Surface Plasmons Part 1

Surface plasmons: outline Time-line of major discoveries Surface plasmons - surface mode of electromagnetic waves on a metal surface Spectroscopy of SPs in nanostructures: Nanoparticles Gratings, nanostructures 4. Applications: sensors, nanophotonics, surface enhanced Raman spectroscopy (SERS) Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012 Time line SPs allow to localize and guide EM waves!!! Excitation of SPs with a prism: Raether, Kretschmann 1941 1907 Rayleigh’s explanation (angle-diffraction orders) 1993- Fano: role of surface waves, surface plasmons 1968 1991 1902 Wood anomalies: reflection on gratings (two types) Nanoplasmonics, extraordinary transmission, etc. First biosensor on SPs 1974 Surface Enhaced Raman Spectroscopy Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Maxwell’s equations (SI units) in a material, differential form density of charges density of current Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012 Wave equation Double vector product rule is used a x b x c = (ac) b - (ab) c Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012 Plane waves Thus, we seek the solutions of the form: From Maxwell’s equations one can see that is parallel to is parallel to Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012 Simple system of a metal bordering a dielectric with incident plane wave Incident light Dielectric, refractive index is dielectric permittivity Reflected light Transmitted light Metal (gold) Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012 Waves at the interface z y In medium 1, z<0, x Assume that incident light is p-polarized, which means that the E-vector is parallel to the incidence plane Then the vector of the magnetic field is perpendicular to the incidence plane and has the form In medium 2, z>0, x Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012 Boundary conditions z y x Stokes's theorem Stokes's theorem Gauss’s theorem Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Relations in an E-M wave the curl operator Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Derivation of the dispersion equation Assume no external currents or free charges, magnetic permeability. One boundary condition is From the other condition => Therefore we have a system of 2 homogeneous equations and a nontrivial solution is possible only if the determinant of this system is equal to 0. Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Surface plasmon dispersion equation We square both sides We introduce , wavenumber of the surface plasmon, then we obtain Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Dispersion equation and properties of surface plasmons We would like to have a solution which is localized to the surface, i.e. it decays with distance from on both sides from the interface. This is possible, if Indeed, then we have waves localized near the interface Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Dispersion equation analysis This is only possible, if If we look again at the dispersion equation Real and positive must k be w,k must be real (propagating wave!), then with negative, we see that the condition for surface waves to exist is Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Relation of Plasmonics to SOME other fields Metamaterials Plasmonics Nanotechnology Optics Biotechnology SERS High harmonics generator coherent control imaging Electronics Opto-electronics molecular interactions nano-sensors proteomics nanostructures nanophotonics nanoantennas

The Growth of the Field of Surface Plasmons illustrated by the number of scientific articles published annually containing the phrase “surface plasmon” in either the title or abstract PIETER G. KIK and MARK L. BRONGERSMA SURFACE PLASMON NANOPHOTONICS, (2007)

Surface plasmons (or surface plasmon polaritons), Part 2: outline Why SP named so? Excitation of SPs: with a prism or a grating Spectroscopy of SPs in nanostructures: Nanoparticles Gratings, nanostructures 4. Applications: sensors, nanophotonics, surface enhanced Raman spectroscopy (SERS) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Dielectric constant of a metal, Drude model For free electrons! Don’t take the imaginary part use only real part epsilon r should be negative for surface plasmon to exist Consequently, plasmon frequency Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Remarks to Drude’s formula Bound electrons should be taken into account, then 1-> , which takes into account the contribution of bound electrons. Also the mass of electron should be replaced with the effective mass of electron in the metal, . Plasmons correspond to , these are eigen (free) oscillations of the electronic plasma. Influence of attenuation For g << wp: Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 Electrons oscillating in the SP field metal dielectric Interface There is a longitudinal component in the electric field of SP, because E-M field is coupled to oscillations of the electronic density (plasmonic oscillations). This is why tp exite SPs one needs a p-polarization of the incident light. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Graphing dispersion equation of SPs Light line: , w For excitation of SPs we need to slow down light! ( Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Surface plasmon excitation: Coupling of light to SPs with a prism Optical arrangement used to excite the surface-plasmon wave based on the Kretschmann-Raether configuration where a thin metal film is sandwiched between the prism and the sample. E. Kretschmann, Z. Phys. 241, 313-324 (1971). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 4

SPR curves for different wavelengths Gold film (d=47nm) contacting water l =1230 nm 1.0 0.8 l =633 nm REFLECTION COEFFICIENT 0.6 0.4 0.2 l =490 nm 0.0 50 60 70 80 90 INCIDENCE ANGLE (deg) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 16

Conditions for the resonance excitation of SPs a photon is converted into a surface plasmon. General laws must be observed: Energy conservation, (2) Momentum conservation, is changing is not changing Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Resonance excitation with a prism wp SP k ksp Conditions for the Surface Plasmon Resonance (SPR): phase matching!!! P=h k Energy conservation Momentum conservation Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Questions? Bulk waves, hearing aided then back to sound

Surface Plasmon Part 3

Graphing dispersion equation of SPs Light line: , w Omegam= maximium sp frequency For excitation of SPs we need to slow down light! ( Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 The influence of the thickness of the gold film on the properties of SPs Gold Glass Air -1 res ) cos ( q e D » k L sp L =propagation lenght SP resonance curves at 633 nm for different film thicknesses. The dependence of the attenuation length on the film thickness for 633 nm and 805 nm. The dielectric constants published by Palik are used. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Approximation of small losses so far infinite film ,but delta k=Correction due to finite thickness A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Derivation of attenuation length in slide31

Examples: changes in the flow cell, bio-molecular binding reactions Example: binding of monoclonal antibody to horseradish peroxidase protein 0.50 550 A C=0% B 500 0.45 C=0.82% B SPR angle (pixels) 450 0.40 400 NHS/EDC HRP 0.64 deg 350 0.35 B B 300 0.30 250 70.50 70.75 71.00 71.25 71.50 10 20 30 40 50 60 Time (min) INCIDENCE ANGLE (deg) A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, Applied Optics 36, 6539-6547 (1997). Applied this sensing technique to myofibers and tubulin molecule.

Sensitivity and detection limit (relationships between different quantities) angular resolution -4deg=2 RU changes of the refractive index n-6 average thickness of the protein layer d=0.03 Å surface concentration d=3 pg/mm2 with mprotein=24 Da surface concentration of molecules ns=1010 cm-2 A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, Applied Optics 36, 6539-6547 (1997). 24

Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 Attenuation lengths of SPs for gold and silver films in contact with air, calculated for a broad spectral range 1. American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, 1972), p. 105. 2. U. Schröder, Surf. Sci. 102, 118-130 (1981). 3. Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic1985). A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Summary of surface plasmons 2 w e e 2 1 2 Propagatin g wave with k = x 2 e + e c 1 2 Z 2 w p Approximat ion of free electrons : e = e - , 1 b 2 E w - e < => p < w plasmon frequency; 1 Condition of existence: Light frequency should be below plasmon frequency SPs: Spatially localized to the surface E-M wave Oscillations of the electronic density. Have E -longitudinal component Are excited with p-polarized light and the local field can significantly exceed the field in the exciting beam. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 Dependence of the near field intensity enhancement factor on the back side of the gold film vs. the angle for two wavelengths 633 nm and 805 nm A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

SP resonance: coupling with a grating (conservation of momentum) θ ki ki θ grating kSP kSP ki sin(θ) ki sin(θ) kg kg Coupling=excitation of kSP = ki sin(θ) + kg kSP = ki sin(θ) - kg +1 order coupling -1 order coupling Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Conditions for the resonance excitation of SPs Light line Light line, suited for resonance excitation , w SP dispersion curve required additional momentum The crossing of the SP curve and the light line means resonance excitation for desired frequency SPs are slower than light, and therefore for the same frequency their momentum is larger. To enable the resonance excitation additional momentum must be provided. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 Schematic of experiment on spectroscopy of SP modes in nanostructures :transmission measurements in the far field This setup maps intensity distribution over angle and wavelength and thus reveals SP modes that affect transmission. λ θ Charge Coupled Device (CCD) Laser beam Grating Sample (nanostructure) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 Study of the Interaction of 7 fs Rainbow Laser Pulses with Gold Nanostructure Grating: Coupling to Surface Plasmons AFM image of the nanostructure: Transmission dependence 5° Angle of Incidence Intensity 0° -5° 650 Wavelength (nm) 800 The valley area (x-structure) the laser light is efficiently converted into SPs, about 80% . A. Kolomenskii et al., Optics Express, 19, 6587-6598 (2011). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Avoided crossing We consider two counter-propagating SP waves with complex amplitudes a and b; the total fields can be presented as linear combinations of these two individual waves. The amplitudes a(z) and b(z) satisfy: Propagation constantBeta=real part k losses where and are the coupling coefficients.

Experimental and calculational results: interaction of SP modes and spectral gap Kg k -Kg Kg SPs travels in two opposite directions. The intersection of the straight line with the dispersion curve gives the point of excitation. Two counter propagating waves interact with each other when they are scattered on 2Kg. K=wavenumber of grating.k=projection of light on plane of propagation

Avoided crossing The coupled-mode equations can be expressed in matrix form: By substituting: We obtain: , I – unit matrix, The two eigenvalues for are: a,b= Where: q can be purely imaginary if Spectral gap!

Questions? Bulk waves, hearing aided then back to sound

Surface Plasmons Part 4

Optical detection of acoustic waves with surface plasmons

Abstract For fast and sensitive detection of acoustic waves the surface plasmon resonance (SPR) can be used, which responds to variations of dielectric properties in close proximity to a metal film supporting surface plasmon waves. When an acoustic wave is incident onto a receiving plate positioned within the penetration depth of the surface plasmons, it creates displacements of the surface of the plate and thus modulates the dielectric properties, affecting SPR and the reflection of the incident light. Here we study characteristics and determine the optimal configuration of such an acousto-optical transducer with surface plasmons for efficient conversion of an acoustic signal into an optical one. We simulate the properties of the transducer and present estimates showing that it can have a large frequency bandwidth and good sensitivity. Abstract

Fig. 1. Schematic of the acousto-optical sensor with surface plasmons Fig. 1. Schematic of the acousto-optical sensor with surface plasmons. The arrangement consists of a glass prism (PR), the adjacent gold film (GF), a spacer (SPA) and a receiving plate (RP). The field of the excited surface plasmon (SP) decays away from the gold film. The acoustic wave (AW) induces displacements of the RP face close to the GF, which results in a quantifiable modification of the SPR curve featuring the resonance by a dip in the dependence of the intensity on the incidence angle . The inset on the right shows a schematic of layers with notations for the dielectric constants and thicknesses of the layers. Here is a schematic of the sensor Different types of configurations including Otto configuration which can measure displacement in acoustic waves, but we decided to use a special Kretschmann configuration because it hadn’t been done before -thus, our configuration is standard Kretschmann configuration but with a receiving plate under gold film -reflection has a dip related to surface plasmons

Changes of the SPR curve due to RP displacement Fig. 2. Illustration of the sensor response to a displacement  =100nm of the RP surface. The solid blue line is the SPR curve at the initial RP position, and the blue dashed line is the SPR curve resulting from the displacement. The black dashed line is the SPR curve without RP; it shows a more pronounced resonance. The displacement  produces a modification of the SPR curve. To quantify the changes two measures are used: a change Rmin of the Rmin value and an angular shift of the SPR minimum, min. Calculation is performed for d2=30nm, n4=√𝜀_4 =1.5, d3=0.4m.

Detection limit for the RP displacement Detection of ΔRmin change   Detection of ΔR change at the steep slope Shot noise only,only small displacments, η=quantum efficiency, Δf=1Ghz or sound 10kHz zta =displacement of receiving plate.p= power on photo detector. d3= size of gap between receiving plate and gold film.

Merit factor S1 for 800nm Fig. 3 The merit factor |S1| for λ=800nm: (a). The dependence of the (n4,d3)- optimized merit factor |S1| on the gold film thickness calculated for λ=800nm. (b). Density plot in false colors showing the merit factor |S1| for the optimal gold film thickness d2=16nm at different values of the gap d3 and the refractive index n4; the overall maximum of |S1|=2.64x10-3nm-1 is obtained at n4=1.45 and the gap value of d3=0.48μm and is shown by a large white dot. Note that the sign of S1 is negative (the value of Rmin decreases for the positive displacement Δζ) above d3=0.395μm, at which value S1 is close to zero. (c). The dependence of the d3- optimized merit factor |S1| for different values of the refractive index n4. Calculations for -gold film= SPR curve is well pronounced,16nm maximum signal ,jump due -800nm=Ti:sapphire and diode lasers 3 parameters varied: -thickness of gold film=d2 -width of air gap=d3 -refractive index of the receiving plate=n4 can choose different materials of the receiving plate -false colors -jumps to other side of curve = goes through zero; for the graph we take the absolute value

Merit factor S2 for 633nm Fig. 6. The merit factor |S2| for λ=633nm: (a). The dependence of the (n4,d3)- optimized merit factor |S2| on the gold film thickness. (b). Density plot in false colors showing the merit factor |S2| for the optimal gold film thickness d2=29nm at different values of the gap d3 and the refractive index n4; the overall maximum of |S2|=1.19x10-3nm-1 is obtained at n4=1.41 and the gap value of d3=0.61μm and is shown by a large white dot. (c). The dependence of the d3-optimized merit factor |S2| for different values of the refractive index n4. 3 parameters varied: -thickness of gold film=d2 -width of air gap=d3 -refractive index of the receiving plate=n4 can choose different materials of the receiving plate

Merit factors of about 10-3nm-1 can be obtained Table 1. Parameters for realization of the transducer at optical wavelength of 800nm and 633nm with maximum |S1| and |S2| values corresponding to plots of Figs. 3-6. Best values of merit factors Conclusion: Merit factors of about 10-3nm-1 can be obtained

Fig. 7. Variation of the reflection coefficient ΔR in response to acoustic wave with displacements Δζ of different magnitudes is presented for optimal parameters of Figs. (3-6) shown in Table 1: (a) and (b) for ΔR response and the wavelengths of 800nm (Fig. 3) and 633nm (Fig. 4) respectively; (c) and (d) for ΔR2 response and the wavelengths of 800nm (Fig. 5) and 633nm (Fig. 6) respectively. The solid blue lines show the responses ΔR, ΔR2 and the dotted red lines depict the linear fits; the vertical dashed lines show the limits within which the response deviates from the linear dependence by less than 10%. Large merit factor is selection criterium=optimum resonse

Quasi-linear response dependences ΔRmin ΔR2 =800nm =633nm Fig. 8. Realizations of the linearity ranges of the sensor response to the displacement Δζ for parameters presented in Table 2: (a) and (b) for ΔR and the optical wavelengths =800nm, and =633nm respectively; (c) and (d) for ΔR2 and the optical wavelengths =800nm, and =633nm respectively. The solid blue lines show the response ΔR for (a,b) and ΔR2 for (c,d), the dotted red lines depict the fitted linear dependences; the vertical dashed lines show the limits within which the response deviates from linear dependences by less than 10%. Linear responds within 10 %, shockwaves with large displacements, large ranges is selection criteria

Estimates   Bulky material membrane

Questions? Bulk waves, hearing aided then back to sound

Surface Plasmons Part 5 Surface plasmon effects on nano particles

Mie theory and dipole approximation t=T/2 Electronic cluster Ionic cluster Electric field Light Electronic plasma oscillations For small nanoparticles (R<<wavelength, or roughly 2R< wavelenght/10): dipole approximation where V is the particle volume,  frequency light, εm and are the dielectric functions of the surrounding medium and the particle material. When is small or varies slowly, the resonance takes place at => Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Extinction spectra of Ag n-particles in solution The oscillations of a n-particle, induced by a pump pulse, modulate (displace) the plasmon absorption band. For efficient detection the probe wavelength was selected at the steeper portion of the slope of this band. S. N. Jerebtsov et al. Phys. Rev. B Vol. 76, 184301 (2007). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Bowtie nano-antenna and measured intensity enhancement Intensity enhancement vs wavelength Fabricated by Electron Beam Lithography (EBL) bowtie antennas. Indium tin oxide substrate. Gap was varied, thickness 20 nm. 3D finite difference time domain (FDTD) simulations Kino et al. In: Surface Plasmon nanophotonics, p.125 (2007). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Experimental setup for study of “hot spots” for SERS Raman signals from individual Ag n-particles Futamata et al. Vibrational Spectroscopy 35, 121-129 (2004). Raman microscope with sensitive CCD cameras for imaging the sample in scattering and using Raman signal. Notch filters were used to suppress the excitation light. Low concentration of n-particles needed to separate individual particles.

Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 Raman spectroscopy Photon scattering on molecules Elastic or Rayleigh scattering Inelastic or Raman scattering h h h(-) h(+) Stocks Anti-Stocks Raman scattering increases when h produces electronic transition Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Surface Enhanced Raman Spectroscopy (SERS) of DNA bases Futamata et al. Vibrational Spectroscopy 35, 121-129 (2004). Spectra of individual n-particles Characteristic stretching modes in heterocycles suited for DNA sequencing : adenine 718 and 893 cm-1;guanine 641cm-1; cytosine 791 cm-1; thymine 616, 743 and 807 cm-1. Time evolution (whole scale 1 s) demonstrates Raman peaks and blinking effect, known for single molecule detection. Stongest enhancement ~1010 from pairs of particles with axis parallel to polarization