Ch7 Plasmon Waveguide-I

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黃鼎偉

Ding-wei Huang

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Introduction7.1 Planar Elements for Surface Plasmon

Polariton Propagation7.2 Surface Plasmon Polariton Band Gap

Structures 7.3 Surface Plasmon Polariton

Propagation Along Metal Stripes

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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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Ch 7.3 Metal Stripe w/t >> 1, t < λ0

w < λ0

Ch 7.4 Nanowire & Taper

Ch 7.5 Gaps and Grooves

Ch 7.6 Nano Particles Ch 7.7 Host with Gain

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• Trade off between confinement and loss in SPP Waveguides

• Example:– SPP on thin metal within a homogenous media

in IR range• Lateral confinement: very weak (widely extended)• Propagation length: several cm (low loss)

– SPP on nanowire or nano-particle waveguide• Lateral confinement: below diffraction limit• Propagation length: smaller than μm (large loss)

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• Routing of SPPs on planar interfaces can be achieved by locally modifying theirdispersion via surface modulations

• The lateral confinement in metal stripe and wire waveguides including focusing of SPPs in conical structures will be discussed.

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• The inverse structure to metal stripes, metal/insulator/metal heterostructures, especially in V-groove geometries, also show high promise for waveguiding with– Good confinement– Acceptable propagation length.

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• Localized plasmon excitations in metal nanoparticles can also be used as waveguiding modalities– Energy is transferred via near-field coupling

between adjacent particles in linear chains.

• Emerging efforts to combat attenuation via optical gain media as waveguide hostswill be discussed.

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(Control the Propagation Direction of SPPs)

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Control the Propagation Direction of SPPs

• The propagation direction of SPPs at the interface of a metal film and a dielectric superstrate (air or dielectric) can be controlled via scattering of the propagating, two-dimensional waves at locally created defects in the otherwise planar film. – Scatterers can be introduced in the form of

surface undulations• Nanoscale particle-like structures• Milling of holes into the film.

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Control the Propagation Direction of SPPs

• Their controlled positioning enables the generation of functional elements such as– Bragg mirrors for reflecting SPPs [Ditlbacher

et al., 2002b], – Focusing elements for increasing lateral

confinement [Yin et al., 2005, Liu et al., 2005].

• This way, a planar two-dimensional photonic infrastructure for the guiding of SPPs can be created.

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Control SPP propagation via Scattering

• A simple and compelling example of control over SPP propagation via scattering from height modulations was demonstrated Ditlbacher et al b

Ditlbacher, H., Krenn, J. R., Schider, G., Leitner, A., and Aussenegg, F. R. (2002b). Twodimensional optics with surface plasmon polaritons. Appl. Phys. Lett., 81(10):1762–1764.

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Control SPP propagation via Scattering

Figure 7.1.Routing of SPPs on a planar silver film using surface modulations. A laser beam focused on a nanowire or nanoparticle defect for phase-matching acts as a local source for SPPs. The micrograph shows a Bragg reflector consisting of lines of regularly spaced, particle-like undulations (Fig. 7.2). [Ditlbacher et al., 2002b].

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d

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Figure 7.2.(a) SEM image of a SPP Bragg reflector consisting of ordered particle arrays on a metal film substrate. (b) SPP propagation imaged via monitoring of the emission of a fluorescent superstrate. [Ditlbacher et al., 2002b].

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Splitter & Interferometer for SPPs

[Ditlbacher et al., 2002b].

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Dielectric Optical Elements for SPPs

Calculation for the SPP dispersion relations for a glass/gold/superstrate three-layer system for both the s mode (open symbols) and the a mode [Hohenau et al., 2005b]

x

zd

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Figure 7.3.Calculated SPP dispersion relations for a glass/gold/superstratethree-layer system for both the s mode (open symbols) and the a mode (filled symbols). Increasing the dielectric constant ε3 of the superstrate from ε3 = 1 (circles) to ε3 = 2.25 (triangles) leads to an increase in propagation constant and thus a decrease in phase velocity of the SPP. For ε1= ε3,these two modes would evolve into the symmetric (s) or asymmetric (a) mode. [Hohenau et al., 2005b]

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[Hohenau et al., 2005b]

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Dielectric Optical Elements for SPPsFigure 7.4. Focusing (top row) or reflection and refraction (bottom row) of SPPs via a cylindrical or triangular 40 nm thick dielectric structure deposited on top of a gold film. Images of the leakage radiation (a, b, d, e) and of the optical near field (c, f) clearly show the modification of SPP propagation for SPPsimpinging on the dielectric structures (b, c, e, f). Reprinted with permission from [Hohenau et al., 2005b]. Copyright 2005, Optical Society of America.

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[Hohenau et al., 2005b]

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Figure 7.5.Experimental setup of the excitation and near-field imaging for SPP focusing on a holey metal film (left). (a) SEM and (b) near-field optical image of the nanohole focusing array which couples the launched SPPs into a 250 nm wide silver stripe guide. [Yin et al., 2005]

23[Yin et al., 2005]

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Figure 7.6.Generation and focusing of SPPs via illumination of circular or elliptic slits milled into a metallic film. The SPP intensity is monitored via near-field microscopy (a,c) or the exposure of a photoresist superstrate (b, d). [Liu et al., 2005]

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• The concept of constructively reflecting SPPs on a metal film via Bragg reflectors created using periodically arranged metallic nanoparticles presented in Figs and

can be extended to the creation of band gaps for SPP propagation using regular metal nanoparticle latticesdeposited on a metal film

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• First Experiment demonstration by Bozhevolnyi in 2001

[Bozhevolnyi et al.,2001]

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Figure 7.7. Topography (a) and near-field optical images (b,c) of a 35×35 μm2 SPP band gapstructure consisting of a 900 nm triangular lattice of 378 nm wide and 100 nm high gold dots ona 40 nm thick gold film. SPPs excited via prism coupling of radiation of wavelength 1550 nm (b) or 1600 nm (c) propagate from the right into the lattice structure in the ΓK direction, and are strongly attenuated if their frequency is inside the band gap (c). [Marquart et al., 2005].

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Figure 7.8. Topographical (a) and near-field optical (b) image of a channel defect waveguide in a triangular lattice of period 950 nm consisting of 438 nm wide and 80 nm high gold scatters on an gold film. A SPP excited at λ0 = 1515 nm incident from the right propagates through the channel. [Marquart et al., 2005].

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Ch 2 Thin Metal Film of Infinite Width (IMI)Hy EzEx

x

z

y

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Ch 2 Thin Metal Film of Infinite Width (IMI)Odd Mode (LRSPP) Even Mode (SRSPP)

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LRSPP and SRSPP Modes

[Sarid,1981]

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Metallic Stripes Embedded in aHomogeneous Dielectric

• Symmetric Mode (as the Odd Mode in Ch2)• Asymmetric Mode (as the Even Mode in Ch2)

– Due to the different definitions between Ch7 & Ch2

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Modes in Metallic Stripes Embedded in aHomogeneous Dielectric

ssb0 sab

0[Berini，2000]

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Modes in Metallic Stripes Embedded in aHomogeneous Dielectric

asb0 aab

0[Berini，2000]

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Propagation Constant (Real Part) [Berini，2000]

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Propagation Constant (Imag. Part)[Berini，2000]

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z b0

[Berini，2000]

For small thickness t Gaussian-like lateral distribution

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• For ssb0 mode in a Metallic Stripe Embedded in a

Homogeneous Dielectric– is similar to the LRSPP mode in Ch 2.

– extends over many wavelengths into the dielectric host medium as its confinement decreases with thickness.

• Confinement is defined by the fraction of the power flowing through the stripe itself to the total power in the mode

– its loss decrease with thickness as well.• MIM configuration has better confinement

than IMI configuration. [Zia et al., 2005c]

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General Principle• Tight field localization to the metal interfaces

Significant amount of the total mode energy resides inside the metalPropagation loss increases due to Ohmic heating.

• Guiding of electromagnetic energy with sub-wavelength mode confinement– Micro-meter even sub-micron propagation

lengths.• The LRSPP modes of metal stripes can show 1/e attenuation lengths approaching 1 cm in the near-infrared, due to the low confinement for a film thickness on the order of 20 nm.

42[Zia et al.,2005c]



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Experimental Demonstration of SPP in Metal Stripes

• The first experimental demonstration of the long ranging mode [Charbonneau et al., 2000].

t =20 nm thick and w = 8 μm wide gold stripe embedded in glass

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Experimental Demonstration of SPP in Metal Stripes

Metal film embedded in a polymer host with a propagation loss of only 6 ×8 dB/cm

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SPP Propagates Along Sub wavelength Nanowires

[Leosson et al.,2006]

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SPP Propagates Along Sub wavelength Nanowires

[Leosson et al.,2006]

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Metal Stripe SPP Waveguides

[Charbonneau et al.,2005]

Micron-sized widths of stripe waveguides have already enabled the demonstration of useful optical elements such as bends and couplers

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Bragg Reflectors on SPP Waveguides

[Jette-Charbonneau et al.,2005]

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Metallic Stripes Embedded inAsymmetric Dielectric

• For metal stripes embedded in an asymmetricenvironment– Usually the SPP excited by Prism– LRSPP mode is absent in this case, due to the

phase mismatch between the SPPs at the two different metal/insulator interfaces [Berini, 2001].

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Metallic Stripes Embedded inAsymmetric Dielectric

• The modes excited on the metal/air interface in stripes using prism coupling are inherently leaky modes

• The stripe width has a a lower bound,below which no propagating leaky modes exists

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Surface Plasmon Propagation in Micro-Scale Metal Stripes

[Lamprecht et al.,2001]

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[Zia et al.,2005b]

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[Zia et al.,2005b]

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[Zia et al.,2005b]

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Optical near-field distributions of SPP waveguide modes

[Weeber et al.,2003]

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Integrated Plasmon and Dielectric Waveguides

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• Well-established dielectric waveguide theory can be applied to SPP waveguides if the effective index neff is calculated via the SPP dispersion as neff = β/k0.

• The transverse dimensions of SPP stripe waveguides have to obey a diffraction limit Δx ≥ λ0/2neff, limiting the amount of transverse confinement and thus the integration density of such waveguides.

6363

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