Squeezing Light Through
Small Holes
Taco D. Visser
VU University Amsterdam
How much light is transmitted by
a small aperture in a metal plate?
10 mm
2 mm
Metal
10 incident rays
20 % of the metal plate is open, so only 2 out of 10 rays can
pass through. The others are reflected or absorbed.
Geometrical optics predicts a transmission of 20%.
But what about nano-holes?
100 nanometer
20 nanometer
Metal
For holes that are smaller than the wavelength
geometrical optics is no longer valid.
So what happens to the transmission? Is it still 20%?
Extraordinary Optical Transmission
T.W. Ebbesen et al., Nature 391, 1998.
The round holes are 20% of the surface.
But the transmission is more than 20%!
How is this extraordinary transmission possible?
Hole Shape Influences the Transmission
Three types of holes:
a. Circular holes, with an area of 28,000 nm2
b. Rectangular holes with an area of 16,000 nm2
c. Rectangular holes with an area of 32,000 nm2
Klein Koerkamp et al. Physical Review Letters 92, 2004.
Influence of the hole shape
• Surprisingly, at 900 nm the small rectangular holes
transmits more light than the larger holes!
This again shows that geometrical optics is not a good
model for this situation.
• The circular holes always transmit less.
Slit in a Metal Plate
Depending on the slit width w, zero, one, two or more
guided modes can exist in the hole.
Their number influences the transmission.
A Scattering Approach
1. Split field into two parts:
Einc = field around metal plate without slit
Esca = scattered field due to slit
2. Convert Maxwell’s equation into an
integral equation:
EE
inc

 i (m   0 )  G E d x
2
slit
3. Solve integral equation numerically
Transmission vs. Slit Width
for Silver Plate
T
E || slit
Silver (n = 0.05 + i 2.87)
l = 500 nm
thickness = 100 nm
w/l
Question:
How can transmission be > 1 ?
Effective index of first TE mode
in silver
When the width w = 0.4 l, the first TE mode kicks in.
Power flow for Silver
w=
T=
Annihilation
w=
T=
More Topological Structures
source
saddle
sink
monkey saddle
vortex
dipole
Many Annihilations
If we increase the slit width a little, a host of structures annihilate,
leading to a smoother power flow and thus an enhanced transmission
This annihilation of vortices and saddle points
coincides with the onset of the first guided mode
PRE 67, 036608 (2003)
Optical Vortices
In the example of a narrow slit in a silver film, the vortices seem to
concentrate the power flow and that way more light is `pushed
through’ the slit than you would expect.
But what happens when we change the material from a metal into a
semiconductor such a silicon?
Silver vs. Silicon
T
E || slit
l = 500 nm
thickness = 100 nm
w/l
red = silicon (n = 4.3 – i 0.74)
blue = silver (n = 0.05 – i 2.87)
Transmission for a slit in a silicon plate is less than expected.
Changing the handedness of the
vortices: Silicon
• A narrow slit in a silicon plate has a low transmission, i.e. T< 1
it transmits less light than you would expect.
• This anomalously low transmission coincides with a
change in handedness of the optical vortices (b and c) .
• Notice the two saddles (a and d) and the two sinks.
J. of Optics A 6, S277 (2004).
Creating a monkey saddle
• The two saddle points have joined to form a monkey saddle (e).
• The two vortices (b and c) have moved sideways, but still push
the light “the wrong way.”
Surface Plasmons - I
• When an incident TM field hits the slit, surface plasmons are
generated.
• They travel away from the slit to the left and to the right.
• Eventually the plasmons are absorbed by the metal.
surface plasmon
surface plasmon
incident TM wave
Surface Plasmons - II
• Until now we have only analyzed a single slit.
• If we have two slits, are they independent?
d
Incident TM wave
What is the influence of the two slits on each other?
Surface Plasmons - III
Transmitted plasmon field
Incident TM wave
• A part of the incident field at the left slit is converted into
surface plasmons that travel to the right.
• There the surface plasmons can change back into a free field again.
• The same thing happens at the right slit.
• So, in each slit there are two fields: the directly transmitted field
and the surface plasmons from the other slit.
Surface Plasmons Interference
d
interference
incident TM wave
• At each slit the total field consists of two contributions:
1. The directly transmitted field.
2. The surface plasmon field coming from the other slit.
• The two fields can interfere in a constructive or in a
destructive manner.
Changing the phase of the
Surface Plasmons
Plasmon Interference (changing d )
Maximum intensity at the slits
Minimum intensity at the slits
Experiment (changing l)
The total transmission varies
strongly with the wavelength,
just as predicted.
Distance between slits = 25 mm, Width slit = 200 nm
Thickness plate (gold) = 200 nm, TM polarization
Phys. Rev. Lett., 94, 053901, 2005.
Steering the Plasmons
Surface plasmons generated at the slit travel to left and to the right
surface plasmon
surface plasmon
incident TM beam
Can we control the direction in which the plasmons are launched?
Until now only static schemes (built-in asymmetry) have been proposed.
piezo
A narrow slit in a gold film allows only two TM modes,
one is symmetric (TM0), the other anti-symmetric (TM1).
Beam B only excites the even mode.
Beams A and –A have the same amplitude but are p phase shifted.
Together they only excite the odd mode.
By varying the phase of beam B with a piezo we can control the
superposition of the two guided modes.
-- Total magnetic field
on interface
By tuning the superposition of the two modes we can get complete
cancellation of the field at one side of the slit exit.
Plasmons will only be generated on the opposite side:
Unidirectional plasmon launching
By simply changing the phase of the normally incident beam,
we get dynamic plasmon switching
Optics Express 20, 15326 (2012).
Steering the Radiation Field
The transmitted light is radiated symmetrically.
incident laser beam
Can we also control the direction of radiation?
Minima of the far-zone radiation of a slit coincide with
phase singularities in the near-field along the line of sight.
Physical Review Letters, vol. 93, 173901 (2004).
Using the same method of selective mode excitation,
we can steer the radiation continuously from left to right
by varying the voltage across the piezo.
Two different voltage settings across the piezo give radiation
to the left (blue) or to the right (red).
Physical Review Letters, vol. 111, 153901 (2013).
Conclusions
•
The extraordinary transmission of light through nano-apertures is
accompanied by optical vortices that funnel the light.
•
Very low transmission (as in silicon) is accompanied by optical
vortices steering the light away from the slit.
•
The onset of guided modes is accompanied by the annihilation of
vortices and saddles.
•
Surface plasmons generated at one hole can travel to another hole
where they interfere with the directly incident field.
Depending on the hole separation this either
increases or decreases the transmission.
• There is a connection between the direction of minimal radiation
and the presence of phase singularities near the slit.
•
By selective excitation of the guided modes we can dynamically
steer both the plasmons and the radiated field.
and finally….
Thanks to
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Shreyas Raghunathan (Delft)
Hugo Schouten (Amsterdam)
Thomas van Dijk (Urbana Champain)
Greg Gbur (Charlotte)
Wim Ubachs (Amsterdam)
Erik Eliel (Leiden)
Dave Fischer (NASA, Cleveland)
Phillipe Lalanne (Paris/Bordeaux)