Plasmonics is the study of plasma oscillations in metals. Plasmons are density waves in the electron gas in metals that are excited by light. They have shorter wavelengths than light and can propagate signals at the nanoscale. This allows for applications in nanophotonics like enhanced optical transmission and biosensing. Plasmons can be excited by coupling light to collective electron oscillations at metal surfaces or in nanostructures like nanoparticles. Metamaterials aim to control plasmons for applications such as cloaking, perfect lenses, and transformation optics. Plasmonics may lead to faster optoelectronic devices by transmitting data with plasmonic waves instead of electric currents.

1. By –
Pragya Kulshresth
Stained glass rose window at
Notre Dame de Paris

2. Plasmonics
 The long wavelength of light (≈m) creates a
problem for
 extending optoelectronics into the nanometer
regime.
 A possible way out is the conversion of light into
Plasmons.
 They have much shorter wavelengths than light
and are
 able to propagate electronic signals.

3. “Plasmonics is the study of the
interaction between
electromagnetic field and free
electrons in a metal. Free electrons
in the metal can be excited by the
electric component of light to have
collective oscillations.”

4. What is a Plasmon ?

5.  A Plasmon is a density wave in an electron
gas. It is analogous to a sound wave, which
is a density wave in a gas consisting of
molecules.
 Plasmons exist mainly in metals, where
electrons are weakly bound to the atoms
and free to roam. The free electron gas
model provides a good approximation (also
known as jellium model).

6.  The electrons in a metal can wobble
like a piece of jelly, pulled back by
the attraction of the positive
metal ions that they leave behind.
 In contrast to the single electron
wave function that we encountered
already, a plasmon is a collective
wave where billions of electrons
oscillate in sync.

8. The Plasmon Resonance
Right at the plasmon frequency p the electron gas has a resonance,
it oscillates violently. This resonance frequency increases with the
electron density n , since the electric restoring force is proportional
to the displaced charge (analogous to the force constant of a spring).
Similar to an oscillating spring one obtains the proportionality:
p  n
The plasmon resonance can be observed in
electron energy loss spectroscopy (EELS).
Electrons with and energy of 2 keV are re-
flected from an Al surface and lose energy
by exciting 1, 2, 3,… plasmons. The larger
peaks at multiples of 15.3 eV are from bulk
plasmons, the smaller peaks at multiples of
10.3 eV from surface plasmons.
1
2
3
4 5

9. Simplified sketch of electron oscillations (plasmons) at the
metal/air interface. Orange and yellow clouds indicate
regions with lower and higher electron concentration,
respectively. Arrows show electric field lines in and outside
of the metal.
Credit: Hans-Peter Wagner and Masoud Kaveh-Baghbadorani, CC BY-ND

10. •Plasmonics could revolutionize the way computers or smart phones
transfer data
•Data transfer in current electronic integrated circuits happens via the
flow of electrons in metal wires.
• In plasmonics, it's due to oscillatory motion about the positive nuclei.
•Since plasmonic data transfer happens with light-like waves and not
with a flow of electrons (electrical current) as in conventional metal
wires, the data transmission would be superfast (close to the speed of
light) – similar to present glass fiber technologies.
• But plasmonic metal films are more than 100 times thinner than glass
fibers. This could lead to faster, thinner and lighter information
technologies.

12. Why are Metals Shiny ?
•An electric field cannot exist inside a metal, because metal electrons react to it by creating
an opposing screening field .
• An example is the image charge, which exactly cancels the field of any external charge.
•This is also true for an electromagnetic wave, where electrons respond to the changing
external field and screen it at any given time.
• As a result, the electromagnetic wave cannot enter a metal and gets reflected back out.
•However, at high frequency (= high photon energy) there comes a point when the external
field oscillates too fast for the electrons to follow. Beyond this frequency a metal loses its
reflectivity. The corresponding energy is the plasmon energy
Ep = ħp (typically 10-30 eV,
deep into the ultraviolet).
The reflectivity of aluminum
cuts off at its plasmon energy
Data (dashed) are compared
to the electron gas model (full).
Ep

14. Plasmons and Energy-Saving Window Coatings
The reflectivity cutoff at the plasmon energy can be used for
energy-saving window coatings which transmit visible sunlight
but reflect thermal radiation back into a heated room.
To get a reflectivity cutoff in the infrared one needs a smaller
electron density than in a metal. A highly-doped semiconductor
is just right, such as indium-tin-oxide (ITO). We encountered
this material already as transparent front electrode for solar
cells and LCD screens.
An ITO film transmits visible
light and reflects thermal
infrared radiation, keeping
the heat inside a building.
R = Reflectivity
T = Transmission

15. Low-Dimensional Plasmons in Nanostructures
We know how single electron waves become quantized by
confinement in a nanostructure. Likewise, collective electron waves
(= plasmons) are affected by the boundary conditions in a thin film,
a nano-rod, or a nano-particle.
Plasmons in metal nanoparticles are often called Mie-resonances,
after Gustav Mie who calculated them hundred years ago. Their
resonance energy and color depend strongly on their size, similar
to the color change induced in semiconductor nanoparticles by
confinement of single electrons .In both cases, smaller particles have
higher resonance energy (blue shift).

16. Nanotechnology in Roman Times: The Lycurgus Cup
Plasmons of gold nanoparticles in glass reflect green, transmit red.

17. Quantum Numbers of Plasmons
Like any other particle or wave in a (crystalline) solid, a plasmon
has the energy E and the momentum p as quantum numbers, or
the circular frequency  = E/ħ and the wavevector k = p/ħ . One
can use the same E(k) plots as for single electrons (Lecture 7b).
Surface Plasmon
Photon
Bulk Plasmon

18. Coupling of Light and Plasmons
To combine optoelectronics with plasmonics one has to convert
light (photons) into plasmons. This is not as simple as it sounds.
Bulk plasmons are longitudinal oscillations (parallel to the propa-
gation direction), while photons are transverse (perpendicular to
the propagation). They don’t match.
Surface plasmons are transverse, but they are mismatched to
photons in their momentum. The two E(k) curves never cross.
It is possible to provide the necessary momentum by a grating,
which transmits the wavevector k = 2/d (d = line spacing) .

19. Attenuated Total Reflection
Another method to couple photons and surface plasmons uses
attenuated total reflection at a metal-coated glass surface.
The exponentially damped (evanescent) light wave escaping
from the glass can be matched to a surface plasmon (or thin
film plasmon) in the metal coating. This technique is surface
sensitive and can be used for bio-sensors.
Gold
film

20. Plasmons and the Dielectric Constant 
The dielectric constant is a complex number:  = 1 + i 2
The real part 1 describes refraction of light,
The imaginary part 2 describes absorption .
The bulk plasmon occurs at an energy Ep where 1 = 0,
the surface plasmon occurs at an energy Es where 1 = -1 .
(More precisely: Im[1/] and Im[1/(+1)] have maxima.)
Typical behavior of the dielectric constant
versus energy E for a solid with an optical
transition at E=E0 . A metal has E0=0 .
E
0
1
1
2
-1
Ep
Es
0 E0

21. Photonics
In photonics one tries to manipulate the dielectric constant via
nanostructured dielectric materials ( “metamaterials” ).
Particularly interesting is a gap in the E(k) relation of photons,
analogous to the band gap of electrons in a semiconductor. The
photonic band gap causes total reflection of light in all directions.
An artificial crystal lattice made from
polystyrene beads (similar to an opal,
an iridescent gemstone). The photonic
band gap causes a reflectance maximum.

22. Cloaking: Making an Object Invisible
Surrounding an object with a material having the right kind of
dielectric properties (negative refractive index) can make the
object invisible.
Cloaking simulation in two dimensions:
A. The black disc blocks the light coming from the left and reflects it back,
leaving a shadow towards the right (green/yellow).
B. The surrounding ring of cloaking material guides the light around the disc
and thereby fills in the shadow.
A B

23. Actual Metamaterials
Most metamaterials with negative refractive index have been
made for microwaves (below left). Such devices are interesting
for making an airplane invisible to radar (wavelength  3 cm) .
To produce analogous metamaterials for visible light requires
nanotechnology with structures small compared the wavelength
of light (above right). Even with that under control, it is hard
to cloak an object at all wavelengths. Metamaterials are active
only near a resonance, which occurs at a particular wavelength.

24. The Perfect Lens
A medium with refractive index n = -1 acts as perfect lens.
Since n =    , one expects both  and  (magnetic permeability)
to be negative.
Negative n refracts light towards the same side of the normal (not the opposite side).
Lens

25. Sources
• Optical Properties of Solids (Oxford Master Series in
Physics) - Mark Fox
• Principles of Optics: Electromagnetic Theory of
Propagation, Interference and Diffraction of Light - M.
Born, E. Wolf
• Plasmonics: Fundamentals and Applications –Stefan
Alexander Maier
• http://webstaff.itn.liu.se/~alira/hjo_coe_seminar.ppt
• http://web.pdx.edu/~larosaa/Applied_Optics_464-
564/Lecture_Notes_Posted/2010_Lecture-
7_SURFACE%20PLASMON%20POLARITONS%20AT%20%20
METALINSULATOR%20INTERFACES/Lecture_on_the_Web_
SURFACE-PLASMONS-POLARITONS.pdf
• https://phys.org/news/2015-06-plasmonics-
revolutionizing-light-based-technologies-electron.html

26. Questions???