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than the wavelength geometrical optics is no longer valid.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 nm 2 b. Rectangular holes with an area of 16,000 nm 2 c. Rectangular holes with an area of 32,000 nm 2 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:

E

inc = field around metal plate without slit

E

sca = scattered field due to slit 2. Convert Maxwell’s equation into an integral equation: 

E



E

inc  i  (  m   0 ) slit 

G E

d 2 x 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 silve r 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 sink vortex saddle monkey saddle 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 concentrate the power flow and that way more light is `pushed through’ the slit than you would expect. film, the vortices seem to But what happens when we change the material from a metal semiconductor such a silicon? into a

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 < it transmits

less

light than you would expect.

1 • 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 destructive manner. in a constructive or in a

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 m m, 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 (TM 0 ), the other anti-symmetric (TM 1 ). Beam B only excites the even mode.

Beams A and –A have the same amplitude but are p Together they only excite the odd mode. phase shifted. 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

• 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)