the average plane of the grating surface, however this data becomes cumbersome to record at microwave wavelengths. Hence, a new technique is developed which requires no moving detector and records the reflectivities as a function of the angle between the plane of incidence and the normal to the grating grooves. These reflectivities are initially recorded from a silver- coated grating at visible wavelengths, but are also recorded from non-lossy metallic gratings in the microwave regime. A large amount of beam spread is inherent in microwave experiments, and therefore the apparatus is further developed to collimate the incident beam. Finally, two samples are considered where a dielectric grating is deposited onto a planar metal substrate. The data recorded from the first sample demonstrates that it is possible to couple microwave radiation to SPPs that propagate along the planar metal-dielectric interface. Furthermore, it demonstrates that if the dielectric is lossy, the absorption on resonance of the modes is greatly enhanced. The second study illustrates the novel result that with near-grazing incident radiation and with the dielectric-grating grooves orientated such that they are parallel to the plane of incidence, coupling is possible to SPPs at three different energies. 2 "He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever." Chinese Proverb 3 TABLE OF CONTENTS TABLE OF CONTENTS ABSTRACT __________________________________________________________ 2 TABLE OF CONTENTS _______________________________________________ 4 LIST OF FIGURES AND TABLES _______________________________________ 8 ABBREVIATIONS ___________________________________________________ 22 ACKNOWLEDGEMENTS _____________________________________________ 23 CHAPTER 1: Introduction _________________________________________________________ 25 CHAPTER 2: A review of the properties of radiatively coupled surface plasmon polaritons. 2.1. Introduction_________________________________________________________ 28 2.2. Historical Overview __________________________________________________ 28 2.3. Surface Plasmon Polaritons at the Interface of Semi-infinite Media___________ 33 2.3.1. The Dispersion Relation ___________________________________________________ 33 2.3.2. Brewster and Fano Modes __________________________________________________ 37 2.3.3. Spatial Extent of the Surface-plasmon Fields ___________________________________ 41 2.4. Excitation of Surface Plasmons _________________________________________ 44 2.4.1. Prism Coupling __________________________________________________________ 45 2.4.2. Grating Coupling _________________________________________________________ 47 2.5. Polarisation Conversion _______________________________________________ 51 2.6. Photonic Energy Gaps in the Propagation of SPPs on Gratings ______________ 52 2.6.1. False Momentum Gaps ____________________________________________________ 55 2.6.2. Coupling to the high and low energy branches__________________________________ 55 2.7. Summary ___________________________________________________________ 58 CHAPTER 3: The influence of the interface profile and properties of the surrounding media on the reflectivity from a grating sample. 3.1. Introduction_________________________________________________________ 59 4 TABLE OF CONTENTS 3.2. Grating modelling theories_____________________________________________ 60 3.3. The Differential Formalism of Chandezon et al. ____________________________ 63 3.4. Representation of the surface profile ____________________________________ 64 3.5. The reflectivity features and the Littrow angle ____________________________ 68 3.6. The profile of the grating ______________________________________________ 72 3.6.1. Variation of a1 , the fundamental amplitude ___________________________________ 73 3.6.2. Variation of a2 , the first harmonic __________________________________________ 75 3.6.3. Variation of a3 , the second harmonic ________________________________________ 77 3.7. The permittivity of the grating substrate _________________________________ 79 3.8. The use of overlayers _________________________________________________ 84 3.9. Summary ___________________________________________________________ 87 CHAPTER 4: Surface plasmon polariton study of the optical dielectric function of titanium nitride. 4.1. Introduction_________________________________________________________ 88 4.2. TiN x properties and applications________________________________________ 89 4.3. Previous measurements of ε(ω) of TiN x._________________________________ 89 4.4. Experimental ________________________________________________________ 91 4.4.1. Sample preparation _______________________________________________________ 91 4.4.2. Reflectivity Measurements _________________________________________________ 93 4.4.3. Using the grating modelling theory___________________________________________ 96 4.5. Results _____________________________________________________________ 97 4.6. Discussion _________________________________________________________ 100 4.6.1. The free-electron behaviour of TiN, and its interband transitions __________________ 101 4.6.2. The Drude-Lorentz model _________________________________________________ 103 4.7. Summary __________________________________________________________ 106 CHAPTER 5: The plasmon study of the optical dielectric function of indium 5.1. Introduction________________________________________________________ 107 5.2. Background ________________________________________________________ 107 5 TABLE OF CONTENTS 5.3. Experimental _______________________________________________________ 109 5.4. Results ____________________________________________________________ 112 5.5. Discussion _________________________________________________________ 113 5.6. Summary __________________________________________________________ 118 CHAPTER 6: Azimuthal dependent reflectivity data from metallic gratings 6.1. Introduction________________________________________________________ 119 6.2. Experimental _______________________________________________________ 120 6.2.1. Experimental Geometry___________________________________________________ 120 6.2.2. Experimental Procedure___________________________________________________ 121 6.3. Results ____________________________________________________________ 125 6.4. Summary __________________________________________________________ 128 CHAPTER 7: An experimental study of grating-coupled surface plasmon polaritons at microwave frequencies. 7.1. Introduction________________________________________________________ 129 7.2. Background ________________________________________________________ 131 7.3. Experimental _______________________________________________________ 133 7.4. Results ____________________________________________________________ 139 7.4.1. Sample #1 (mono-grating)_________________________________________________ 139 7.4.2. Sample #2 (bi-grating)____________________________________________________ 141 7.5. Discussion _________________________________________________________ 143 7.5.1. Sample #1 (mono-grating)_________________________________________________ 143 7.5.2. Sample #2 (bi-grating)____________________________________________________ 148 7.6. Summary __________________________________________________________ 150 CHAPTER 8: The coupling of microwave radiation to surface plasmon polaritons and guided modes via dielectric gratings. 8.1. Introduction________________________________________________________ 151 8.2. Background ________________________________________________________ 151 6 TABLE OF CONTENTS 8.3. Experimental _______________________________________________________ 158 8.4. Results ____________________________________________________________ 160 8.5. Discussion _________________________________________________________
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