黃鼎偉 Ding-wei Huang. Ch 1 Metal/Dielectric Interface. Ch 2 Metal Film. Ch 7.1 Bragg Mirror & Diffractive Elements. Ch 7.2 SPP PBG

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1 Ch 1 Metal/Dielectric Interface Ch 2 Metal Film 黃鼎偉 Ding-wei Huang Ch 7.1 Bragg Mirror & Diffractive Elements Ch 7.2 SPP PBG Metal Nanowires and Conical Tapers for High-Confinement Guiding and Focusing 7.5 Localized Modes in Gaps and Grooves 7.6 Metal Nanoparticle Waveguides 7.7 Surface Plasmon Polariton Propagation Along Metal Stripes Ch 7.3 Metal Stripe w/t >> 1, t < λ 0 Ch 7.5 Gaps and Grooves Ch 7.6 Nano Particles Ch 7.4 Nanowire & Taper w < λ 0 Ch 7.7 Host with Gain 2 4

2 Transverse Confinement Below the Diffraction Limit In a dielectric waveguide, ε core > 0 and k x, k y are REAL β, k x, k y ε core ω/c = 2πn core /λ 0. A three-dimensional optical waves is limited by the effective wavelength in the core medium (Diffraction Limit). d x d y n 0 core 5 7 Transverse Confinement Below the Diffraction Limit Transverse Confinement Below the Diffraction Limit Metal waveguides of a cross section <<λ 2 can exhibit transverse mode confinement below the diffraction limit in the surrounding dielectric. For propagation along the z-direction, the relationship between propagation constant β (=k z ), the transverse components of the wave vector k x, k y and the frequency ω of the guided radiation in a general waveguide is k k x y 2 c core 2 6 In a metallic core medium, ε core <0 (ignoring attenuation for simplicity) One or both of the transverse wave vector components k x, k y must be IMAGINARY k k x y 2 c core 2 The Diffraction Limit can be overcome The mode size can be substantially below the diffraction limit of the surrounding dielectric cladding. 8

3 SPPs excited by prism coupling usually have Leaky Mode propagation characteristics. Observed by conventional microscopy [Dickson and Lyon, 2000] Observed by near-field fiber probe [Krenn et al., 2002] 9 [Krenn et al.,2002] 11 w =200nm t= 50 nm λ 0 = 800 nm [Krenn et al.,2002] 10 [Krenn et al.,2002] 12

4 A leaky mode along a metal nanowire may exist by prism coupling excitation. A truly bound SPP mode outside the light cone of the substrate can be excited by using a high NA objective coupling scheme. Ditlbacher and co workers have used this technique to excite a bound SPP propagating along a μm long silver wire with w = 120 nm [Ditlbacher et al., 2005]. Using far-and near-field optical microscopy, a comparatively large SPP propagation length L μm has been confirmed. [Ditlbacher et al., 2005] 13 [Ditlbacher et al., 2005] 15 [Ditlbacher et al., 2005] 14 [Ditlbacher et al., 2005] 16

5 Such a hugely increased propagation length can possibly be The mode excited using focused illumination is a bound mode, thus not suffering losses due to leakage radiation into the supporting substrate. The nanowires under study were prepared using a chemical synthesis method instead of electron beam lithography resulting in a highly crystalline structure further decreasing losses [Ditlbacher et al., 2005] 17 [Ditlbacher et al., 2005] 19 The shortening of the wavelength as the SPPs propagate along the taper to regions of ever-decreasing diameter enables nanofocusing, with accompanying giant field enhancement at the apex [Ditlbacher et al., 2005] 18 [Babadjanyan et al.,2000] 20

6 The travel time of SPPs to an infinitely sharp tip should be logarithmically divergent [Stockman,2004] A careful analysis of non-local effects on the SPP dispersion: radius r, propagation constant, IE 2 r decreases An additional and easily amenable structure offering sub wavelength confinement are Metal Insulator Metal waveguides where the mode is confined to the dielectric core in the form of a coupled gap SPP between the two interfaces. h: propagation constant [Ruppin, 2005] 22 [Zia et al.,2005c] 24

7 [Tanaka and Tanaka,2003] 25 [Veronis and Fan, 2005] 27 [Tanaka and Tanaka,2003] 26 [Pile et al.,2005] 28

8 [Pile et al.,2005] 29 [Novikov and Maradudin,2002] 31 A bound SPP mode exists at the bottom of the groove offering sub wavelength mode confinement Due to the phase mismatch between the SPP modes propagating at the bottom of the groove and the inclined plane boundaries the mode stays confined at the bottom without spreading laterally upwards [Novikov and Maradudin,2002] 30 [Novikov and Maradudin,2002] 32

9 [Pile and Gramotnev,2004] 33 [Pile and Gramotnev,2004] 35 [Pile and Gramotnev,2004] 34 [Bozhevolnyi et al., 2005b] 36

10 λ= 1.44 um 1.5 um 1.57 um [Bozhevolnyi et al., 2005b] 37 [Bozhevolnyi et al., 2005b] 39 [Bozhevolnyi et al., 2005b] 38 [Bozhevolnyi et al.,2006] 40

11 Closely Spaced Metallic Nanoparticles as SPP Waveguides Closely spaced metallic nanoparticles A one dimensional particle array can exhibit coupled modes due to near field interactions between adjacent nanoparticles Can be used for guiding electromagnetic waves with a transverse confinement below the diffraction limit For a center to center spacing d << λ, where λ is the wavelength of illumination in the surrounding dielectric, neighboring particles couple via dipolar interactions, with the nearfield term scaling as d -3 dominating [Bozhevolnyi et al.,2006] Nanoparticle Chain Mie Scattering Theory 42 [Quinten et al.,1998] 44

12 Nanoparticle Chain Point Dipoles A representation of the particles as point dipoles allowed the computation of the quasi static dispersion relation Nanoparticle Chain Considering Higher Order Multipoles Multipolar corrections [Brongersma et al.,2000] 45 [Park and Stroud,2004] 47 Nanoparticle Chain Considering Higher Order Multipoles The group velocity for energy transport, given by the slope of the dispersion curves, is highest for excitation at the single particle plasmon frequency, occurring at the center of the first Brillouin zone. Corrections to this solution by considering higher order multipoles - albeit still in the quasi-static approximation - have also been obtained. Nanoparticle Chain Full Maxwell s Eqs. [Brongersma et al.,2000] 46 [Weber and Ford,2004] 48

13 Nanoparticle Chain Full Maxwell s Eqs. Nanoparticle Chain Full Maxwell s Eqs. [Weber and Ford,2004] 49 [Weber and Ford,2004] 51 Nanoparticle Chain Full Maxwell s Eqs. [Weber and Ford,2004] 50 [Maier et al., 2003a] 52

14 [Maier et al., 2003a] 53 [Maier et al., 2003b] 55 [Maier et al., 2003a] 54 [Maier et al., 2003b] 56

15 Nanoparticle Chain SNOM Experiment [Maier et al., 2003b] 57 [Girard and Quidant, 2004] 59 Nanoparticle Chain SNOM Experiment [Maier et al., 2003b] 58 [Girard and Quidant, 2004] 60

16 Nanoparticle Chain with SPP Condenser Nanoparticle Chain with SPP Condenser [Nomura et al., 2005] 61 [Nomura et al., 2005] 63 Nanoparticle Chain with SPP Condenser Nanoparticle Chain with SPP Condenser [Nomura et al., 2005] 62 [Nomura et al., 2005] 64

17 Grading of Nanoparticles for the Confinement in SPP Waveguides [Li et al.,2003] 65 [Maier et al.,2005] 67 Grading of Nanoparticles for the Confinement in SPP Waveguides Grading of Nanoparticles for the Confinement in SPP Waveguides [Maier et al.,2004] 66 [Maier et al.,2005] 68

18 Grading of Nanoparticles for the Confinement in SPP Waveguides [Maier et al.,2005] Grading of Nanoparticles for the Confinement in SPP Waveguides Particle Chains Embedded in a Gain Medium An analytical study of particle chains embedded in a gain medium suggests that the accompanying increase in interparticle coupling strength can lead to greatly enhanced propagation distances particularly for confined transverse modes close to the light line Citrin a [Maier et al.,2005] 70 72

19 Particle Chains Embedded in a Gain Medium Particle Chains Embedded in a Gain Medium The effective index of the SPP at an interface between a metal and a dielectric via the dispersion relation as n eff d d In the resonant limit of surface plasmons,defined by Re[ε] = ε d, the effective index and thus the amount of localization is limited by the non-vanishing imaginary part of ε due to attenuation [Citrin,2005a] Particle Chains Embedded in a Gain Medium The localization of the fields to the interface will be increased Avrutsky [Avrutsky,2004] 74 [Nezhad et al.,2004] 76

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