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Surface plasmon polaritons (SPPs) are
electromagnetic waves In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) lig ...
that travel along a
metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
or metal–air interface, practically in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
or
visible Visibility, in meteorology, is a measure of the distance at which an object or light can be seen. Visibility may also refer to: * A measure of turbidity in water quality control * Interferometric visibility, which quantifies interference contrast ...
-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal ("
surface plasmon Surface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such ...
") and electromagnetic waves in the air or dielectric ("
polariton In physics, polaritons are quasiparticles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation. They are an expression of the common quantum phenomenon known as level repulsion, also ...
"). They are a type of
surface wave In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occu ...
, guided along the interface in much the same way that light can be guided by an optical fiber. SPPs have a shorter wavelength than light in vacuum at the same frequency (photons). Hence, SPPs can have a higher momentum and local field intensity. Perpendicular to the interface, they have subwavelength-scale confinement. An SPP will propagate along the interface until its energy is lost either to absorption in the metal or scattering into other directions (such as into free space). Application of SPPs enables subwavelength optics in microscopy and
photolithography In integrated circuit manufacturing, photolithography or optical lithography is a general term used for techniques that use light to produce minutely patterned thin films of suitable materials over a substrate, such as a silicon wafer, to protect ...
beyond the
diffraction limit The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to th ...
. It also enables the first steady-state micro-mechanical measurement of a fundamental property of light itself: the momentum of a photon in a dielectric medium. Other applications are
photonic Photonics is a branch of optics that involves the application of generation, detection, and manipulation of light in form of photons through emission, transmission, modulation, signal processing, switching, amplification, and sensing. Though ...
data storage, light generation, and bio-photonics.


Excitation

SPPs can be excited by both electrons and photons. Excitation by electrons is created by firing electrons into the bulk of a metal. 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 relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
s (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 Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
. Nevertheless, coupling of photons into SPPs can be achieved using a coupling medium such as a
prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...
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.


Fields and dispersion relation

The properties of an SPP can be derived from
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
. We use a coordinate system where the metal–dielectric interface is the z=0 plane, with the metal at z<0 and dielectric at z>0. The
electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s as a function of position (x,y,z) and time ''t'' are as follows: :E_(x,y,z,t) = E_0 e^ :E_(x,y,z,t) = \pm E_0 \frac e^ :H_(x,y,z,t) = H_0 e^ where * ''n'' indicates the material (1 for the metal at z<0 or 2 for the dielectric at z>0); * ''ω'' is the
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
of the waves; * the \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 In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...
; 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_ is generally different from k_ * \frac = -\frac, where \varepsilon_1 is the
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
of material 1 (the metal), and ''c'' is the
speed of light in vacuum The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit f ...
. As discussed below, this can also be written\frac = \frac. A wave of this form satisfies Maxwell's equations ''only'' on condition that the following equations also hold: :\frac + \frac = 0 and :k_^2+k_^2=\varepsilon_n \left(\frac\right)^2 \qquad n=1,2 Solving these two equations, the dispersion relation for a wave propagating on the surface is :k_=\frac \left(\frac\right)^. In the free electron model of an electron gas, which neglects attenuation, the metallic dielectric function is :\varepsilon(\omega)=1-\frac, where the bulk plasma frequency in SI units is :\omega_=\sqrt where ''n'' is the electron density, ''e'' is the
charge Charge or charged may refer to: Arts, entertainment, and media Films * '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqu ...
of the electron, ''m'' is the effective mass of the electron and is the permittivity of free-space. The
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
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 In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing Limit (mathematics), limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very larg ...
called the "surface plasma frequency". 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 :\omega_=\omega_/\sqrt. In the case of air, this result simplifies to :\omega_=\omega_/\sqrt. If we assume that ''ε''2 is real and ''ε''2 > 0, then it must be true that ''ε''1 < 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 In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
. The dielectric function of a metal is expressed ''ε''1 = ''ε''1′ + ''i''⋅''ε''1″ where ''ε''1′ and ''ε''1″ are the real and imaginary parts of the dielectric function, respectively. Generally >> ''ε''1″ so the wavenumber can be expressed in terms of its real and imaginary components as :k_=k_'+i k_''=\left frac \left( \frac\right)^\right+ i \left frac \left( \frac\right)^ \frac\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.


Propagation length and skin depth

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 An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
, so at a distance ''x'', the intensity has decreased by a factor of \exp\. 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=\frac. 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 Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the con ...
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_=\frac \left(\frac \right)^ 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.


Animations

File:SPP silver-air interface 370nm.gif, The
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
(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 In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
of silver at this frequency is . The picture is 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 . The picture is 6 μm across horizontally.


Experimental applications

Nanofabricated systems that exploit SPPs demonstrate potential for designing and controlling the propagation of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
in matter. In particular, SPPs can be used to channel light efficiently into
nanometer 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
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 A biosensor is an analytical device, used for the detection of a chemical substance, that combines a biological component with a physicochemical detector. The ''sensitive biological element'', e.g. tissue, microorganisms, organelles, cell recep ...
, 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 A metamaterial (from the Ancient Greek, Greek word Meta, μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally ...
''. Artificial SPP modes can be realized in
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
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 Surface plasmon resonance (SPR) is the resonant oscillation of conduction electrons at the interface between negative and positive permittivity material in a particle stimulated by incident light. SPR is the basis of many standard tools for measu ...
(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 In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
or
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
.
Surface plasmon Surface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such ...
-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.


Materials used

Surface plasmon polaritons can only exist at the interface between a positive-
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
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.


Metals

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 Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability i ...
. (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_ for a SPP is defined as \frac. 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 th
AlAgAu
an
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.


Other materials

The fewer electrons a material has, the lower (i.e. longer-wavelength) its
plasma frequency Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability i ...
becomes. Therefore, at infrared and longer wavelengths, various other plasmonic materials also exist besides metals. These include
transparent conducting oxide Transparent conducting films (TCFs) are thin films of optically transparent and electrically conductive material. They are an important component in a number of electronic devices including liquid-crystal displays, OLEDs, touchscreens and phot ...
s, 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
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s 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.


Effects of roughness

In order to understand the effect of roughness on SPPs, it is beneficial to first understand how a SPP is coupled by a
grating A grating is any regularly spaced collection of essentially identical, parallel, elongated elements. Gratings usually consist of a single set of elongated elements, but can consist of two sets, in which case the second set is usually perpendicul ...
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 \Delta k = k_- k_. The grating
harmonics A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
of a periodic grating provide additional momentum parallel to the supporting interface to match the terms. :k_=k_ \pm n\ k_\text=\frac \sin \pm n \frac, where k_\text is the wave vector of the grating, \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 A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables rep ...
be defined for a rough surface :G(x,y)=\frac\int_A z(x',y')\ z(x'-x,y'-y)\, dx'\, dy', 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 Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
of the form :G(x,y)=\delta^2\exp\left(-\frac\right) where \delta is the
root mean square In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...
height, r is the distance from the point (x,y), and \sigma is the correlation length, then the
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
of the correlation function is :, s(k_\text), ^2=\frac \sigma^2 \delta^2 \exp \left( - \frac\right) where s is a measure of the amount of each
spatial frequency In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier tra ...
k_\text 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=\frac, 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 In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The poi ...
d \Omega per incident intensity I_ is :\frac=\frac\frac, t_^p, ^2 \ , W, ^2 , s(k_\text), ^2 where , W, ^2 is the radiation pattern from a single
dipole In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: *An electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system i ...
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(\theta,, \varepsilon_, )\ \sin^2 \ \varepsilon_1, )^ - \sin2 with : A(\theta,, \varepsilon_1, ) = \frac \frac where \psi is the polarization angle and \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 \psi=0 (s-polarization), then , W, ^2=0 and the scattered light \frac=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.


See also

*
Surface plasmon Surface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such ...
*
Surface plasmon resonance Surface plasmon resonance (SPR) is the resonant oscillation of conduction electrons at the interface between negative and positive permittivity material in a particle stimulated by incident light. SPR is the basis of many standard tools for measu ...
*
Localized surface plasmon A localized surface plasmon (LSP) is the result of the confinement of a surface plasmon in a nanoparticle of size comparable to or smaller than the wavelength of light used to excite the plasmon. When a small spherical metallic nanoparticle is irra ...
*
Plasmonic lens In nano-optics, a plasmonic lens generally refers to a lens (optics), lens for surface plasmon polaritons (SPPs), i.e. a device that redirects SPPs to converge towards a single Focus (optics), focal point. Because SPPs can have very small wavelength ...
*
Superlens A superlens, or super lens, is a lens (optics), lens which uses metamaterials to go beyond the diffraction limit. For example, in 1995, Guerra combined a transparent grating having 50nm lines and spaces (the "metamaterial") with a conventional micro ...
* Graphene plasmonics *
Surface wave In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occu ...
*
Dyakonov surface waves Dyakonov surface waves (DSWs) are surface electromagnetic waves that travel along the interface in between an isotropic and an uniaxial-birefringent medium. They were theoretically predicted in 1988 by the Russian physicist Mikhail Dyakonov. Unlik ...


Notes


References


Further reading

* * Free PDF download. * Free PDF download. * Free PDF download.


External links

* "''Submitted as coursework for AP272. Winter 2007''". {{DEFAULTSORT:Surface Plasmon Polaritons Quasiparticles Metamaterials Plasmonics Surface waves