# SURFACE PLASMONS AND THEIR APPLICATIONS IN ELECTRO-OPTICAL DEVICES

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1 SURFACE PLASMONS AND THEIR APPLICATIONS IN ELECTRO-OPTICAL DEVICES Igor Zozouleno Solid State Electronics Department of Science and Technology Linöping University Sweden Brief outline: motivation basic theory of the surface plasmons application of surface plasmons

2 MOTIVATION Surface plasmons have a combined electromagnetic wave and surface charge character They reside at the interface between a metal and a dielectric material. The miniaturization of conventional photonic circuits is limited by the diffraction limit, such that the minimum feature size is of the order of wavelength. optical fiber Using the surface plasmons one can overcome the diffraction limit, which can lead to miniaturization of photonics circuits with length scales much smaller than those currently achieved light propagation in a plasmonic waveguide

3 BASIC THEORY OF THE SURFACE PLASMONS Maxwell s equations:

4 Games Cler Maxwell (83-879): Interplay of electric and magnetic field could result in electromagnetic waves (860) Maxwell s accomplishments are the most profound and the most fruitful that physics has experienced since the time of Newton (A. Einstein): Electricity magnetism OPTICS Before Maxwell: After Maxwell: Electricity magnetism OPTICS

5 Maxwell s equations what the equation describes Charges produce electric field No magnetic charges Changing magnetic flux produces electric field Electric current and changing electric flux produce magnetic field

6 Maxwell s equations Charge neutrality, ρ = 0 No direct current, j = 0 Nonmagnetic materials, μ r = (μ = μ 0 )

7 Boundary conditions In inhomogeneous media consisting of several dielectrics, the field lines of E, H will experience discontinuity or bending at the boundary E E The boundary conditions for E, H can be derived from Maxwell equations normal components: E E tangential components: E t E t

8 Electromagnetic waves Maxwell s E E = wave t μ00 x equations: B B (in vacuum) = t μ x 0 0 E = electric field B = magnetic field 0 = permittivity (vacuum) μ = permeability (vacuum) 0 y E r speed of light c = μ 0 0 = m s z B r E B x, t) ( 0 x, t) = E sin ω ( 0 = B sin ω ( t x) ( t x) x

9 The electromagnetic spectrum

10 r r r r v μ μ μ μ μ = = = = c = n refraction index n c v = Electromagnetic waves in matter x B t B x E t E = = μ μ vacuum: ) relative permeability; ( permeability : dielectric constant) ( permittivity : 0 0 = = = = r r r r r μ μ μ x B t B x E t E = = μ μ matter:

11 The dependence of the wave speed v and index of refraction n on the wavelength λ is called dispersion What is the wavelength of light in a medium with the refractive index n? v λ mat = λvac = c λ n vac λvac λ mat λvac

12 POLARIZATION Plane Polarized Electromagnetic Waves Illustrating vertical and horizontal polarized waves.

13 p-polarization: E-field is parallel to the plane of incidence s-polarization: E-field is perpendicular to the plane of incidence (German senrecht = perpedicular) E z E H z H z=0 H y E x θ z=0 E y H x θ y x y x θ θ z z Any linearly polarized radiation can be represented as a superposition of p- and s-polarization.

14 p-polarized incident radiation will create polarization charges at the interface. We will show that these charges give rise to a surface plasmon modes Boundary condition: (a) transverse component of E is conserved, (b) normal component of D is conserved E z y z=0 x H y E E x E z H y E E x creation of the polarization charges z if one of the materials is metal, the electrons will respond to this polarization. This will give rise to surface plasmon modes

15 Polarization charges are created at the interface between two material. The electrons in metal will respond to this polarization giving rise to surface plasmon modes

16 s-polarized incident radiation does not create polarization charges at the interface. It thus can not excite surface plasmon modes Boundary condition (note that E-field has a transverse component only): transverse component of E is conserved, y z z=0 H z x E y H H x H z E y H H x compare with p-polarization: no polarization charges are created no surface plasmon modes are excited! In what follows we shall consider the case of p-polarization only

17 More detailed theory Let us chec whether p-polarized incident radiation can excite a surface mode dielectric z=0 E z H y E E x ~ e i z z ; z intensity = ± iκ z y z x ~ e i( x x ωt ) wave propagating in x-direction we are looing for a localized surface mode, decaying into both materials z metall components of E-, H-fields: E = (E x, 0, E z ); H = (0, H y, 0) Thus, the solution can be written as

18 solution for a surface plasmon mode: dielectric E z y z=0 x H y E E x z metall Let us see whether this solution satisfies Maxwell equation and the boundary conditions: + condition imposed on -vector

19 λvac λ mat = ; n = n λvac λ mat λvac wave vector in vacuum dielectric n ~ i( x ωt ) e π π n = = = n λ λ

20 z x dielectric n ~ e i z z ; z = ± iκ z intensity ( n ) z = ± = x metall ( n ) ( n ) x + z n x < 0 x > z we are looing for a localized surface mode, decaying into both materials z has to be imaginary ω light cone ω = c The plasmonic dispersion curve lies beyond the light cone, therefore the direct coupling of propagating light to plasmonic states is difficult!

21 z x dielectric r n ~ e izz ; z = ± iκ intensity z sign of z : z z = = + ( n ) ( n ) x x metall r z = ± ( n ) z x z and z are of opposite signs! recall the condition imposed on -vector: because z and z are of opposite signs, this condition will be satisfied only if r and r are of opposite signs. This is the case when one material is dielectric r >0, and the second material is metal, r < 0. also, recall the condition x > ( n ) = r this condition is always satisfied for metals, where r < 0

22 dielectric ~ e i z z ; z = ± iκ z ~ i( x x ωt ) e intensity localized surface mode, decaying into both materials metall z Thus, we have established that on the surface between a metal and dielectric one can excite a localized surface mode. This localized mode is called a surface plasmon

23 What is the wavelength of the surface plasmon? π λ = let us find : ( ) ( ) x z x z n n = + = substitute r r r r x + = ω x r r r r x c ω + = light cone ω = c The surface plasmone mode always lies beyond the light line, that is it has greater momentum than a free photon of the same frequency ω

24 x = r r + r r Ideal case: r and r are real (no imaginary components = no losses) Dielectric: r >0 Metal: r < 0, r >> r x is real resonant width = 0 lifetime = x = r r + r r

25 Realistic case: r is real, and r is complex, x = = K = r r + ' x r + i '' x ' '' r r i r + r = imaginary part describes losses in metal = r r ' '' ( r + i r ) ' '' ( + i ) + r r resonant width (gives rise to losses) '' x = 3/ r '' r ' ( ) r Dielectric functions of Ag, Al ' r '' r '' r ' ( ) r

26 decay into metal surface plasmon length scales: metall decay into dielectric dielectric z propagation length

27 How to excite a surface plasmon? is it possible to excite a plasmon mode by shining light on a dielectric/metal interface? dielectric metall ω x x ω = c light cone ω = c r r r + r The surface plasmone mode always lie beyond the light line, that is it has greater momentum than a free photon of the same frequency ω. This maes a direct excitation of a surface plasmon mode impossible!

28 Total internal reflection n sinθ = n sinθ Snell s law of refraction: n sinθ sinθ n < n = > n θ θ Total internal reflection θ glass n n n air n θ n θ n θ = 90o critical angle of the total internal reflection: θ = 90 sinθ 0 0 n sin 90 c = = n n n

29 Otto geometry x-component x = n sinθ z x n θ dielectric n x-component x = n sinθ (x-component is conserved) dielectric n metall to excite a plasmon mode in the region : x > n n > θ > sinθ n sin n n condition for the total internal reflection!

30 Utilization of a grating to excite a plasmon mode Grating The grooves in the grating surface brea the translation invariance and allow x of the outgoing wave to be different from that of the incoming wave x (outgoing) = x (incoming) ± NG, where G = π/d plasmon n sinθ reciprocal lattice vectors

31 APPLICATION OF SURFACE PLASMONS Extraordinary transmission through sub-wavelength hole arrays, T. W. Ebbesen et al., Nature 39, 667 (998). Directional beaming, H. J. Lezec et al., Science 97, 80 (00) Plasmonic nanowire waveguides, J. B. Kren et al., Europhys. Lett. 60, 663 (00) Nanofocusing in plasmonic waveguides, M. Stocman, Phys. Rev. Lett. 93, (004). Nanoparticle plasmon waveguide, S. A. Maier et al., Nature Materials, 9 (003). Surface plasmon enhanced solar cells

32 a 0 d light thin metallic plate classical (ray optics) expectation: transmission = area of the plate area occupied by holes

33 wave optics: diffraction effect L d if λ/ > d, the transmission through the hole will be strongly suppressed λ =L Transmission Hans Bethe 944 d ~ λ 4 λ experiment 0d The experimental findings imply that that the array itself is an active element, not just a passive geometrical object in the path of incident light d d

34 absolute transmission intensity = transmitted light fraction of area occupied by the holes = 00% ~0d This observation implies that the light impinging on the metal between holes can be transmitted. In other words, the whole structure acts lie an antenna Explanation: all the observed features are related to excitation of the surface plasmons. [No enhanced transmission is observed for semiconductor hole arrays.] The resonant peas occur when surface plasmon momentum matches the momentum of the incident photon and the grating as follows

35 Standard diffraction theory: diffraction on a slit: position of the central maximum: λ sinθ = b b b θ m= λ sin θ = θ = o 90 diffraction puts a lower limit on the size of the feature that can be used in photonics.

36 Resolving power is given by the diffraction limit. diffraction pattern of two point sources To increase resolution people usually use smaller wavelength Transmission electron microscope λ el = nm resolution: nm θ ~ first minimum λ a λ θ c ~ a first minimum coincides with the maximum

37 Overcoming the diffraction limit with the help of surface plasmons metallic (Ag) film 50 nm surface plasmon 660nm directionality is ± 3 o 500 nm light

38 The coupling of light into SP modes is governed by geometrical momentum, selection rules (i.e., occurs only at a specific angle for a given wavelength), the light exiting a single aperture will follow the reverse process in the presence of the periodic structure on the exit surface. x (outgoing) = x (incoming) ± NG, where G = π/d plasmon n sinθ reciprocal lattice vectors Yu et al., Phys. Rev. B 7, (R) (005)

39 The miniaturization of dielectric waveguides is limited by diffraction to dimentions of the order of the wavelength in the waveguide core.

40 Metal nanowires sustaining surface plasmons can be used as optical waveguides. Thereby, the use of a metal allows to overcome the limitations of miniaturization imposed on conventional dielectric waveguides due to diffraction.

41 STM microphotography of the device 8 μm Optical near-field intensity It has been shown that the diffraction limit restricting the further miniaturization of dielectric waveguides can be broen by using gold nanowires to guide light fields via surface plasmons excitation. A propagation length of.5 µm was found for gold nanowires.

42 The central problem of the nano-optics is the delivery and concentration (nanofocusing)of the optical radiation energy on the nanoscale, This represents a difficult tas, because the wavelength of light is on the microscale, many orders of magnitude too large.

43 It was shown show that it is possible to focus and concentrate in three dimensions the optical radiation energy on the nanoscale without major losses. This can be done by exciting the surface plasmons propagating toward a tip of a tapered metal-nanowire surfaceplasmonic waveguide.

44 Both the phase and group velocity of surface plasmons asymptotically tend to zero toward the nanotip. Consequently, the surface plasmons are slowed down and adiabatically stopped at z = 0. This phenomenon leads to a giant concentration of energy on the nanoscale. The local field increase by 3 orders of magnitude in intensity and four orders in energy density.

45 metallic particles support plasmonic resonances: condition for plasmonic resonance: metall '( ω) = m host dielectric material

46 Watching energy transfer: Excitation and detection of energy transport in metal nanoparticle chains by near-field optical microscopy. The nanoparticle waveguide is locally excited by light emanating from the tip of an near-field scanning optical microscope (NSOM). The electromagnetic energy is transported along the waveguide towards a fluorescent dye nanosphere sitting on top of the nanoparticles. The NSOM tip is scanned along the nanoparticle chain, and the fluorescence intensity for varying tip positions along the particle chain is collected in the far-field by a photodiode.

47 a chain of Ag nanoparticles 00µm 00µm grid of plasmon waveguides 50 nm topography fluorecsence fluorescent dye particles

48 fluorescence from nanospheres sitting on top of metal nanoparticles was significantly broader than that from isolated nanospheres. grid of plasmon waveguides Energy transport would results in dye emission even when the microscope tip is located away from the dye, and thus manifest itself in an increased spatial width of the fluorescence spot of a dye nanosphere attached to a plasmon waveguide compared with a single free dye nanosphere.

49 PLASMONS IN ORGANIC SOLAR CELLS PLASMONS IN ORGANIC SOLAR CELLS Glass Transparent electrode (ITO) Organic layer(s) Metal ', '' APFO3 40 Al ', '' λ, nm ' '' ' '' to provide total internal reflection λ, nm 900 Glass Transparent electrode (ITO) Organic layer(s) Metal

50 Estimation of the position of a plasmonic resonance 5 APFO3, m - 3.0x0 7.5 APF03-Al dispersion relation ', '' λ, nm ' '' 900 ' pl Δ ' y = y.5 + Δ = α π d ' y.0 y.5 y, m - = 0 ' pl x0 7 normal incidence where d is a period of grating (sinusoidal, tiranglar or step-lie) π = α d d=πα/ y, μm d=0.3 μm 600 λ, nm

51 R We applied the recursive Green s function technique (A.Rahachou, I.Zozouleno, Phys. Rev. B, 7, 557 (005)) to calculate spectra and intensity of the magnetic (H z ) field d h H z APFO3-Al d=0.3 mm, h=0.0, infinite dielectric λ, nm Resonance pea position agrees very well with the analytical estimation: 45 versus 450 nm

52 Effect of surface roughness d h d h d=0.3 μm, h=0nm no roughness roughness=0 nm roughness=0 nm R λ, nm

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