My PhD thesis - Condensed Matter Theory - Imperial College London

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CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO SLAB SYSTEMS The left-hand side is the modified Helmholtz equation in one dimension, which has the Green’s function Adapting this to equation (8.49) gives the full solution The electric field is then easy to calculate: where G(z, z ′ ) = 1 2k e−k|z−z′| . (8.50) φ z (z) = − ρ 0 2kɛ 0 ( e −k|z| ± e −k|z−s|) . (8.51) E = −∇φ (8.52) = − ρ 0 2ɛ 0 e i(ωt−kx) [f x (z)ˆx + f z (z)ẑ] (8.53) f x (z) = i ( e −k|z| ± e −k|z−s|) (8.54) f z (z) = sgn(z) e −k|z| ± sgn(z − s) e −k|z−s| (8.55) The components of the field are plotted in figure 8.4. For all surface plasmons, ω < ω p . 8.1.5 Bulk plasmons Solutions also exist for the bulk plasmons. When ω = ω p , the boundary condition on E z (equation (8.28c)) implies that at the interface E (v) z the field in the vacuum is E (v) z = E (v) x = ⎧ ⎪⎨ E 0 e −Kvz with K v given by equation (8.32). If E (v) z when z > s ⎪⎩ E 1 e Kvz when z < 0 ⎧ ⎪⎨ ik K v E 0 e −Kvz when z > s ⎪⎩ − ik K v E 1 e Kvz when z < 0 = 0. The general form of (8.56) (8.57) = 0 at z = s and z = 0 then both E 0 and E 1 are also zero, and consequently there is no field in the vacuum. Consideration of equation (8.23) shows that this is also true in the special case k = k p = ω p /c. 130
CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO SLAB SYSTEMS 0.6 E x E z 0.4 0.2 Eε 0 /ρ 0 0 -0.2 -0.4 -0.6 -40 -20 0 20 40 60 z (a) Antisymmetric 0.6 E x E z 0.4 0.2 Eε 0 /ρ 0 0 -0.2 -0.4 -0.6 -40 -20 0 20 40 60 z (b) Symmetric Figure 8.4: The x- and z-components of the longitudinal electric field associated with the surface plasmon oscillations. 131
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Improving the accuracy of surface s
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Acknowledgements I am greatly indeb
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CONTENTS 3.3.4 Importance-sampled d
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CONTENTS 10 Conclusions 181 A The q
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LIST OF FIGURES 5.3 The LDA energy
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LIST OF FIGURES 8.4 The x- and z-co
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LIST OF FIGURES 8.20 Electron densi
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List of Tables 8.1 The function F k
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Chapter 1 Introduction In recent de
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CHAPTER 1. INTRODUCTION A successfu
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CHAPTER 2. MECHANICS THE SIMPLIFICA
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CHAPTER 3. QUANTUM MONTE CARLO METH
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Chapter 4 Errors in QMC simulations
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CHAPTER 4. ERRORS IN QMC SIMULATION
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CHAPTER 5. THE JELLIUM SLAB The jel
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CHAPTER 5. THE JELLIUM SLAB 0.08 0.
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CHAPTER 5. THE JELLIUM SLAB The DMC
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CHAPTER 5. THE JELLIUM SLAB -9.125
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Chapter 10 Conclusions The original
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CHAPTER 10. CONCLUSIONS pling and o
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APPENDIX A. THE QUASI-2D EWALD SUM
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APPENDIX B. THE CUSP CONDITIONS may
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APPENDIX B. THE CUSP CONDITIONS wit
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APPENDIX C. INTEGRATING THE CUSP FU
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APPENDIX C. INTEGRATING THE CUSP FU
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APPENDIX D. RECONSTRUCTING A PROBAB
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Bibliography [1] P. H. Acioli and D
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BIBLIOGRAPHY [19] A. G. Eguiluz and
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BIBLIOGRAPHY [39] P. R. C. Kent, R.
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BIBLIOGRAPHY [59] H. J. Monkhorst a
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BIBLIOGRAPHY [80] C. J. Umrigar, K.
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My PhD thesis - Condensed Matter Theory - Imperial College London

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