Surface
Plasmon
Amplification by
Stimulated
Emission of
Radiation
By:
Jonathan Massey-Allard
Graham Zell
Justin Lau
Surface Plasmons (SPs)
• Quanta of electron oscillations in a plasma.
o Electron gas in metals.
• Exist at the interface between two materials where the
dielectric constant changes sign.
o Metal sheet in air.
• Incident fields on material surface excite plasmons.
o Need negative dielectric constant for absorption.
o Skin depth = depth for which material absorbs field.
• SPs are bosons like photons.
o Interact very weakly with one another.
o Many SPs may accumulate in a single mode.
o Can get stimulated emission with SPs.
Lasers vs. Spasers
Similarities
Differences
Propagating modes are
created by feedback between
the gain medium and the
resonant cavity.
Lasers amplify photons while
spasers amplify surface
plasmons.
Both work on the principles of
stimulated emission and
population inversion.
Made possible by the fact that
bosons (photons and SPs)
can exist in the same mode in
large numbers.
Spasers can function in "dark"
modes that don't couple to
the far field.
The cavity size of a spaser is
determined by a metal's skin
depth rather than the
emission wavelength.
Resonator
• Need metals good at supporting SPs.
o Noble metals like Au and Ag.
• Can use metal nanoparticles.
o Shell thickness less than skin
depths of ~25 nm.
• Resonant lifetime of SP
modes characterized by their Q factor.
o Want high-Q modes for greatest
field enhancement.
M.I. Stockman, J. Opt., 12 (2010)
Gain Medium
• Need spectral and spatial overlap
with SP resonant modes.
• Can use ordinary dye molecules
or nano quantum dots (NQDs).
• NQDs better because they have a
tuneable emission spectrum and
don't suffer from excited state
quenching and photobleaching like
dyes do.
M.I. Stockman, J. Opt., 12 (2010)
Basic Spasing
Mechanism
M.I. Stockman, N. Photonics, 2 (2008).
QM of Stimulated Emission
The Spaser Hamiltonian:
Matrix notation of Hamiltonian:
Spontaneous emission is described by Fermi's Golden Rule:
•
•
•
•
Perturbing Hamiltonian has odd parity
Integral vanishes if spatial part is a pure eigenstate
Dark modes exist if system is fully symmetric
If asymmetric, spatial part is superposition of eigenstates
Of Lasers and Spasers
Density matrix statistical description of ensemble:
Resulting undamped equations of motion:
Include population relaxation:
Recognize these? Hint: PHYS 460
Conditions for Effective Spasing
Spasing frequency:
For spasing:
Order of magnitude
approximation:
Q
Desired conditions for spasing:
• Strong dipole transition µ12
• Low decay rate Γ12
• High chromophore density Nc/Vn
• High quality factor Q
Near-field Scanning Optical
Microscopy
Latest work in field concentrates
light by shining laser beams on
pointed tips, to generate strong
evanescent fields.
Laser sprays energy everywhere
and heats up the surface, causing
noise.
Spasers could generate these
fields via dark modes, without
transferring extra energy to the
sample.
L. Novotny and S. Stranick, Annu. Rev. Phys. Chem., 57, (2006).
Nanolasers
An array of weakly antisymmetric
split ring currents may radiatively
couple to the far field.
Radiation is coherent, making a
laser, but how do we generate the
currents efficiently?
Nanolasers with Spasers
Combine split ring array with
supporting gain medium
Tune resonant frequency of
rings to the emission of the
gain medium.
Surface plasmons set up
currents and amplify pump
light coherently.
Theoretical gain of ~35 dB
in near-infrared.
N. Zheludev et al., N. Photonics, 2 (2008).
Plasmonic Circuits
• Can we use plasmons in nanocircuits to do ultrafast
computation?
• Would need:
1.useful source of local fields
2.plasmon waveguides
3.nanoamplifiers?
4.nanoswitches?
• The spaser acts like a laser: it cannot amplify by definition!
o Can we get around that?
o What about achieving bistable operation like transistors?
Spaser Switch
• Bistable application <=> MOSFET transistor.
o Two stable states
can be attained.
 Logic "1" =
fixed SP population
 Logic "0" =
no SP population
• Use saturable absorbers
in the gain medium.
o Absorption over the spasing line but not with the pumping
frequency (introduce losses).
M.I. Stockman, J. Opt., 12 (2010)
Nanoamplifier
In steady-state
operation, the surface
plasmon gain exactly
offsets the loss in the
metal, so the spaser
has exactly zero
amplification.
When pumping is turned on, the initial population of SPs
affects how quickly CW operation is reached. For ~100 fs,
the spaser achieves positive amplification of SPs.
Time delay before steady state may have uses in circuits.
M.I. Stockman, J. Opt., 12 (2010)
Nanoamplifier
When the spaser is hit
with a pulse of pump
light to induce a sudden
inversion in the gain
medium, the response
is a series of
oscillations in the SP
population.
Magnitude depends on the initial population of surface
plasmons. Amplification!
First pulse is always above a given level (here, 100) while
the later ones fall below.
M.I. Stockman, J. Opt., 12 (2010)
Successful Weaponization
Larks, with frickin' spaser beams on their heads.
D. Evil, J. App. Evil, 17 (2003)
Artist's rendering of a
spaser in future
applications.
Questions?
http://media.photobucket.com/image/spaser/yvan33/photos91.jpg
Giovanni di Simone, Pisa, Italy, 1 (1173).