surface plasmon polariton

{{Multiple image|direction=vertical|align=right|image1=Prism_Coupler.png|image2=Grating_Coupler.png|width=300|caption1=Figure 1: (a) Kretschmann and (b) Otto configuration of an Attenuated Total Reflection setup for coupling surface plasmons. In both cases, the surface plasmon propagates along the metal/dielectric interface {{anchor|fig2anchor}}|caption2=Figure 2: Grating Coupler for Surface Plasmons. The wave vector is increased by the spatial frequency }}

SPPs can be excited by both electrons and photons. Excitation by electrons is created by firing electrons into the bulk of a metal.{{Cite journal| last = Bashevoy | first =M.V.|author2=Jonsson, F. | author3=Krasavin, A.V. |author4=Zheludev, N.I. |author5=Chen Y. |author6=Stockman M.I. | title =Generation of traveling surface plasmon waves by free-electron impact | journal =Nano Letters| volume =6| year =2006| issue =6| pages =1113–5| doi =10.1021/nl060941v | pmid =16771563| arxiv =physics/0604227| bibcode =2006NanoL...6.1113B| s2cid =9358094}} As the electrons scatter, energy is transferred into the bulk plasma. The component of the scattering vector parallel to the surface results in the formation of a surface plasmon polariton.

For a photon to excite an SPP, both must have the same frequency and momentum. However, for a given frequency, a free-space photon has less momentum than an SPP because the two have different dispersion relations (see below). This momentum mismatch is the reason that a free-space photon from air cannot couple directly to an SPP. For the same reason, an SPP on a smooth metal surface cannot emit energy as a free-space photon into the dielectric (if the dielectric is uniform). This incompatibility is analogous to the lack of transmission that occurs during total internal reflection.

Nevertheless, coupling of photons into SPPs can be achieved using a coupling medium such as a prism or grating to match the photon and SPP wave vectors (and thus match their momenta). A prism can be positioned against a thin metal film in the Kretschmann configuration or very close to a metal surface in the Otto configuration (Figure 1). A grating coupler matches the wave vectors by increasing the parallel wave vector component by an amount related to the grating period (Figure 2). This method, while less frequently utilized, is critical to the theoretical understanding of the effect of surface roughness. Moreover, simple isolated surface defects such as a groove, a slit or a corrugation on an otherwise planar surface provide a mechanism by which free-space radiation and SPs can exchange energy and hence couple.

The properties of an SPP can be derived from Maxwell's equations. We use a coordinate system where the metal–dielectric interface is the $z=0$ plane, with the metal at and dielectric at $z>0$. The electric and magnetic fields as a function of position $(x,y,z)$ and time t are as follows:

:$E\_\{x,n\}(x,y,z,t)\; =\; E\_0\; e^\{i\; k\_x\; x\; +\; i\; k\_\{z,n\}\; |z|\; -\; i\; \backslash omega\; t\}$

:$E\_\{z,n\}(x,y,z,t)\; =\; \backslash pm\; E\_0\; \backslash frac\{k\_x\}\{k\_\{z,n\}\}\; e^\{i\; k\_x\; x\; +\; i\; k\_\{z,n\}\; |z|\; -\; i\; \backslash omega\; t\}$

:$H\_\{y,n\}(x,y,z,t)\; =\; H\_0\; e^\{i\; k\_x\; x\; +\; i\; k\_\{z,n\}\; |z|\; -\; i\; \backslash omega\; t\}$

where

• n indicates the material (1 for the metal at or 2 for the dielectric at $z>0$);
• ω is the angular frequency of the waves;
• the $\backslash pm$ is + for the metal, − for the dielectric.
• $E\_x,E\_z$ are the x- and z-components of the electric field vector, $H\_y$ is the y-component of the magnetic field vector, and the other components ($E\_y,H\_x,H\_z$) are zero. In other words, SPPs are always TM (transverse magnetic) waves.
• k is the wave vector; it is a complex vector, and in the case of a lossless SPP, it turns out that the x components are real and the z components are imaginary—the wave oscillates along the x direction and exponentially decays along the z direction. $k\_x$ is always the same for both materials, but $k\_\{z,1\}$ is generally different from $k\_\{z,2\}$
• $\backslash frac\{H\_0\}\{E\_0\}\; =\; -\backslash frac\{\backslash varepsilon\_1\; \backslash omega\}\{k\_\{z,1\}c\}$, where $\backslash varepsilon\_1$ is the permittivity of material 1 (the metal), and c is the speed of light in vacuum. As discussed below, this can also be written$\backslash frac\{H\_0\}\{E\_0\}\; =\; \backslash frac\{\backslash varepsilon\_2\; \backslash omega\}\{k\_\{z,2\}c\}$.

A wave of this form satisfies Maxwell's equations only on condition that the following equations also hold:

:$\backslash frac\{k\_\{z1\}\}\{\backslash varepsilon\_1\}\; +\; \backslash frac\{k\_\{z2\}\}\{\backslash varepsilon\_2\}\; =\; 0$

and

:$k\_\{x\}^2+k\_\{zn\}^2=\backslash varepsilon\_n\; \backslash left(\backslash frac\{\backslash omega\}\{c\}\backslash right)^2\; \backslash qquad\; n=1,2$

Solving these two equations, the dispersion relation for a wave propagating on the surface is

:$k\_\{x\}=\backslash frac\{\backslash omega\}\{c\}\; \backslash left(\backslash frac\{\backslash varepsilon\_1\backslash varepsilon\_2\}\{\; \backslash varepsilon\_1+\backslash varepsilon\_2\}\backslash right)^\{1/2\}.$

File:Dispersion Relationship.png

In the free electron model of an electron gas, which neglects attenuation, the metallic dielectric function is

:$\backslash varepsilon(\backslash omega)=1-\backslash frac\{\backslash omega\_\{\backslash rm\; P\}^2\}\{\backslash omega^2\},$

where the bulk plasma frequency in SI units is

:$\backslash omega\_\{\backslash rm\; P\}=\backslash sqrt\{\backslash frac\{n\; e^2\}\{\{\backslash varepsilon\_0\}m^*\}\}$

where n is the electron density, e is the charge of the electron, m^∗ is the effective mass of the electron and $\{\backslash varepsilon\_0\}$ is the permittivity of free-space. The dispersion relation is plotted in Figure 3. At low k, the SPP behaves like a photon, but as k increases, the dispersion relation bends over and reaches an asymptotic limit called the "surface plasma frequency".{{efn|name="dispersion"}} Since the dispersion curve lies to the right of the light line, ω = k⋅c, the SPP has a shorter wavelength than free-space radiation such that the out-of-plane component of the SPP wavevector is purely imaginary and exhibits evanescent decay. The surface plasma frequency is the asymptote of this curve, and is given by

:$\backslash omega\_\{\backslash rm\; SP\}=\backslash omega\_\{\backslash rm\; P\}/\backslash sqrt\{1+\backslash varepsilon\_2\}.$

In the case of air, this result simplifies to

:$\backslash omega\_\{\backslash rm\; SP\}=\backslash omega\_\{\backslash rm\; P\}/\backslash sqrt\{2\}.$

If we assume that ε₂ is real and ε₂ > 0, then it must be true that ε₁ < 0, a condition which is satisfied in metals. Electromagnetic waves passing through a metal experience damping due to Ohmic losses and electron-core interactions. These effects show up in as an imaginary component of the dielectric function. The dielectric function of a metal is expressed ε₁ = ε₁′ + i⋅ε₁″ where ε₁′ and ε₁″ are the real and imaginary parts of the dielectric function, respectively. Generally {{abs|ε₁′}} >> ε₁″ so the wavenumber can be expressed in terms of its real and imaginary components as

:$k\_\{x\}=k\_\{x\}\text{'}+i\; k\_\{x\}$=\left[\frac{\omega}{c} \left( \frac{\varepsilon_1' \varepsilon_2}{\varepsilon_1' + \varepsilon_2}\right)^{1/2}\right] + i \left[\frac{\omega}{c} \left( \frac{\varepsilon_1' \varepsilon_2}{\varepsilon_1' + \varepsilon_2}\right)^{3/2} \frac{\varepsilon_1}{2(\varepsilon_1')^2}\right].

The wave vector gives us insight into physically meaningful properties of the electromagnetic wave such as its spatial extent and coupling requirements for wave vector matching.

As an SPP propagates along the surface, it loses energy to the metal due to absorption. The intensity of the surface plasmon decays with the square of the electric field, so at a distance x, the intensity has decreased by a factor of $\backslash exp\backslash \{-2k\_\{x\}$ x\}. The propagation length is defined as the distance for the SPP intensity to decay by a factor of 1/e''. This condition is satisfied at a length

:$L=\backslash frac\{1\}\{2\; k\_\{x\}\text{'}\text{'}\}.$

Likewise, the electric field falls off evanescently perpendicular to the metal surface. At low frequencies, the SPP penetration depth into the metal is commonly approximated using the skin depth formula. In the dielectric, the field will fall off far more slowly. The decay lengths in the metal and dielectric medium can be expressed as

:$z\_\{i\}=\backslash frac\{\backslash lambda\}\{2\; \backslash pi\}\; \backslash left(\backslash frac\{|\backslash varepsilon\_1\text{'}|+\backslash varepsilon\_2\}\{\backslash varepsilon\_i^2\}\; \backslash right)^\{1/2\}$

where i indicates the medium of propagation. SPPs are very sensitive to slight perturbations within the skin depth and because of this, SPPs are often used to probe inhomogeneities of a surface.

File:SPP silver-air interface 370nm.gif|The electric field (E-field) of an SPP at the silver-air interface, at the frequency where the free-space wavelength is 370 nm. The animation shows how the E-field varies over an optical cycle. The permittivity of silver at this frequency is {{nowrap|(−2.6 + 0.6i)}}. The picture is {{nowrap|(0.3 × 370 nm)}} across horizontally; the SPP wavelength is much smaller than the free-space wavelength.

File:SPP silver-air interface 10um.gif|The E-field of an SPP at the silver-air interface, at a much lower frequency corresponding to a free-space wavelength of 10μm. At this frequency, the silver behaves approximately as a perfect electric conductor, and the SPP is called a Sommerfeld–Zenneck wave, with almost the same wavelength as the free-space wavelength. The permittivity of silver at this frequency is {{nowrap|(−2700 + 1400i)}}. The picture is 6 μm across horizontally.

Nanofabricated systems that exploit SPPs demonstrate potential for designing and controlling the propagation of light in matter. In particular, SPPs can be used to channel light efficiently into nanometer scale volumes, leading to direct modification of resonate frequency dispersion properties (substantially shrinking the wavelength of light and the speed of light pulses for example), as well as field enhancements suitable for enabling strong interactions with nonlinear materials. The resulting enhanced sensitivity of light to external parameters (for example, an applied electric field or the dielectric constant of an adsorbed molecular layer) shows great promise for applications in sensing and switching.

Current research is focused on the design, fabrication, and experimental characterization of novel components for measurement and communications based on nanoscale plasmonic effects. These devices include ultra-compact plasmonic interferometers for applications such as biosensing, optical positioning and optical switching, as well as the individual building blocks (plasmon source, waveguide and detector) needed to integrate a high-bandwidth, infrared-frequency plasmonic communications link on a silicon chip.

In addition to building functional devices based on SPPs, it appears feasible to exploit the dispersion characteristics of SPPs traveling in confined metallo-dielectric spaces to create photonic materials with artificially tailored bulk optical characteristics, otherwise known as metamaterials. Artificial SPP modes can be realized in microwave and terahertz frequencies by metamaterials; these are known as spoof surface plasmons.

The excitation of SPPs is frequently used in an experimental technique known as surface plasmon resonance (SPR). In SPR, the maximum excitation of surface plasmons are detected by monitoring the reflected power from a prism coupler as a function of incident angle, wavelength or phase.

Surface plasmon-based circuits, including both SPPs and localized plasmon resonances, have been proposed as a means of overcoming the size limitations of photonic circuits for use in high performance data processing nano devices.

The ability to dynamically control the plasmonic properties of materials in these nano-devices is key to their development. A new approach that uses plasmon-plasmon interactions has been demonstrated recently. Here the bulk plasmon resonance is induced or suppressed to manipulate the propagation of light. This approach has been shown to have a high potential for nanoscale light manipulation and the development of a fully CMOS- compatible electro-optical plasmonic modulator.

CMOS compatible electro-optic plasmonic modulators will be key components in chip-scale photonic circuits.

In surface second harmonic generation, the second harmonic signal is proportional to the square of the electric field. The electric field is stronger at the interface because of the surface plasmon resulting in a non-linear optical effect. This larger signal is often exploited to produce a stronger second harmonic signal.

The wavelength and intensity of the plasmon-related absorption and emission peaks are affected by molecular adsorption that can be used in molecular sensors. For example, a fully operational prototype device detecting casein in milk has been fabricated. The device is based on monitoring changes in plasmon-related absorption of light by a gold layer.

Surface plasmon polaritons can only exist at the interface between a positive-permittivity material and a negative-permittivity material. The positive-permittivity material, often called the dielectric material, can be any transparent material such as air or (for visible light) glass. The negative-permittivity material, often called the plasmonic material, may be a metal or other material. It is more critical, as it tends to have a large effect on the wavelength, absorption length, and other properties of the SPP. Some plasmonic materials are discussed next.

For visible and near-infrared light, the only plasmonic materials are metals, due to their abundance of free electrons, which leads to a high plasma frequency. (Materials have negative real permittivity only below their plasma frequency.)

Unfortunately, metals suffer from ohmic losses that can degrade the performance of plasmonic devices. The need for lower loss has fueled research aimed at developing new materials for plasmonics and optimizing the deposition conditions of existing materials. Both the loss and polarizability of a material affect its optical performance. The quality factor $Q\_\{SPP\}$ for a SPP is defined as $\backslash frac\{\backslash varepsilon\text{'}^\{2\}\}\{\backslash varepsilon\text{'}\text{'}\}$. The table below shows the quality factors and SPP propagation lengths for four common plasmonic metals; Al, Ag, Au and Cu deposited by thermal evaporation under optimized conditions. The quality factors and SPP propagation lengths were calculated using the optical data from the [http://refractiveindex.info/?shelf=main&book=Al&page=McPeak Al], [http://refractiveindex.info/?shelf=main&book=Ag&page=McPeak Ag], [http://refractiveindex.info/?shelf=main&book=Au&page=McPeak Au] and [http://refractiveindex.info/?shelf=main&book=Cu&page=McPeak Cu] films.

Silver exhibits the lowest losses of current materials in both the visible, near-infrared (NIR) and telecom wavelengths. Gold and copper perform equally well in the visible and NIR with copper having a slight advantage at telecom wavelengths. Gold has the advantage over both silver and copper of being chemically stable in natural environments making it well suited for plasmonic biosensors. However, an interband transition at ~470 nm greatly increases the losses in gold at wavelengths below 600 nm. Aluminum is the best plasmonic material in the ultraviolet regime (< 330 nm) and is also CMOS compatible along with copper.

The fewer electrons a material has, the lower (i.e. longer-wavelength) its plasma frequency becomes. Therefore, at infrared and longer wavelengths, various other plasmonic materials also exist besides metals. These include transparent conducting oxides, which have typical plasma frequency in the NIR-SWIR infrared range. At longer wavelengths, semiconductors may also be plasmonic.

Some materials have negative permittivity at certain infrared wavelengths related to phonons rather than plasmons (so-called reststrahlen bands). The resulting waves have the same optical properties as surface plasmon polaritons, but are called by a different term, surface phonon polaritons.

In order to understand the effect of roughness on SPPs, it is beneficial to first understand how a SPP is coupled by a grating Figure2. When a photon is incident on a surface, the wave vector of the photon in the dielectric material is smaller than that of the SPP. In order for the photon to couple into a SPP, the wave vector must increase by $\backslash Delta\; k\; =\; k\_\{SP\}-\; k\_\{x,\; \backslash text\{photon\}\}$. The grating harmonics of a periodic grating provide additional momentum parallel to the supporting interface to match the terms.

:$k\_\{SPP\}=k\_\{x,\; \backslash text\{photon\}\}\; \backslash pm\; n\backslash \; k\_\backslash text\{grating\}=\backslash frac\{\backslash omega\}\{c\}\; \backslash sin\{\backslash theta\_0\}\; \backslash pm\; n\; \backslash frac\{2\backslash pi\}\{a\},$

where $k\_\backslash text\{grating\}$ is the wave vector of the grating, $\backslash theta\_0$ is the angle of incidence of the incoming photon, a is the grating period, and n is an integer.

Rough surfaces can be thought of as the superposition of many gratings of different periodicities. Kretschmann proposed that a statistical correlation function be defined for a rough surface

:$G(x,y)=\backslash frac\{1\}\{A\}\backslash int\_A\; z(x\text{'},y\text{'})\backslash \; z(x\text{'}-x,y\text{'}-y)\backslash ,\; dx\text{'}\backslash ,\; dy\text{'},$

where $z(x,y)$ is the height above the mean surface height at the position $(x,y)$, and $A$ is the area of integration. Assuming that the statistical correlation function is Gaussian of the form

:$G(x,y)=\backslash delta^2\backslash exp\backslash left(-\backslash frac\{r^2\}\{\backslash sigma^2\}\backslash right)$

where $\backslash delta$ is the root mean square height, $r$ is the distance from the point $(x,y)$, and $\backslash sigma$ is the correlation length, then the Fourier transform of the correlation function is

:$|s(k\_\backslash text\{surf\})|^2=\backslash frac\{1\}\{4\; \backslash pi\}\; \backslash sigma^2\; \backslash delta^2\; \backslash exp\; \backslash left(\; -\; \backslash frac\{\backslash sigma^2\; k\_\backslash text\{surf\}^2\}\{4\}\backslash right)$

where $s$ is a measure of the amount of each spatial frequency $k\_\backslash text\{surf\}$ which help couple photons into a surface plasmon.

If the surface only has one Fourier component of roughness (i.e. the surface profile is sinusoidal), then the $s$ is discrete and exists only at $k=\backslash frac\{2\backslash pi\}\{a\}$, resulting in a single narrow set of angles for coupling. If the surface contains many Fourier components, then coupling becomes possible at multiple angles. For a random surface, $s$ becomes continuous and the range of coupling angles broadens.

As stated earlier, SPPs are non-radiative. When a SPP travels along a rough surface, it usually becomes radiative due to scattering. The Surface Scattering Theory of light suggests that the scattered intensity $dI$ per solid angle $d\; \backslash Omega$ per incident intensity $I\_\{0\}$ is

:$\backslash frac\{dI\}\{\; d\; \backslash Omega\backslash \; I\_\{0\}\}=\backslash frac\{4\; \backslash sqrt\{\backslash varepsilon\_\{0\}\}\}\{\backslash cos\{\backslash theta\_0\}\}\backslash frac\{\backslash pi^4\}\{\backslash lambda^4\}|t\_\{012\}^p|^2\; \backslash \; |W|^2\; |s(k\_\backslash text\{surf\})|^2$

where $|W|^2$ is the radiation pattern from a single dipole at the metal/dielectric interface. If surface plasmons are excited in the Kretschmann geometry and the scattered light is observed in the plane of incidence (Fig. 4), then the dipole function becomes

:$|W|^2=A(\backslash theta,|\backslash varepsilon\_\{1\}|)\backslash \; \backslash sin^2\{\backslash psi\}\; \backslash \; [(1+\backslash sin^2\; \backslash theta\; /|\backslash varepsilon\_1|)^\{1/2\}\; -\; \backslash sin\{\backslash theta\}]^2$

with

:$A(\backslash theta,|\backslash varepsilon\_1|)\; =\; \backslash frac$

where $\backslash psi$ is the polarization angle and $\backslash theta$ is the angle from the z-axis in the xz-plane. Two important consequences come out of these equations. The first is that if $\backslash psi=0$ (s-polarization), then $|W|^2=0$ and the scattered light $\backslash frac\{dI\}\{\; d\; \backslash Omega\backslash \; I\_\{0\}\}=0$. Secondly, the scattered light has a measurable profile which is readily correlated to the roughness. This topic is treated in greater detail in reference.

• Dyakonov surface waves
• Graphene plasmonics
• Localized surface plasmon
• Plasmonic lens
• Superlens
• Surface plasmon
• Surface plasmon resonance
• Surface wave

{{notelist|refs=

{{efn|name="dispersion"|This lossless dispersion relation neglects the effects of damping factors, such as the intrinsic losses in metals. For lossy cases, the dispersion curve backbends after the reaching the surface plasmon frequency instead of asymptotically increasing.}}

}}

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{{cite journal |first1=Bai Cao |last1=Pan |first2=Zhen |last2=Liao |first3=Jie |last3=Zhao |first4=Tie Jun |last4=Cui |date= 2014 |title= Controlling rejections of spoof surface plasmon polaritons using metamaterial particles |journal=Optics Express |volume=22 |issue=11 |pages= 13940–13950 |doi=10.1364/OE.22.013940 |pmid=24921585 |bibcode=2014OExpr..2213940P |doi-access=free }}

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{{cite book |last=Raether |author-link=Heinz Raether |first=Heinz |year=1988 |title=Surface Plasmons on Smooth and Rough Surfaces and on Gratings |location=New York |publisher=Springer-Verlag |isbn=978-3540173632| series=Springer Tracts in Modern Physics 111}}

{{cite journal|title=Size dependence of Au NP-enhanced surface plasmon resonance based on differential phase measurement |journal=Sensors and Actuators B: Chemical |year=2013|doi=10.1016/j.snb.2012.09.073|volume=176|pages=1128–1133|last1=Zeng|first1=Shuwen|last2=Yu|first2=Xia|last3=Law|first3=Wing-Cheung|last4=Zhang|first4=Yating|last5=Hu|first5=Rui|last6=Dinh|first6=Xuan-Quyen|last7=Ho|first7=Ho-Pui|last8=Yong|first8=Ken-Tye |bibcode=2013SeAcB.176.1128Z |url=https://www.researchgate.net/publication/268225952 }}

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{{cite journal

|last1=Barnes|first1=William L.|last2=Dereux|first2=Alain|last3=Ebbesen|first3=Thomas W.|title=Surface plasmon subwavelength optics|doi=10.1038/nature01937|pmid=12917696|year=2003|pages=824–30|issue=6950|volume=424

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• PDF from arxiv.org – [https://arxiv.org/PS_cache/arxiv/pdf/1003/1003.1154v2.pdf Transformation Optics for Plasmonics]. 15 pages.

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}}

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• {{cite journal|last1=Hendry|doi=10.1103/PhysRevLett.100.123901|first1=E.|last2=Garcia-Vidal|first2=F.|last3=Martin-Moreno|first3=L.|last4=Rivas|first4=J.|last5=Bonn|first5=M.|last6=Hibbins|first6=A.|last7=Lockyear|first7=M.|title=Optical Control over Surface-Plasmon-Polariton-Assisted THz Transmission through a Slit Aperture|pmid=18517865|year=2008|page=123901|issue=12|volume=100|journal=Physical Review Letters |url=http://shannon.ex.ac.uk/research/emag/pubs/pdf/Hendry_PRL_2008.pdf|bibcode=2008PhRvL.100l3901H|hdl=10036/33196|hdl-access=free}} Free PDF download.
• {{cite journal|last1=Barnes|first1=William L.|last2=Dereux|first2=Alain|last3=Ebbesen|first3=Thomas W.|title=Surface plasmon subwavelength optics|doi=10.1038/nature01937|pmid=12917696|year=2003|pages=824–30|issue=6950|volume=424|journal=Nature|url=http://access.ex.ac.uk/research/emag/wlb/nature_2003_424_824.pdf|bibcode=2003Natur.424..824B|s2cid=116017 |url-status=dead|archive-url=https://web.archive.org/web/20110811024623/http://access.ex.ac.uk/research/emag/wlb/nature_2003_424_824.pdf|archive-date=2011-08-11}} Free PDF download.
• {{cite journal|last1 =Pitarke|first1 =J M|last2 =Silkin|first2 =V M|last3 =Chulkov|first3 =E V|last4 =Echenique|first4 =P M|doi =10.1088/0034-4885/70/1/R01|title =Theory of surface plasmons and surface-plasmon polaritons|year =2007|pages =1|volume =70|issue =1|journal =Reports on Progress in Physics

|url =http://dipc.ehu.es/etxenike/admin/documentos/archivos/publicaciones/307RPP2007.pdf|arxiv = cond-mat/0611257 |bibcode = 2007RPPh...70....1P |s2cid =46471088}} Free PDF download.

• {{Cite web

| last =White

| first =Justin

| title =Surface Plasmon Polaritons

| publisher =Stanford University. Physics department

| date =March 19, 2007

| url =http://large.stanford.edu/courses/2007/ap272/white1/

| format =Online

}} "Submitted as coursework for AP272. Winter 2007".

{{DEFAULTSORT:Surface Plasmon Polaritons}}

Category:Quasiparticles

Category:Metamaterials

Category:Plasmonics

Category:Surface waves