Squeezing Light Through Small Holes Taco D. Visser VU University Amsterdam TexPoint fonts used in EMF: AAAAAAA

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about nano-holes? 100 nanometer 20 nanometer Metal For holes that are smaller than the wavelength geometrical optics is no longer valid.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 = field around metal plate without slit Split field into two parts: = field around metal plate without slit = scattered field due to slit 2. Convert Maxwell’s equation into an integral equation: 3. Solve integral equation numerically

Transmission vs. Slit Width for Silver Plate w/l Silver (n = 0.05 + i 2.87) l = 500 nm thickness = 100 nm 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 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 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 red = silicon (n = 4.3 – i 0.74) l = 500 nm T w/l red = silicon (n = 4.3 – i 0.74) blue = silver (n = 0.05 – i 2.87) l = 500 nm thickness = 100 nm 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 Can we control the direction in which the plasmons are launched? Until now only static schemes (built-in asymmetry) have been proposed. surface plasmon surface plasmon incident TM beam

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. Can we also control the direction of radiation? incident laser beam

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)