Plasmonic nanoguides and circuits

Plasmonic nanoguides and circuits Introduction: need for plasmonics? Strip SPPs Cylindrical SPPs Gap SPP waveguides Channel plasmon polaritons Dielectric-loaded SPP waveguides PLASMOCOM

1. Intro: need for plasmonics The Question: Why do we need surface plasmon polaritons for waveguiding components and circuits?

1. Intro: need for plasmonics As data rates AND component packing densities INCREASE, electrical interconnects become progressively limited by RC-delay: L A R L / B max A 10 16 C A 2 L L B max (bit/s), and A 1 A 2 RC L << L 2 (!) Electronics is aspect-ratio limited in speed!

1. Intro: need for plasmonics The bit rate in optical communications is fundamentally limited only by the carrier frequency: B max < f ~ 100 Tbit/s (!), but the light propagation is subjected to diffraction: core a cladding n core = n clad + δn = n + δn V = π λ 2 2 2 a ncore nclad 2π λ a 2nδn well guided mode : V π a λ / 2 2nδn mode size : δn << 1(!) Photonics is diffraction-limited in size!

1. Intro: need for plasmonics NB: Why do we need the transverse light confinement? The transverse light confinement sets the fundamental limit on the acceptable bend angle (for insertion loss) and thereby on the density of the components! W θ 3W L Area per component : S WL W W λ / n / θ θ W 3 cr cr n / λ W W = Γλ Density depends on the confinement as ~ Γ -3 (!)

1. Intro: need for plasmonics Diffraction limit RC-delay limit

1. Intro: need for plasmonics MURI projects in USA: www.stanford.edu/group/plasmonmuri www.plasmonmuri.caltech.edu

1. Intro: need for plasmonics Characteristics to compare: 1. Signal delay (bandwidth) 2. Energy dissipated per bit 3. Cross talk (density) 4. (e.g., coupling to optics)

2. Strip SPPs The idea is to laterally confine the SP propagation by using finite-width metal λ = 800 nm stripes: SP guiding with a 2.5-µm-wide and 40-nm-thick gold stripe on a glass substrate (wavelength = 800 nm) SP-based Bragg reflector for a stripe SP guide W. L. Barnes, A. Dereux & T. W. Ebbesen, Nature 424, 824 (2003)

2. Strip SPPs The main issue is that, typically, the SP mode is very close to the kd = k0 ε d light line: ω ε The effective (SP) waveguidein width SP : k m sp = = k0 ε sp c ε m + 1 k normalized parameter : 1 0W V = k0w ε sp = ε + 1 ω k0 = c E sp W Note that k d > k sp > k 0 (all modes are leaky into a substrate) Efficient guiding: V 1 W λ( ε +1 ) 0.5 /2π W λ (λ 700 nm) W = 1.5 µm, λ = 800 nm R. Zia, M. D. Selker, and M. L. Brongersma, Phys. Rev. B 71, 165431 (2005)

2. Strip SPPs Pros and contras: (+) - a conceptually attractive configuration using a very simple (!) metal circuitry on boards; (+) - based on straightforward planar fabrication compatible (in principle) with microelectronics (!); ( ) - fundamentally limited (above the wavelength!) in achievable confinement due to a very low refractiveindex contrast.

3. Cylindrical SPPs The SP mode confinement and propagation constant increase with the decrease in the rod diameter (+), but the SP propagation loss drastically (!) increases as well (-). ε m = -19, ε d = 4 2a E There is no cutoff! J. Takahara et al., Opt. Lett. 22, 475 (1997)

3. Cylindrical SPPs Polycrystalline silver does not work! 100-nm-diameter (crystal) silver wires show the SP propagation over 10 μm at the wavelength of 785 nm.

3. Cylindrical SPPs E The SP propagation constant increases faster than propagation loss with the decrease in the rod diameter resulting in SP slowing E down to a halt! 2R k rsp Rod SP : k rsp = ω n( R) = k0 n( R) c M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004)

3. Cylindrical SPPs

3. Cylindrical SPPs Pros and contras: (+) - the SP mode confinement increases with the decrease in the rod diameter without cutoff (!); ( ) - at the same time, the SP propagation loss drastically (!) increases; ( ) - perfectly symmetrical (!) environment is needed; ( ) - fabrication is very complicated (!); ( ) - surface quality is crucial (!).

4. Gap SPP waveguides The coupling of two SPs gap SP modes that very efficiently fill and exploit the available (lossless) dielectric space! SP : k sp ( w) = ω n c eff ( w) E k SP I. P. Kaminow et. al., Appl. Opt. 13, 396 (1974). Opt. Express 14, 9467 (2006).

4. Gap SPP waveguides The reflectance spectra reveal the GSP propagation over 3 μm in 14-nm-narrow gaps of ~ 100-nm width.

4. Gap SPP waveguides The main idea is to use the dependence of the SP propagation constant on gap width and to laterally vary the gap! E w 0 w 1 d SP w 1 gap > w 0 waveguides : n 1 eff < n 0 eff k sp V ( w) gap = ω n c = k 0 eff d ( w) = 0 neff ( w) 0 2 1 ( n ) ( n ) 2 Theoretical example of a 4-port branching nano- Parameters: λ = 573 nm, C x C y 500 circuit: nm, w 0 = d 18 nm, w 1 36 nm eff k eff silver K. Tanaka & M. Tanaka, Appl. Phys. Lett. 82, 1158 (2003); Opt. Express 13, 256 (2005).

4. Gap SPP waveguides Pros and contras: (+) - the gap SP mode confinement (in both lateral dimensions) increases with the decrease in the gap width without cutoff (!); (+) - the corresponding increase in the SP propagation loss lags (!) allowing for the optimization; ( ) - fabrication is very complicated (!); ( ) - surface quality is crucial (!).

5. Channel plasmon polaritons (CPPs) S(x 1 ) = -A exp(-x 12 /R 2 ) ω p R = c eep narrow channels: strong sub-wavelength confinement + low propagation loss (propagation loss similar to that of the plane SPP can be achieved for deep narrow channels)

5. Channel plasmon polaritons (CPPs) Modal shape of the CPP fundamental mode for increasing wavelength λ = (a) 0.6, (b) 1, (c) 1.4 µm (close to cutoff). These panels display the time averaged electric field. (d) Instantaneous transverse electric field at λ =1.4 µm for a structure with groove edges rounded with a 100 nm radius of curvature. All panels have a lateral size of 2 µm. Opt. Lett. 31, 3447 (2006). Note progressive (with the wavelength) hybridization of the fundamental CPP mode with wedge SP modes!

5. Channel plasmon polaritons (CPPs) a 500 nm d 5 µm d θ a 3 µm 3 µm b c b e 3 µm c f λ = 1510 nm: low output Normalized output 0.7 0.6 0.5 0.4 0.3 0.2 0.1 λ = 1525 nm: high output sample N1 sample N2 WR-resonator 0.0 1480 1500 1520 1540 1560 1580 Wavelength (nm) Nature 440, 508 (2006).

5. Channel plasmon polaritons (CPPs) Using the waveguide-ring resonator for add-drop multiplexing: through add (a) (b) (c) 5 μm t1 t2 (d) 5 μm input drop Nano Letters 7, 880 (2007).

5. Channel plasmon polaritons (CPPs) Using periodic wells in grooves for wavelength filtering: (a) 2 µm (b) 1440 nm Λ = 750 nm Normalized transmission 0.7 0.6 0.5 0.4 0.3 0.2 1420 1440 1460 1480 1500 1520 Wavelength (nm) (c) 1470 nm (d) 1500 nm The grating length is less than 4 μm! Nano Letters 7, 880 (2007).

5. Channel plasmon polaritons (CPPs) Pros and contras: (+) - the CPP mode confinement (in both lateral dimensions) increases with the decrease in groove angle without cutoff (!); (+) - the corresponding increase in the CPP propagation loss lags (!) allowing for the optimization; ( ) - fabrication (FIB) is extremely complicated (!); ( ) - surface quality is crucial (!).

6. Dielectric-loaded SPP waveguides k sp = ω c ε ε m m εd + ε d dielectric metal It is very important to use as thick as possible stripes in order to achieve a large refractive-index contrast!

6. Dielectric-loaded SPP waveguides It is very important to use as thick as possible (within single-mode guiding regime) stripes in order to achieve a large-refractive index contrast and, thereby, strong lateral confinement of the DLSPPW mode! w = t = 600 nm, λ = 1.55 μm N ef = 1.29; L = 44.4 μm Phys. Rev. B 75, 245405 (2007).

6. Dielectric-loaded SPP waveguides UV lithography: targeting t 600 nm, w 600 nm (for λ ~ 1.5 μm) Direct coupling to the polymer/gold interface Appl. Phys. Lett. 92, 011124 (2008).

6. Dielectric-loaded SPP waveguides Direct coupling to the polymer/gold interface (80-µm-long DLSPPWs): DLSPPW mode width ~ 800 nm DLSPP propagation length ~ 50 µm Phys. Rev. B, in press.

6. Dielectric-loaded SPP waveguides Opt. Express 16, 13585 (2008).

6. Dielectric-loaded SPP waveguides Opt. Express 16, 13585 (2008).

6. Dielectric-loaded SPP waveguides Pros and contras: ( /+) - the DLSPPW mode confinement is diffractionlimited ( ) but still subwavelength (+) due to the large refractive-index contrast (!); (+) - straightforward and cost-effective fabrication allowing the use of different techniques (!); (+) - DLSPPW efficiently exploit the immediate (!) dielectric environment (not being perturbed by it) opening the way to various functionalities.

6. Dielectric-loaded SPP waveguides PLASMOCOM partners: The Queen s University of Belfast, UK Coordinator: Prof. Anatoly Zayats Laser Zentrum Hannover ev, Germany Aalborg University, Denmark Université de Bourgogne, Dijon, France SILIOS Technologies, France ICFO, Barcelona, Spain

Instead of outlook: Among contributors: Junichi Takahara Stefan Maier Kazuo Tanaka Guo Ping Wang Harry Atwater Meir Orenstein Esteban Moreno Dmitri Gramotnev Valentyn Volkov Mark Stockman Mark Brongersma http://www.worldscibooks.com/nanosci/v017.html